Application of machine learning models to predict secondary metabolites for the first time in the valuable medicinal plant (Dracocephalum moldavica L.)

Application of machine learning models to predict secondary metabolites for the first time in the valuable medicinal plant (Dracocephalum moldavica L.) | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Application of machine learning models to predict secondary metabolites for the first time in the valuable medicinal plant (Dracocephalum moldavica L.) Shahnaz Fathi, Roya Movlodzadeh, Sajad Heidari, Sharareh Najafian This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6105806/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Background The aim of this project was to predict, for the first time, the levels of important secondary metabolites during stress in medicinal plants, including carotenoids, amino acid proline, and soluble sugars, without the use of expensive and dangerous chemicals for humans. For this project, artificial neural network models including radial basis function (RBF) and multilayer perceptron (MLP) were used. Results The effectiveness of the models was generally evaluated on experimental datasets through a 5-fold cross-validation method to obtain reliable performance measures. Among the performances were R-squared (R2), mean point error (MAPE), and root mean square error (RMSE). In our study, the RBF model was functionally and optimally better than the MLP model with R2 values ​​of 0.90, 0.975, and 0.941 for soluble sugar, carotenoid pigment, and the highly important amino acid proline, respectively. The associated RMSEs were 0.29, 0.235, and 0.98, while the associated MAPEs were 1.971, 1.124, and 1. 229.The research results demonstrated the RBF model's exceptional ability to effectively represent nonlinear relationships between input variables and biological characteristics. While the MLP model generated plausible forecasts, it was ineffective at estimating the levels of soluble sugars, carotenoids, and proline in the plant. We concluded that the best model was the RBF model, which can be an efficient tool for strategic management of medicinal plants, reducing chemical consumption, reducing environmental pollution, reducing costs, and ultimately developing sustainable agriculture. It can also predict the performance of medicinal plants efficiently and be an effective step towards the sustainable development of agricultural sciences, pharmaceuticals, and the food and medical industries. Conclusions This study emphasizes the value of using computer modeling in agriculture, which is essential for evaluating important aspects of this field, especially with regard to different plant species and environmental conditions. Biological sciences/Biochemistry Biological sciences/Biotechnology Biochemical Cleaner production Ecological sustainability Secondary metabolites Dracocephalum moldavica Machine learning Proline accumulation Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Introduction For millennia, conventional medicine has employed aromatic and therapeutic herbs globally. They remain crucial for dietary assistance and medicinal treatment [ 1 ]. Dracocephalum moldavica L., often referred to as Moldavian dragon's head or Moldavian mumy, is a fragrant herbthat began in temperate Asia and is now prevalent throughout the Northern Hemisphere [ 2 ]. Because it contains geranial, neral, and geranyl acetate, D. moldavica essential oil (DMEO) has a citrus taste and resembles other lemonscented plants like lemon balm and lemon catnip [ 3 ]. Earlier research suggests that the herb possesses antioxidant [ 5 ] and antibacterial [ 4 ] properties. Many researchers aim to enhance the cultivation of D. moldavica and its phytochemical properties due to the rising demand for natural products in the pharmaceutical, cosmetic, and culinary industries. This entails enhancing D. moldavica cultivation and conducting phytochemical assessments to increase its therapeutic effectiveness and market worth. In Iran, especially in the West Azerbaijan area, D. moldavica is grown over 300 hectares [ 6 ]. Globally, a substantial level of plant death has been caused by stress factors. The production of secondary metabolites, such as sugars, sugar alcohols, and amino acids, is one of the surprisingly potent defenses that some plants possess against these circumstances. In reaction to different abiotic stressors, like temperature stress, plants gather the amino acid "proline." An excess of proline may occur due to protein hydrolysis, new synthesis, reduced intake, or breakdown. Proline enhances stress tolerance by preserving osmotic balance, ensuring cell turgidity, and indirectly managing the metabolism of reactive oxygen species. Proline's relationships with various Osmo protectants and signaling compounds additionally enhance defenses against stress [ 7 ]. Carotenoids are elongated isoprenoid molecules with conjugated structures that fall under the hydrocarbon category, having around 1,117 recognized structures. They participate in numerous biological functions in both humans and plants. Plasmids are the organelles found in plant cells that mainly regulate the production, stability, and function of carotenoids, along with their variety. Carotenoids expand the spectrum of light absorption and serve as additional light-harvesting pigments in photosynthetic tissues. They are essential for photoprotection as well. Carotenoids function as colorants and precursors of isoprenoids in non-photosynthetic tissues. Conversely, carotenoids enhance the fundamental dermal protection against UV in human cells, contributing to skin health. All of these phytochemicals provide a certain level of protection against inflammatory diseases, cancer, and diabetes (8). A novel field in computer science known as artificial intelligence (AI) offers great potential for addressing numerous complex problems in today's world. Contemporary biological systems encounter a plethora of intricate data generated by high-throughput analysis methods and "omic" strategies, which, if not correctly handled, could produce misleading results. AI technologies have been successfully utilized in plant biology to detect nutrient deficiencies, recognize species, oversee plant distribution, evaluate diseases and stress levels, and administer agrochemicals in agriculture [ 9 ]. AI algorithms represent a promising approach for investigating the mechanisms of how plants express stress tolerance, as they can identify and classify individual traits from extensive experimental data ([ 10 ]). Furthermore, a developing range of studies shows that AI is quite proficient in forecasting how plants will react to stress [ 11 ]. Although researchers are striving to widely implement machine learning (ML) in different agricultural fields, it is still uncertain if ML can consistently predict secondary metabolites in medicinal plants, especially D. moldavica L. Its application for accurately predicting the biochemical makeup of these plants has not been thoroughly explored (Fig. 1 ). Artificial neural networks (ANNs), which have shown exceptional results in various scientific fields, have not been as commonly applied to forecast important secondary metabolites like proline, carotenoids, and sugars (Fig. 2 ). Plant health evaluation and stress tolerance may be enhanced by the early and precise ANN-based prediction of these important biochemical components in medicinal plants. Most importantly, ANN-based predictive models in medicinal plants are more appealing and can greatly improve the efficiency of phytochemical assessments by doing away with the need for time-consuming chemical analyses in the lab, the risks that chemicals pose to people, the high expense of purchasing chemicals, and the tedious laboratory work. These developments will enable real-time cultivation strategy optimization and plant health monitoring by researchers and practitioners. This study's main goals are to: (1) use radial basis function neural networks (RBFNNs) and multilayer perceptron neural networks (MLPNNs) to apply predictive models for key and critical secondary compounds in D. moldavica for the first time; (2) compare the accuracy and efficiency of RBFNN and MLPNN models for these significant key compounds; and (3) offer useful insights into the integration of data-driven approaches for sustainable medicinal plant cultivation for the first time in Iran. This research seeks to promote sustainable farming, especially for important medicinal plants such as D. moldavica , while also assisting skilled, underprivileged Iranian youth in their development. Due to the elevated expense of chemicals in Iran, this study not only lowers costs and operational duration but also enables both researchers and farmers to monitor medicinal plants by incorporating easily seen morphological characteristics into predictive models. In addition, the advancement of efficient machine learning (ML) methods corresponds with the rising need for data-oriented solutions in optimizing resources, cultivating medicinal plants, and promoting sustainable practices. It also addresses concerns linked to environmental conservation and sustainable farming. Moreover, it can be integrated with the substitution of chemical drugs for herbal treatments and act as a launchpad for improving the quality and efficacy of products obtained from medicinal plants, guaranteeing their ongoing relevance in the food and pharmaceutical sectors. Materials and Methods Materialization Experimental conditions in the greenhouse Actualization Conditions for the experiment in the greenhouse The Shahid Bakeri Miandoab Higher Education Center's research farm served as the site of this investigation. In Isfahan, Iran, we bought pure seeds from Pakan Bazr Company. Prior to planting, the seeds were cleaned with distilled water and a 10% bleach solution. The seeds were planted in 4 kg plastic pots with a 1:1:1 soil, sand, and well-rotted animal manure mixture. Twenty seeds were planted in each pot at the proper spacing after the prepared soil mixture was added.The temperature and relative humidity conditions of the greenhouse were adjusted during the experiment. 30°C during the day and 20°C at night and with a relative humidity of 60 to 80%. The plant species under investigation, Dracocephalum moldavica L. , was identified by Abolfazl Alirezalu, a faculty member of Urmia University, and assigned herbarium code 1536 by the Herbarium of Urmia University. Four biostimulants—Kadostim, Fosnutren, Humiforte, and Aminolforte-e—were used. The experiments were carried out under salinity conditions with concentrations of 0, 20, 40, and 60 mM NaCl. Table 1 shows the chemical composition of the biostimulants used in this study [ 12 ]. Table 1 The compounds of amino acid, organic fertilizers Biostimulants Free amino acids (mg/L) Organic matters (%) Nitrogen (%) P2O5 (%) K2O (%) Kadostim 3750 2 - 3 - Fosnutren 3750 2 3.8 6 - Humiforte 3750 2 6 5 3 Aminolforte 3750 2 1.1 - - Amount and type of amino acids = Glysin 11.2%, Valine 5.1%, Proline 8.3%, Alanin 13.2%, Aspartic acid 4.4%, Arginine 8.3%, Glutamic acid 0.9%, Lysine 5.1%, Lucine 16.4%, Isolucine 4.4%, Phenylalanin 5.1%, Methionine 4.2%, Serin 3.9%, Treonine 0.3%, Histidine 0.3%, Tyrosine 1.5%, Glutamine 0.9%, Systein 0.3%, Aspargine 0.4%, and Tryptophan 0.4%. Measurement of Growth Parameters At the start of flowering, simple growth metrics were measured. Crown diameter (mm) is measured with a caliper, while stem length (cm) is measured with a ruler. A caliper is used to measure the internode length (in centimeters). The number of internodes was counted from the stem's base to its tip. Number of lateral stems: The total number of branches or lateral stems from the plant's base was counted. A ruler was used to measure the lateral stem's length. Leaf width (mm): The leaf's width was measured with calipers [ 12 ]. A ruler is used to measure the leaf length (mm). Number of leaves: Every plant's total number of leaves was meticulously tallied. Root length (cm): The root's length was measured from the tip to the root collar after the surrounding soil had been cleaned and removed. The shoot's fresh weight was measured using an analytical balance. Dry weight of shoots: A digital scale was used to measure the samples' dry weight after they had been dried for 48 hours at 70°C. The Moloudzadeh et al. approach was used to determine the relative water content, or RWC [ 12 ]. Quantification of soluble sugars With a minor adjustment, we used the Dubois et al. method to assess the soluble sugars in a few chosen plant samples [ 13 ]. Using a digital scale, 0.1 g of the plant sample was initially weighed in this way. In order to liberate the soluble sugars in the solution, we made sure that the plant components were thoroughly mixed before homogenizing the sample in 10 milliliters of distilled water. After that, we filtered to produce a clear liquid extract. After that, we filtered the extract once again to get rid of any unwanted particles. One by one, we then moved 1 milliliter of the filtered extract to a sterile test tube and filled it with 1 milliliter of a 5% phenol solution. We dissolved a suitable quantity of phenol in distilled water to create the phenol solution. As you are aware, when sulfuric acid is present, phenol reacts with sugars to produce a color combination that is proportionate to the sugar content. Five milliliters of concentrated sulfuric acid (H2SO4) are now carefully added to the test tube. We must proceed cautiously and slowly because this reaction is exothermic, and we must be mindful that the exothermic reaction will cause the test tube to heat up significantly. Similarly, the hydrolysis of sugar molecules and the development of a yellowish-brown hue are significantly influenced by the quantity of concentrated sulfuric acid. We now leave the mixture of sulfuric acid in the test tube for ten to fifteen minutes at room temperature. As we saw, the phenol-sulfuric acid mixture now interacts and creates a colorful complex with the dissolved sugars. We must be mindful that the incubation period is crucial since too short a time may result in a weak or irregular color, while too long may produce a change in color intensity and lead to an incorrect diagnosis. Following a thorough incubation period and the proper amount of time, the absorbance of the resultant solution is measured using a spectrophotometer set at 485 nm. As you are aware, the concentration of soluble sugars in the sample directly correlates with the color's intensity. A standard glucose solution was made beforehand, and the lab technician plotted the absorbance values of known glucose concentrations to create a calibration curve that would precisely indicate the amount of soluble sugars in the necessary samples. By comparing the sample's absorbance with the calibration curve, the concentration of soluble sugars in the plant sample was precisely determined. Following that, the outcome was expressed as glucose equivalents in milligrams per gram of fresh plant weight. It should be mentioned that precise standard curve preparation by the technician, precise reagent availability, and precise and suitable incubation period all affect measurement accuracy for determining plant solution sugar. Despite its effectiveness, this strategy necessitates close attention to every step in order to minimize errors. Furthermore, the spectrophotometric tube must be clean and the measurements must be made with the appropriate level of accuracy. To guarantee accuracy, the calibration curve must also be meticulously created for every set of data [ 12 ]. Measurement of carotenoids in plant leaves The carotenoid content of plant leaves was measured using the method of Lichtenthaler and Wellburn (1983) with slight modifications [ 14 ]. First, 0.1 g of fresh leaves were thoroughly ground with 10 ml of 80% acetone until completely homogeneous. Now it is time to transfer the desired mixture to the prepared centrifuge tubes and store them in a completely dark environment at 4°C for 24 hours according to the procedure. Now, we centrifuged the samples after one day for 10 minutes at 4000 rpm. Then, we carefully separated the supernatant and read them according to the instructions at wavelengths of 663, 645 and 470 nm for chlorophyll a, chlorophyll b and for total carotenoids. The concentrations of chlorophyll a, chlorophyll b and carotenoids were obtained using the exact equations of the instructions [ 12 ]. Measurement of Proline in plant leaves The Bates method was used to calculate the proline in leaves (9). To do this, 0.2 g of leaf tissue was weighed and thoroughly ground in 3 ml of 3% sulfosalicylic acid in a porcelain mortar. For fifteen minutes, the resultant homogenate was centrifuged at 18,000 rpm. Next, two milliliters of glacial acetic acid and two milliliters of ninhydrin reagent were added. The tubes were sealed at 100°C and then submerged in a hot water bath for an hour. Each tube was cooled, then filled with 4 cc of toluene and vortexed for 15 seconds. The red indicator containing proline dissolved in toluene was removed and placed in a spectrophotometer at the same time as the standard samples, and the absorbance of the samples was read at a wavelength of 520 nm. The proline concentration was determined in mg/g of fresh leaf tissue. Artificial neural network (ANN) models Artificial neural networks are computational models made up of interconnected nodes or "neurons" that will simulate data processing and analysis. These neurons possess the inherent capacity to store, learn from, and interpret large sets of empirical data, thereby providing a robust framework for addressing complex real-world challenges. Key features of ANNs include their ability to efficiently process vast amounts of information, accurately map complex data relationships, tolerate noisy or incomplete data, adapt dynamically to varying inputs, generalize learned patterns across different contexts, and exhibit resilience under uncertain conditions. These attributes make ANNs an invaluable tool for predictive modeling, optimization, and performance enhancement in engineering and other domains. Their application allows for more precise solutions to intricate problems, contributing to significant reductions in both operational costs and time, and making them indispensable in solving modern, multifaceted engineering problems [ 15 , 16 ]. Multilayer Perceptron Neural Network (MLPNN) The MLPNN consists of three primary layers: an input layer, one or more hidden layers, and an output layer (Fig. 3 ). These networks are composed of interconnected neurons, with each neuron characterized by a bias value, connection links, and associated weights for these links. The training process relies on input data paired with corresponding target outputs and utilizes specific learning algorithms to optimize the network. The mathematical behavior of a neuron (k) is described by equations ( 1 ) and ( 2 ): $$\:{y}_{k}=f\left({u}_{k}+{b}_{k}\right)$$ 1 $$\:{u}_{k}\:=\:\sum\:_{i=1}^{N}{w}_{ki}{x}_{i}$$ 2 It is important to note that in these equations, x1, x2, x3, …, xn represent the input signals, while wk1, wk2, wk3, …, wkn represent the weights of the neuron connections. uk describes the linear combination of the weighted inputs, bk is the bias, f is the activation function, and uk, as is well known, represents the output of the neuron. MLPNNs are trained using the backpropagation algorithm, which employs an error-correction strategy. The network, generates predicted outputs based on input data and compares them to the target values to calculate the error. Weights and biases are iteratively adjusted to minimize this error. This process continues until the error falls below a predefined threshold. According to Hashemi et al., the mean square error (MSE) is known as a performance measure for reducing errors during this optimization process [ 17 ]. Radial Basis Function Neural Networks (RBFNN) RBFNNs, as you know, are widely used in various fields, including function approximation and pattern recognition. These networks are renowned for their simple architecture, exceptional resilience to input noise, and fast, efficient training procedures. Additionally, RBFNNs demonstrate superior generalization capabilities, enabling them to effectively handle patterns outside their training dataset. As you can see from Fig. 4 , an RBFNN has three main layers, which are described below 1. Input layer, 2. Hidden layer, and 3. Output layer. The role of the input layer is to transfer data to the hidden layer, which uses radial basis functions to process the inputs, while the output layer calculates a linear combination of the responses of the hidden neurons to produce the final output. The output of an RBFNN is mathematically described by Eq. 3 $$\:{y}_{i}\left(x\right)=\:\sum\:_{j=1}^{k}{w}_{ij}\phi\:\left(‖x-{c}_{j}‖\right)$$ 3 In the formula you see, the symbol x represents the input vector, the symbol yi represents the i-th output of the network, the symbol K represents the number of neurons in the hidden layer, the symbol cj is the center associated with the j-th hidden neuron, and finally w ij corresponds to the weight that connects the j-th hidden neuron to the i-th output neuron, and ||. || represents the Euclidean distance.The function φ serves as the radial basis function used by the hidden neurons, which quantifies the distance between the input vector and a designated center vector. Among the various types of radial basis functions discussed in research, the Gaussian function is the most prevalent. It is defined as: $$\:\phi\:\:\left(‖x-{c}_{j}‖\right)=\:{e}^{\left(-{\frac{‖x-{C}_{j}‖}{{2\sigma\:}_{j}^{2}}}^{2}\right)}$$ 4 In this context, σ_j represents the width parameter of the j-th hidden neuron. A key point in designing and training an RBF-NN is to accurately determine the centers, widths, and connection weights for the hidden neurons. The researchers proved that the number of hidden neurons required depends on the dimensionality and distribution of the input data. They also showed that, typically, reducing the dimensionality of the input data leads to a lower need for the number of hidden neurons [ 17 ]. Data partitioning and K-fold cross-validation Cross-validation with K-fold data partitioning K-fold cross-validation was employed in this study to guarantee full representation of the data set in every iteration and to reduce the impact of random sample fluctuation. Pachouly et al. recently demonstrated that the data set is divided into subsets that do not overlap [ 18 ]. The dataset is separated into non-overlapping subsets, as demonstrated by Pachouly et al. and Kamensky et al. In each cycle, we used one subset for testing and the other subsets for training. However, because this process was carried out k times, it was seen that every subset could be analyzed as the test set precisely once. Pachouly et al. shown that this approach provides the strongest evaluation of overfitting risk. Despite being a widely used method for offline evaluation of machine learning algorithms, k-fold cross-validation can have problems with certain data types when samples within classes are gathered in close proximity to one another without being randomly assigned to the other class or classes. The training and test sets for time-series data, like EEG, contain examples from the same class that are highly correlated because of their temporal proximity. This is achieved by randomly splitting all samples into k divisions. This goes against the independence assumption, which is essential to k-fold cross-validation's efficacy [ 19 ]. As a result, rather than identifying any actual class-related differences, the classifier may identify differences between the classes that are just connected to this temporal correlation of some data [ 20 ]. We used 5-fold cross-validation using the method of Phinzi et al [ 21 ]. In this method, the data set is divided into five separate parts, four subsets of which will be selected for training and one subset as the test set. We carefully calculated the performance indicators of each iteration and also obtained the average results from all iterations to determine the overall evaluation of the model. We were able to accurately evaluate the exact performance. Recently, Ghafoorian Heidari et al., in addition to the above, considered data diversity and a reliable standard for evaluating the flexibility and conditional consistency of the model, which was fruitful [ 22 ]. For computational analysis, we used MATLAB software (R2017b) in this study to develop RBF and MLP neural network models. Model Performance Evaluation In the present study, we used MLP and RBF models to estimate the concentrations of three very important secondary metabolites in the medicinal plant ( D. moldavica) , which included the content of leaf amino acids, carotenoids and soluble sugars of the bark, and used three important and key statistical criteria: 1. Root mean square error (RMSE), 2. Mean absolute percentage error (MAPE) and finally 3. Coefficient of determination (R²). These criteria are mathematically defined in equations. In the following formula (5), (6) and (7) respectively, and together they provide a general framework for examining the accuracy of the models. Specifically, the deviation between the predicted and observed values ​​(RMSE), as well as the percentage error relative to the actual observations (MAPE) and the proportion of variance in the dataset accurately explained by the model (R2) were investigated and also quantified. \(\:MAPE=\:\frac{1}{n}\sum\:_{i=1}^{n}\left|\frac{{\left({Y}_{est}\right)}_{i}-\:{\left({Y}_{meas}\right)}_{i}}{{\left({Y}_{meas}\right)}_{i}}\right|\times\:100\) (5) \(\:{R}^{2}=1-\:\frac{{\sum\:_{i=1}^{n}\left[{\left({Y}_{est}\right)}_{i}-\:{\left({Y}_{meas}\right)}_{i}\right]}^{2}}{\sum\:_{i=1}^{n}{\left({Y}_{est}-\stackrel{-}{Y}\right)}_{i}^{2}}\) (6) \(\:RMSE=\sqrt{\frac{1}{n}\:\sum\:_{i=1}^{n}{\left[{\left({Y}_{est}\right)}_{i}-\:{\left({Y}_{meas}\right)}_{i}\right]}^{2}}\:\) (7) As you can see, n represents the total number of data points in the dataset, and \(\:{Y}_{est}\) and \(\:{Y}_{meas}\) represent the predicted and actual observed concentrations, respectively, while \(\:Y\) is the average of the observed values. As has been proven, the model performance is considered optimal when the MAPE and RMSE values ​​are minimized, and the coefficient of determination R² reaches its maximum, which, according to Heidari et al., indicates the best fit between the predicted and observed values [ 23 , 24 ]. Results and Discussion In the present study, the levels of amino acid proline, carotenoids, and soluble sugar levels in the stem of D. moldavica were investigated using two types of neural networks, MLP and RBF, for modeling. The data were obtained from a study designed to investigate the effect of applied stimuli on salinity stress with the permission of the author of the study, who is also present in this study. We selected 13 easily measured physiological and morphological traits here and used them as input variables. These 13 traits are stem length (cm), crown diameter (mm), internode length (cm), number of internodes, number of lateral stems, lateral stem length (cm), leaf width (mm), leaf length (mm), number of leaves, relative weight and root weight of stem (cm), relative weight of stem (cm), dry weight of branch (cm), dry stem length, and 3 very important traits that are very important during salt stress of plants and are measured in the laboratory by different and very difficult and expensive methods were considered as target output variables. These 3 traits include the very important amino acid proline, which is also known as the stress amino acid, carotenoids, and finally soluble sugars, which were vital biochemical indicators that we selected due to their physiological importance. The purpose of this research is to minimize the high laboratory costs, minimize the damage of chemicals and very high speed of operation, and efficiently estimate these vital traits. Designing and optimizing RBF After data collection, the next step is to select an appropriate learning algorithm and design a neural network architecture suited to the problem at hand. The choice of learning algorithm depends on several factors, such as data size, problem type (classification, regression, etc.), and computational resources. Achieving optimal performance in the RBF model requires careful and methodical tuning of its parameters. These parameters include the selection of the transfer function, the spread value, and the method used for data normalization [ 25 ]. The data are standardized in such a way that their distribution has a mean of zero and a standard deviation of one. To perform the optimization, various training functions for the RBF network were examined. Several RBF networks were trained using these functions, including the radial basis network (newrb), exact radial basis network (newrbe), generalized regression neural network (newgrnn), and probabilistic neural network (newpnn). A Among the configurations evaluated, the RBF model optimized with the newgrnn function exhibited superior predictive performance, achieving the lowest mean squared error (MSE) and the highest R² value [ 26 ]. To optimize the spread parameter, which plays a crucial role in determining the width of Gaussian basis functions in the RBF model and directly influences the balance between overfitting and underfitting, various values of this parameter were tested [ 27 , 28 ]. The results indicated that the minimum RMSE was achieved at the optimal value of the spread, demonstrating the model's best generalization performance. This optimization was conducted by analyzing the RMSE curve as a function of the spread, where the optimal spread value was found to be 0.529, resulting in an RMSE of 0.484 (Fig. 5 ). Designing and Optimizing the MLP Model In this study, the MLP model was designed and optimized through a systematic approach for selecting the optimal number of layers and neurons. Due to the absence of a definitive method for determining the optimal number of neurons in the hidden layers, an iterative approach was employed in this study to systematically identify both the number of layers and the number of neurons per layer [ 23, 29]. Among the diverse computational approaches examined—including Levenberg-Marquardt, Bayesian regularization, scaled conjugate gradient, steepest descent, elastic backpropagation, and Newton's method the Levenberg-Marquardt algorithm demonstrated superior performance and was consequently selected as the most effective learning algorithm, consistent with the results of Nait Amar et al. (2022). Additionally, the log-sigmoid activation function was selected for the hidden layer based on comparative analysis of various transfer functions [ 30 ]. Evaluation of Neural Network Models for Predicting Key Biochemical Molecules Table 2 offers a comprehensive evaluation of the MLP and RBF models' performance, utilizing 5-fold cross-validation to estimate carotenoid, proline, and shoot soluble sugar levels. The models were assessed based on R², RMSE, and MAPE, with calculations performed for the training set, test set, and overall dataset. This approach ensures a thorough analysis of the models' predictive ability to generalize across different data subsets. Table 2 Performance comparison of RBFNN and MLPNN models for predicting carotenoid, proline, and shoot soluble sugar. Model types Train Test Total R 2 RMSE MAPE R 2 RMSE MAP R 2 RMSE MAPE Carotenoid MLPNN 0.948 0.257 2.010 0.858 0.386 2.612 0.935 0.299 2.291 RBFNN 0.996 0.066 0.412 0.902 0.295 1.971 0.983 0.148 0.783 Proline MLPNN 0.963 0.170 1.097 0.903 0.289 1.869 0.957 0.199 1.371 RBFNN 0.999 0.052 0.556 0.975 0.235 1.124 0.996 0.115 0.831 Shoot soluble sugar MLPNN 0.944 1.166 1.338 0.876 1.619 1.965 0.937 1.276 1.463 RBFNN 0.999 0.178 0.206 0.941 0.948 1.229 0.992 0.455 0.411 Carotenoid Prediction The results of this study for carotenoid content in this plant showed that the RBFNN model is more suitable for superior prediction performance compared to MLPNN. It was also observed that in the RBFNN model, the entire dataset changed to an overall R² of 0.983, RMSE of 0.148 and MAPE of 0.783, while it changed to an R² of 0.935, RMSE of 0.299 and MAPE of 2.291 in the MLPNN model. It is worth noting that in the important traits tested, RBFNN showed higher accuracy and better performance than the MLPNN model. Therefore, it can be said that according to our results, the RBFNN model performed more robustly and better for predicting carotenoid content, and consistently showed lower prediction errors and higher accuracy measures in all evaluation criteria. This observation aligns with findings from various studies that have highlighted the efficacy of RBFNN models in capturing complex, non-linear relationships in plant biochemistry [ 32 ]. Specifically, the RBFNN model's superior performance in terms of lower RMSE and MAPE values, and higher R² values across all datasets, suggests its enhanced capacity for generalization and accuracy in predicting carotenoid levels under varying experimental conditions. In agreement with our results, previous research has demonstrated the advantages of RBFNN over other neural network architectures in predicting biochemical traits. For instance, Li et al. [ 33 ] proposed a generalized residual shelf-life prediction model for post-harvest table grapes. By employing an optimized radial basis function (RBF) neural network, their model demonstrated significantly higher accuracy compared to traditional shelf life (SL) prediction methods. Guardado Yordi et al. [ 33 ] emphasized the potential of machine learning algorithms, particularly the Random Forest model, in accurately predicting antioxidant properties based on the structural-topological features of flavonoids. Their findings highlight the effectiveness of integrating artificial intelligence methods with chemical structure analysis to enhance predictive accuracy in biochemical research, aligning with our approach to estimating secondary metabolites in medicinal plants [ 33 ]. RBFNN's ability to model complex patterns in plant biochemical data can be attributed to its unique structure, which allows for effective representation of the relationships between input features and output biochemical traits. Unlike MLPNN, which uses multiple hidden layers to learn data representations, RBFNN relies on radial basis functions to map input data directly to output variables in a less computationally intensive manner. These results are in line with the research of González-Camacho et al., who showed that the RBFNN model is particularly suitable for predicting the amount of plant metabolites that are very important and significant, as well as for nonlinear and multifaceted relationships [ 31 ], Machine learning and deep learning, when combined with hyperspectral imaging, offer a promising solution for early disease detection and monitoring large agricultural areas with minimal labor. These technologies not only enable faster disease diagnosis but also aid in identifying gene regulatory networks and developing disease-resistant crops, revolutionizing modern plant science [ 36 ]. Recently, Jurinjak Tusek et al. [ 37 ] evaluated various modeling techniques, including linear and nonlinear regression and ANN, for predicting the physical and chemical properties of aqueous extracts from nine medicinal plants: dandelion, chamomile, lavender, lemon balm, marigold, mint, nettle, plantain, and yarrow. The chemical properties analyzed were total phenolic content and antioxidant activity, while the physical properties included total dissolved solids and extraction yield. The results showed that while regression models were useful, the ANN model outperformed others, achieving higher accuracy (R² > 0.9) in predicting both physical and chemical properties simultaneously. These findings contribute to the growing body of literature suggesting that RBFNN models offer significant advantages for predicting biochemical compounds in medicinal and aromatic plants. Proline Prediction For proline prediction, the RBFNN model showed better performance compared to the MLPNN model. In this study, the RBFNN model was shown to have an outstanding overall R² of 0.996, RMSE of 0.115, and MAPE of 0.831 on the entire dataset and also significantly outperformed MLPNN which recorded an overall R² of 0.957, RMSE of 0.199, and MAPE of 1.371. Finally, in the experimental data of this study, the RBFNN showed further superiority with R² of 0.975, RMSE of 0.235, and MAPE of 1.124, surpassing the MLPNN performance criteria of R² = 0.903, RMSE = 0.289, and MAPE = 1.869. Our research is consistent with the research of Zhang and Wang, who showed better performance of the RBFNN model for estimating secondary metabolites in medicinal plants than other methods [ 38 ]. Researchers have shown that secondary metabolites such as proline are very important and efficient during environmental stress. Also, the application of machine learning models such as RBFNN has been promising in accurately predicting the amount of this amino acid with high accuracy. In our project, the RBFNN model was better than the MLPNN model with lower RMSE and MAPE in both the complete and experimental datasets of this amino acid, showing its potential for reliable and accurate predictions of the data. In contrast, the MLPNN model showed relatively lower accuracy. In addition, the work of Jamir and HP [ 39 ] also showed in a project the prediction of plant secondary metabolites targeting therapeutic outcomes, such as α-glucosidase inhibition and considered the role of machine learning to be very important in the advancement of medicinal plant research. In addition, Nazarenko et al. [ 40 ] also considered the application of machine learning in the analytical control of medicinal plant preparations and emphasized its investigation for the prediction and accurate analysis of plant compounds. These advances indicate that the integration of RBFNN with multi-source data in the future can significantly increase the predictive power of secondary metabolites in medicinal plants, including proline, carotenoids, and sugars. Shoot Soluble Sugar Prediction For soluble sugar in the branch, the RBFNN model also showed significantly more accurate prediction with an overall R² of 0.992, RMSE of 0.455 and MAPE of 0.411 for the complete dataset, as for the amino acid proline. The MLPNN model, however, showed slightly lower overall performance measures with R² of 0.937, RMSE of 1.276 and MAPE of 1.463. In the dataset of this project, RBFNN showed R² of 0.941, RMSE of 0.948, and MAPE of 1.229. While MLPNN showed R² of 0.876, RMSE of 1.619 and MAPE of 1.965. This further underscores the superiority of the RBFNN model in capturing complex relationships between input features and output variables. Recent research highlights the influential role of ML in improving the modeling and optimization of secondary metabolite production in plants. Tan et al. [ 41 ] applied RBFNN to optimize metabolite synthesis in Spirodela polyrhiza , achieving accurate predictions and significant improvements. These findings demonstrate the potential of ML-driven approaches to advance secondary metabolite research and applications in plant biochemistry. Their work emphasizes how machine learning approaches can be employed to predict a variety of plant secondary metabolites, including soluble sugars, with high accuracy. The application of machine learning models such as RBFNN has also been increasingly acknowledged for its superiority in capturing the underlying relationships in complex biological data [ 41 ]. This is consistent with findings from Zhang and Wang [ 38 ] and Jamir and HP [ 39 ], who highlighted the effectiveness of RBFNN in predicting various secondary metabolites in medicinal plants. The ability of RBFNN to model complex data and predict secondary metabolites, such as soluble sugars, amino acids, and carotenoids, reflects its growing role in advancing the field of medicinal plant research. The RBFNN model also provided the best and most accurate prediction for plant sugar content, which is very important for the timing of environmental stress and plant growth and response to stresses. Nazarenko et al. [ 40 ] on the use of machine learning for quality control in medicinal plant preparations emphasized the importance of learning these models in ensuring the stability and reliability of plant-based products. The current results contribute to this broader trend and emphasize that machine learning can be an essential tool for sustainable production and quality control of medicinal plants and reducing the use of chemicals. Figures 6 and 7 compare the regression relationships between predicted and measured values for carotenoid, shoot proline, and shoot soluble sugar using the RBF and MLP neural network models, respectively. The RBF model (Fig. 6 ) demonstrates superior predictive accuracy, with R² values of 0.983, 0.996, and 0.992 for carotenoid, proline, and shoot soluble sugar, respectively. In comparison, the MLP model (Fig. 7 ) achieves R² values of 0.935, 0.957, and 0.937 for the same traits. While the MLP model also exhibits strong predictive performance, the RBF model slightly outperforms it, particularly for carotenoid and shoot soluble sugar predictions, indicating its higher overall reliability for this dataset. Comparative Evaluation of Neural Network Models for Predicting Carotenoid, Proline, and Shoot Soluble Sugar This investigation compared the performance of two neural network models, MLP and RBF, in predicting carotenoid levels, shoot proline, and shoot soluble sugar concentrations. The models were evaluated using three critical metrics: RMSE, MAPE, and R², with the results presented in Figs. 8 , 9 , and 10 , which focused specifically on the test dataset to ensure a thorough analysis of prediction accuracy. Figure 8 displays the RMSE values for both models across all measured variables. It is evident that the RBF model consistently achieved lower RMSE values compared to the MLP, suggesting it outperformed the MLP in terms of accuracy and error reduction. This consistent trend across all three variables emphasizes the RBF's superior capability to effectively capture and predict complex biochemical characteristics with higher precision. Figure 9 showcases the MAPE values for both models, where the RBF consistently outperformed the MLP model, exhibiting significantly lower error percentages across all variables. Notably, this advantage was most pronounced in the prediction of shoot soluble sugar, where the RBF achieved a substantial reduction in prediction error compared to the MLP. Furthermore, Fig. 10 presents the R² values for both models, reflecting their efficacy in explaining the variance within the measured data. The RBF model demonstrated consistently higher R² values, signifying a stronger alignment between its predictions and the actual values. This further underscores the RBF's capability to effectively capture the underlying relationships in the dataset. In conclusion, the comparative evaluation confirms that the RBF model outperformed the MLP in predicting carotenoid, shoot Proline, and shoot soluble sugar concentrations. This is evidenced by its superior performance in terms of lower RMSE and MAPE values and higher R² scores, establishing the RBF as a more reliable and precise tool for predicting biochemical properties. Researchers have shown that RBF networks are suitable for predicting biochemical traits in plants due to their ability to handle nonlinear relationships [ 42 ]. In contrast, while MLP networks can also model non-linearities, they often require more data and fine-tuning to achieve comparable accuracy, especially for tasks involving intricate biochemical interactions [ 43 ]. This aligns with the findings in the present study, where the RBF model consistently outperformed the MLP in all three prediction scenarios. Additionally, RBF networks have been widely applied in plant science, where they have demonstrated strong predictive capabilities for estimating various physiological and biochemical traits under different environmental conditions [ 29 ]. Studies have shown that RBF's inherent flexibility in adjusting to the complexity of plant biochemical responses under stress conditions (e.g., salinity, drought) enhances its accuracy in prediction [ 44 ]. These advantages make RBF an appealing choice for applications in plant biotechnology and agronomy, where accurate prediction of biochemical traits is crucial for crop improvement and sustainability. Evaluation of Predicted and Actual Data Using the Optimized RBF Model Table 3 shows all the statistical properties including sum, mean, standard deviation, minimum and maximum values ​​for both actual and predicted data sets. It can be stated that the accuracy and consistency of the RBF model for all three variables of this study were proven and their minimum deviation was shown in the statistical parameters. Table 3 Comparison of observed and predicted values for carotenoid, proline, and shoot soluble sugar using the final RBF model. Element Phases Data Sum Average Standard deviation Minimum Maximum Carotenoid Total Actual 539.407 8.990 1.178 6.822 11.540 Predicted 540.836 9.014 1.197 6.841 11.390 Train Actual 428.075 8.918 1.247 6.822 11.540 Predicted 428.066 8.918 1.238 6.841 11.390 Test Actual 111.332 9.278 0.786 7.943 10.622 Predicted 112.770 9.397 0.925 7.899 11.275 Proline Total Actual 387.041 6.451 1.939 2.272 10.302 Predicted 386.940 6.449 1.932 2.301 10.254 Train Actual 299.823 6.246 2.050 2.272 10.302 Predicted 299.816 6.246 2.047 2.301 10.254 Test Actual 87.218 7.268 1.075 5.704 9.412 Predicted 87.124 7.260 1.041 5.748 9.077 soluble sugar Total Actual 3660.866 61.014 5.175 49.214 69.420 Predicted 3652.846 60.881 5.104 49.610 69.318 Train Actual 2893.552 60.282 5.327 49.214 69.420 Predicted 2893.414 60.279 5.313 49.610 69.318 Test Actual 767.314 63.943 3.108 58.600 69.218 Predicted 759.433 63.286 3.180 56.312 69.248 Carotenoids In this study, for the entire carotenoid pigment dataset, the predicted mean value was 9.014 and the observed mean was 8.990, with standard deviations of 1.197 and 1.178, respectively. This close alignment demonstrated the ability of the RBF model to replicate the true distribution of carotenoid concentrations, which is consistent with the consistency of predictions in the training and test subsets. Proline In this study, for the amino acid proline, the accuracy of the results, which was consistently observed in both the training and testing subsets, demonstrated the reliability of the RBF model in predicting proline levels with higher accuracy. The predicted mean (6.449) for the entire dataset was very close to the actual mean (6.451) and was almost identical, with the minimum difference observed in the standard deviations (1.932 vs. 1.939). Shoot Soluble Sugar In this study, the soluble sugar in the shoot also followed a similar trend as proline, with the predicted mean (60.881) being very close to the actual mean (61.014), with only minor differences in standard deviations (5.104 vs. 5.175), which can be seen in both the training and experimental subsets, emphasizing the robustness of the model in accurately predicting the soluble sugar concentration in the shoot. Therefore, the close alignment between the predicted values ​​in this study and the actual values, as well as the minimal deviation in statistical criteria, emphasizes the effectiveness of the optimized RBF model in capturing important biochemical traits in this valuable medicinal plant. Conclusion This project evaluated two neural network models, MLP and RBF, for predicting the levels of key biochemically important metabolites in D. moldavica , especially under plant stress. The results were carefully examined and observed, and consistently for all three secondary metabolites, the performance of the RBF model was superior, as demonstrated by its lower RMSE and MAPE values ​​and higher R² scores across all datasets. This superiority reflects the RBF model’s capability to capture complex, non-linear interactions between morphological and biochemical variables, making it a robust and reliable predictive tool. The practical implications of these results are significant, particularly in precision agriculture and plant biochemical research. In this study, we were able to accurately model the relationships between easily measurable growth parameters and key biochemical characteristics (carotenoids, proline, and soluble sugar levels). We concluded that the best model was the RBF model, which can be an efficient tool for strategic management of medicinal plants, reducing chemical consumption, reducing environmental pollution, reducing costs, and ultimately developing sustainable agriculture. It can also predict the performance of medicinal plants efficiently and be an effective step towards the sustainable development of agricultural sciences, pharmaceuticals, and the food and medical industries. Declarations Clinical trial number : not applicable . Authors' Contributions Sh Najafian: Writing – original draft, Visualization, Investigation, Data curation. Shahnaz Fathi and Roya Movlodzadeh: Resources, Methodology. Sajad Heidari: Conceptualization, Formal analysis, Methodology, Software, original draft, Editing. Shahnaz Fathi review & editing, Project administration, funding acquisition. Ethics declarations Ethical approval and consent to participate. Not applicable. Consent for publication Not applicable Competing interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Compliance with ethical standards The presented manuscript represents the honest research work of the authors. Funding This research received no external funding. Data Availability The data used in this study is openly available, and the data used is available upon request from the corresponding authors SH.N. Author Details 1. Department of Medicinal and aromatic Plants, Shahid Bakeri High Education Center of Miandoab, Urmia University, Urmia, Iran 2. Department of Biosystems Engineering, Shiraz University, Shiraz, Iran 3. Department of Natural Resources and Environment Engineering, School of Agriculture, Shiraz University, Shiraz, IR Iran. References Xu, Y., Liang, D., Wang, G. T., Wen, J. & Wang, R. J. Nutritional and functional properties of wild food medicine plants from the coastal region of South China. J. Evid-Based Integr. Med. 25 , 1–13 (2020). Aćimović, M., Stanković, J., Cvetković, M., Todosijević, M. & Rat, M. The chemical composition of the essential oil of Dracocephalum moldavica L. from Vojvodina Province (Serbia). Biol. Nyssana . 10 , 23–28 (2019). Aćimović, M. et al. Dracocephalum moldavica : Cultivation, chemical composition and biological activity. J. Agron. Technol. Eng. Manag . 2 , 153–167 (2019). Keikhaie, R. K., Jahantigh, H. R., Bagheri, R. & Kehkhaie, R. A. The effect of the ethanol extract of Dracocephalum moldavica (Badrashbu) against strains of antibiotic-resistant Escherichia coli and Klebsiella pneumoniae . Int. J. Infect. 5 , 65295 (2018). Fallah, S., Rostaei, M., Lorigooini, Z. & Sukri, A. A. Chemical compositions of essential oil and antioxidant activity of dragonhead ( Dracocephalum moldavica ) in sole crop and dragonhead-soybean (Glycine max) intercropping system under organic manure and chemical fertilizers. Ind. Crops Prod. 115 , 158–165 (2018). Mafakheri, S. & Asghari, B. Optimization of growth and biochemical production in Dracocephalum moldavica L. through biochar and salicylic acid application in a pot experiment. J. Med. Plants By-Prod (2024). Raza, A. et al. Assessment of proline function in higher plants under extreme temperatures. Plant. Biol. ; 380–395. (2023). Swapnil, P., Meena, M., Singh, S. K., Dhuldhaj, U. P. & Harish, Marwal, A. Vital roles of carotenoids in plants and humans to deteriorate stress with its structure, biosynthesis, metabolic engineering and functional aspects. Curr. Plant. Biol. 26 , 100203 (2021). Soltis, P. S., Nelson, G., Zare, A. & Meineke, E. K. Plants meet machines: prospects in machine learning for plant biology. Appl. Plant. Sci. 8 , e11371 (2020). Fenu, G. & Malloci, F. M. Forecasting plant and crop disease: an explorative study on current algorithms. Big Data Cogn. Comput. 5 (2), 1–16 (2021). Rico-Chávez, A. K. et al. Machine learning for plant stress modeling: A perspective towards hormesis management. Plants 11 , 970 (2022). Moloudzadeh, R., Fathi, S., Yari, F., Najafian, S. & Seyedi, A. The potential of coated iron nanoparticles for modulating negative effects of salinity stress in Ajowan. Hortic. Environ. Biotechnol. 65 , 747–760 (2024). Dubois, M., Gilles, K. A., Hamilton, J. K., Rebers, P. A. & Smith, F. Colorimetric method for the determination of sugars and related substances. Anal. Chem. 28 (3), 350–356 (1956). Lichtenthaler, H. K. & Wellburn, A. R. Determinations of total carotenoids and chlorophylls a and b of leaf extracts in different solvents. Biochem. Soc. Trans. 11 , 591–592 (1983). Gholamzadeh, E., Ghaemi, A., Shokri, A. & Heydari, B. Investigation of boiler energy consumption in the gas refinery units using RSM ANN and Aspen HYSYS. Heliyon ; e41450. (2024). Ghritlahre, H. K. & Prasad, R. K. Exergetic performance prediction of solar air heater using MLP, GRNN and RBF models of artificial neural network technique. J. Environ. Manag . 223 , 566–575 (2018). Hashemi Fath, A., Madanifar, F. & Abbasi, M. Implementation of multilayer perceptron (MLP) and radial basis function (RBF) neural networks to predict solution gas-oil ratio of crude oil systems. Petroleum. ; 6:80–91. (2020). Pachouly, J., Ahirrao, S., Kotecha, K., Selvachandran, G. & Abraham, A. A systematic literature review on software defect prediction using artificial intelligence: Datasets, data validation methods, approaches, and tools. Eng. Appl. Artif. Intell. 111 , 104773 (2022). Roberts, D. R. et al. Cross-validation strategies for data with temporal, spatial, hierarchical, or phylogenetic structure. Ecography 40 , 913–929 (2017). White, J. & Power, S. D. K-Fold cross-validation can significantly overestimate true classification accuracy in common EEG-based passive BCI experimental designs: An empirical investigation. Sensors 23 (13), 6077 (2023). Phinzi, K., Abriha, D. & Szabó, S. Classification efficacy using k-fold cross-validation and bootstrapping resampling techniques on the example of mapping complex gully systems. Remote Sens. 13 , 2980 (2021). Ghafoorian Heidari, S. I., Safehian, M., Moodi, F. & Shadroo, S. Predictive modeling of the long-term effects of combined chemical admixtures on concrete compressive strength using machine learning algorithms. Case Stud. Chem. Environ. Eng. 10 , 101008 (2024). Heidari, S., Mirzaee-Ghaleh, E., Rabbani, H. & Vesali, F. Development of an Android app for estimating the water quality parameters in fish pond. Environ. Sci. Pollut Res. 28 , 34501–34510 (2021). Yan, Z. et al. A multi-energy load prediction of a building using the multi-layer perceptron neural network method with different optimization algorithms. Energy Explor. Exploit. 41 , 273–305 (2023). Shoaib, M. et al. A. stochastic numerical analysis based on hybrid NAR-RBFs networks nonlinear SITR model for novel COVID-19 dynamics. Comput. Methods Programs Biomed. 202 , 105973 (2021). Noroozian, M., Ghaemi, A. & Heidari, Z. Potential of artificial intelligence and response surface methodology to predict CO₂ capture by KOH-modified activated alumina. Case Stud. Chem. Environ. Eng. 8 , 100442 (2023). Messikh, N., Bougdah, N., Bousba, S. & Djazi, F. Modeling the adsorption of chlorobenzene on modified bentonite using an artificial neural network. Curr. Res. Green. Sustain. Chem. 3 , 100026 (2020). Zheng, L., Jiang, L., Zheng, K. & Yu, M. Estimation of explosion limits of gas mixture using a single spread GRNN. 2nd Int Conf Artif Intell Manag Sci Electron Commer (AIMSEC). IEEE ; 1113–1115. (2021). Kumar, M., Mehta, U. & Cirrincione, G. Enhancing neural network classification using fractional-order activation functions. AI Open. 5 , 10–22 (2024). Nait Amar, M., Jahanbani Ghahfarokhi, A. & Shang Wui Ng, C. Predicting wax deposition using robust machine learning techniques. Petroleum 8 , 167–173 (2022). González-Camacho, J. M. et al. Genome-enabled prediction of genetic values using radial basis function neural networks. Theor. Appl. Genet. 125 , 759–771 (2012). Yunan, I., Yassin, I. M., Syed Adnan, S. F. & Fazalul Rahiman, M. H. Identification of essential oil extraction system using Radial Basis Function (RBF) neural network. Proc. IEEE 8th Int. Colloq. Signal. Process. Appl. ; 6194779. (2012). Li, Y., Chu, X., Fu, Z., Feng, J. & Mu, W. Shelf-life prediction model of postharvest table grape using optimized radial basis function (RBF) neural network. Br. Food J. ; (2019). Guardado Yordi, E. et al. Artificial intelligence applied to flavonoid data in food matrices. Foods. 2019; 8(11):573. (2019). González-Camacho, J. M. et al. Genome-enabled prediction of genetic values using radial basis function neural networks. Theor. Appl. Genet. 125 , 759–771 (2012). Das, S., Pattanayak, S. & Behera, P. R. Application of machine learning: a recent advancement in plant diseases detection. J Plant Prot Res. 2022; 62:122–135. (2022). Jurinjak Tušek, A. et al. Application of multivariate regression and artificial neural network modelling for prediction of physical and chemical properties of medicinal plants aqueous extracts. J. Appl. Res. Med. Aromat. Plants . 16 , 100229 (2022). Zhang, Y. & Wang, Y. Recent trends of machine learning applied to multi-source data of medicinal plants. J. Pharm. Anal. 13 (5), 675–689 (2023). Jamir, L. HP P. Employing Machine Learning Models to Predict Potential α-Glucosidase Inhibitory Plant Secondary Metabolites Targeting Type-2 Diabetes and Their In Vitro Evaluation. J Chem Inf Model.2024; 64(2):221–233. (2024). Nazarenko, D. V., Rodin, I. A. & Shpigun, O. A. The use of machine learning in the analytical control of the preparations of medicinal plants. Inorg Mater.2019; 55(6):619–624. (2019). Tan, W. H., Tong, C. Y., Chua, M. X. & Derek, C. J. C. Modelling and optimizing secondary metabolites production in Spirodela polyrhiza using machine learning. J Clean Prod. 2024; 478:143986. (2024). Zhao, Y., Zheng, S., Pei, J. & Yang, X. Multiple discriminants pr eserving support subspace RBFNNs with graph similarity learning. Inf. Sci. 619 , 421–438 (2023). Lee, W. J. & Lee, E. H. Runoff prediction based on the discharge of pump stations in an urban stream using a modified multi-layer perceptron combined with meta-heuristic optimization. Water 14 (1), 99 (2022). Zarbakhsh, S. & Shahsavar, A. R. Artificial neural network-based model to predict the effect of γ-aminobutyric acid on salinity and drought-responsive morphological traits in pomegranate. Sci. Rep. 12 , 16662 (2022). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6105806","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":428150587,"identity":"f5de84f5-ed66-4f94-a3f3-efdd6a93ea2a","order_by":0,"name":"Shahnaz Fathi","email":"","orcid":"","institution":"Urmia University of Medical Sciences","correspondingAuthor":false,"prefix":"","firstName":"Shahnaz","middleName":"","lastName":"Fathi","suffix":""},{"id":428150588,"identity":"34b52851-2b78-49c3-bd0c-1806e6163f2a","order_by":1,"name":"Roya Movlodzadeh","email":"","orcid":"","institution":"Urmia University of Medical Sciences","correspondingAuthor":false,"prefix":"","firstName":"Roya","middleName":"","lastName":"Movlodzadeh","suffix":""},{"id":428150589,"identity":"f7f237e9-dfc7-4536-abde-bbb1f2c02b6e","order_by":2,"name":"Sajad Heidari","email":"","orcid":"","institution":"Department of Biosystems Engineering, Shiraz University, Shiraz, Iran","correspondingAuthor":false,"prefix":"","firstName":"Sajad","middleName":"","lastName":"Heidari","suffix":""},{"id":428150590,"identity":"1d98ee7b-7884-40f3-9a7f-5eeed8df7ac3","order_by":3,"name":"Sharareh Najafian","email":"data:image/png;base64,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","orcid":"","institution":"Department of Natural Resources and Environment Engineering, School of Agriculture, Shiraz University, Shiraz, IR Iran","correspondingAuthor":true,"prefix":"","firstName":"Sharareh","middleName":"","lastName":"Najafian","suffix":""}],"badges":[],"createdAt":"2025-02-25 13:53:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6105806/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6105806/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":78652664,"identity":"f1a1730a-a915-4c06-80e1-98d83dff312d","added_by":"auto","created_at":"2025-03-17 08:51:16","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":200393,"visible":true,"origin":"","legend":"\u003cp\u003eCo-occurrence analysis of the terms used more than 100 times as author and/or index keywords of \u003cem\u003eDracocephalum moldavica\u003c/em\u003e L. The frequency of occurrence is represented by the size of the circle beneath each word. Different colors were employed to depict distinct clusters of highly related keywords, facilitating their categorization. The VOS viewer software was utilized to represent the term cloud, with data collected from the API database.\u003c/p\u003e","description":"","filename":"image1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6105806/v1/1270a28ea1ee1fd46e966c34.jpeg"},{"id":78653661,"identity":"ce32efd3-1350-4046-bd3f-b3b38bc88ad4","added_by":"auto","created_at":"2025-03-17 08:59:16","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":190920,"visible":true,"origin":"","legend":"\u003cp\u003eCo-occurrence analysis of the terms used more than 100 times as author and/or index keywords in machine learning. The frequency of occurrence is represented by the size of the circle beneath each word. Different colors were employed to depict distinct clusters of highly related keywords, facilitating their categorization. The VOS viewer software was utilized to represent the term cloud, with data collected from the API database.\u003c/p\u003e","description":"","filename":"image2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6105806/v1/691fead2485dfd97c3abb90a.jpeg"},{"id":78652665,"identity":"6fabcf57-f47a-42d4-8389-5582e2cdbf14","added_by":"auto","created_at":"2025-03-17 08:51:16","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":273730,"visible":true,"origin":"","legend":"\u003cp\u003eThe structure of a Multilayer Perceptron Neural Network (MLPNN).\u003c/p\u003e\n\u003cp\u003eMLPNNs are trained using the backpropagation algorithm, which employs an error-correction strategy. The network, generates predicted outputs based on input data and compares them to the target values to calculate the error. Weights and biases are iteratively adjusted to minimize this error. This process continues until the error falls below a predefined threshold.\u003c/p\u003e\n\u003cp\u003eAccording to Hashemi et al., the mean square error (MSE) is known as a performance measure for reducing errors during this optimization process [17].\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-6105806/v1/1bd943d44a0afd6f40bdeed1.png"},{"id":78652697,"identity":"5883b57d-76ea-4eae-ad26-ed8c67f47c3c","added_by":"auto","created_at":"2025-03-17 08:51:17","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":198877,"visible":true,"origin":"","legend":"\u003cp\u003eThe structure of a radial basis function neural networks.\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-6105806/v1/7d4ce5cee9646306653398b3.png"},{"id":78652667,"identity":"382a49d3-dbca-4237-9266-dd283ef6b979","added_by":"auto","created_at":"2025-03-17 08:51:16","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":24187,"visible":true,"origin":"","legend":"\u003cp\u003eOptimization of spread constant of RBF model.\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-6105806/v1/3545ee369e396be02e946bb2.png"},{"id":78654038,"identity":"bf9544e5-3332-4235-80a3-594dad0997f0","added_by":"auto","created_at":"2025-03-17 09:07:16","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":71278,"visible":true,"origin":"","legend":"\u003cp\u003eRegression of measured vs. predicted values for carotenoid, shoot proline, and shoot soluble sugar using the RBF neural network.\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-6105806/v1/a49ae38090e1930398cbaeab.png"},{"id":78652670,"identity":"6fc8f406-294b-4538-96f6-c38e0eff0379","added_by":"auto","created_at":"2025-03-17 08:51:16","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":65159,"visible":true,"origin":"","legend":"\u003cp\u003eRegression of measured vs. predicted values for carotenoid, shoot proline, and shoot soluble sugar using the MLP neural network.\u003c/p\u003e","description":"","filename":"image7.png","url":"https://assets-eu.researchsquare.com/files/rs-6105806/v1/fd24b1b452df378faa2e26c1.png"},{"id":78652669,"identity":"e848fb28-ca48-4085-b984-986a99d3333b","added_by":"auto","created_at":"2025-03-17 08:51:16","extension":"jpeg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":134482,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of RMSE values for RBF and MLP models on test datasets for predicting carotenoid, shoot proline, and shoot soluble sugar levels.\u003c/p\u003e","description":"","filename":"image8.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6105806/v1/1962617f9ec617833b6602ec.jpeg"},{"id":78652679,"identity":"9c7e51a8-3f22-4bb9-9c7d-c970b51c9d1f","added_by":"auto","created_at":"2025-03-17 08:51:16","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":626282,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of MAPE values for RBF and MLP models on test datasets for predicting carotenoid, shoot proline, and shoot soluble sugar levels.\u003c/p\u003e","description":"","filename":"image9.png","url":"https://assets-eu.researchsquare.com/files/rs-6105806/v1/1f5df789de0b6d2b38baa4e2.png"},{"id":78652674,"identity":"de3a190f-10b5-4880-954b-d355252d294a","added_by":"auto","created_at":"2025-03-17 08:51:16","extension":"jpeg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":152839,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of R² values for RBF and MLP models on test datasets for predicting carotenoid, shoot proline, and shoot soluble sugar levels.\u003c/p\u003e","description":"","filename":"image10.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6105806/v1/58ceed4a71a0835f85e7b4f6.jpeg"},{"id":96051270,"identity":"64b2103e-d66d-440b-8e5c-692f3bdec7d6","added_by":"auto","created_at":"2025-11-17 06:40:06","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3058263,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6105806/v1/fd11fe4b-f64e-4ace-a2db-085b8133ae41.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Application of machine learning models to predict secondary metabolites for the first time in the valuable medicinal plant (Dracocephalum moldavica L.)","fulltext":[{"header":"Introduction","content":"\u003cp\u003eFor millennia, conventional medicine has employed aromatic and therapeutic herbs globally. They remain crucial for dietary assistance and medicinal treatment [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003cem\u003eDracocephalum moldavica\u003c/em\u003e L., often referred to as Moldavian dragon's head or Moldavian mumy, is a fragrant herbthat began in temperate Asia and is now prevalent throughout the Northern Hemisphere [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Because it contains geranial, neral, and geranyl acetate, \u003cem\u003eD. moldavica\u003c/em\u003e essential oil (DMEO) has a citrus taste and resembles other lemonscented plants like lemon balm and lemon catnip [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Earlier research suggests that the herb possesses antioxidant [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] and antibacterial [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] properties. Many researchers aim to enhance the cultivation of D. moldavica and its phytochemical properties due to the rising demand for natural products in the pharmaceutical, cosmetic, and culinary industries. This entails enhancing \u003cem\u003eD. moldavica\u003c/em\u003e cultivation and conducting phytochemical assessments to increase its therapeutic effectiveness and market worth. In Iran, especially in the West Azerbaijan area, \u003cem\u003eD. moldavica\u003c/em\u003e is grown over 300 hectares [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Globally, a substantial level of plant death has been caused by stress factors. The production of secondary metabolites, such as sugars, sugar alcohols, and amino acids, is one of the surprisingly potent defenses that some plants possess against these circumstances. In reaction to different abiotic stressors, like temperature stress, plants gather the amino acid \"proline.\" An excess of proline may occur due to protein hydrolysis, new synthesis, reduced intake, or breakdown. Proline enhances stress tolerance by preserving osmotic balance, ensuring cell turgidity, and indirectly managing the metabolism of reactive oxygen species. Proline's relationships with various Osmo protectants and signaling compounds additionally enhance defenses against stress [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Carotenoids are elongated isoprenoid molecules with conjugated structures that fall under the hydrocarbon category, having around 1,117 recognized structures. They participate in numerous biological functions in both humans and plants. Plasmids are the organelles found in plant cells that mainly regulate the production, stability, and function of carotenoids, along with their variety. Carotenoids expand the spectrum of light absorption and serve as additional light-harvesting pigments in photosynthetic tissues. They are essential for photoprotection as well. Carotenoids function as colorants and precursors of isoprenoids in non-photosynthetic tissues. Conversely, carotenoids enhance the fundamental dermal protection against UV in human cells, contributing to skin health. All of these phytochemicals provide a certain level of protection against inflammatory diseases, cancer, and diabetes (8). A novel field in computer science known as artificial intelligence (AI) offers great potential for addressing numerous complex problems in today's world. Contemporary biological systems encounter a plethora of intricate data generated by high-throughput analysis methods and \"omic\" strategies, which, if not correctly handled, could produce misleading results. AI technologies have been successfully utilized in plant biology to detect nutrient deficiencies, recognize species, oversee plant distribution, evaluate diseases and stress levels, and administer agrochemicals in agriculture [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. AI algorithms represent a promising approach for investigating the mechanisms of how plants express stress tolerance, as they can identify and classify individual traits from extensive experimental data ([\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]). Furthermore, a developing range of studies shows that AI is quite proficient in forecasting how plants will react to stress [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Although researchers are striving to widely implement machine learning (ML) in different agricultural fields, it is still uncertain if ML can consistently predict secondary metabolites in medicinal plants, especially \u003cem\u003eD. moldavica\u003c/em\u003e L. Its application for accurately predicting the biochemical makeup of these plants has not been thoroughly explored (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Artificial neural networks (ANNs), which have shown exceptional results in various scientific fields, have not been as commonly applied to forecast important secondary metabolites like proline, carotenoids, and sugars (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e\u003cp\u003ePlant health evaluation and stress tolerance may be enhanced by the early and precise ANN-based prediction of these important biochemical components in medicinal plants. Most importantly, ANN-based predictive models in medicinal plants are more appealing and can greatly improve the efficiency of phytochemical assessments by doing away with the need for time-consuming chemical analyses in the lab, the risks that chemicals pose to people, the high expense of purchasing chemicals, and the tedious laboratory work. These developments will enable real-time cultivation strategy optimization and plant health monitoring by researchers and practitioners. This study's main goals are to: (1) use radial basis function neural networks (RBFNNs) and multilayer perceptron neural networks (MLPNNs) to apply predictive models for key and critical secondary compounds in \u003cem\u003eD. moldavica\u003c/em\u003e for the first time; (2) compare the accuracy and efficiency of RBFNN and MLPNN models for these significant key compounds; and (3) offer useful insights into the integration of data-driven approaches for sustainable medicinal plant cultivation for the first time in Iran. This research seeks to promote sustainable farming, especially for important medicinal plants such as \u003cem\u003eD. moldavica\u003c/em\u003e, while also assisting skilled, underprivileged Iranian youth in their development. Due to the elevated expense of chemicals in Iran, this study not only lowers costs and operational duration but also enables both researchers and farmers to monitor medicinal plants by incorporating easily seen morphological characteristics into predictive models. In addition, the advancement of efficient machine learning (ML) methods corresponds with the rising need for data-oriented solutions in optimizing resources, cultivating medicinal plants, and promoting sustainable practices. It also addresses concerns linked to environmental conservation and sustainable farming. Moreover, it can be integrated with the substitution of chemical drugs for herbal treatments and act as a launchpad for improving the quality and efficacy of products obtained from medicinal plants, guaranteeing their ongoing relevance in the food and pharmaceutical sectors.\u003c/p\u003e"},{"header":"Materials and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eMaterialization Experimental conditions in the greenhouse\u003c/h2\u003e \u003cp\u003eActualization Conditions for the experiment in the greenhouse The Shahid Bakeri Miandoab Higher Education Center's research farm served as the site of this investigation. In Isfahan, Iran, we bought pure seeds from Pakan Bazr Company. Prior to planting, the seeds were cleaned with distilled water and a 10% bleach solution. The seeds were planted in 4 kg plastic pots with a 1:1:1 soil, sand, and well-rotted animal manure mixture. Twenty seeds were planted in each pot at the proper spacing after the prepared soil mixture was added.The temperature and relative humidity conditions of the greenhouse were adjusted during the experiment. 30\u0026deg;C during the day and 20\u0026deg;C at night and with a relative humidity of 60 to 80%. The plant species under investigation, \u003cem\u003eDracocephalum moldavica L.\u003c/em\u003e, was identified by Abolfazl Alirezalu, a faculty member of Urmia University, and assigned herbarium code 1536 by the Herbarium of Urmia University. Four biostimulants\u0026mdash;Kadostim, Fosnutren, Humiforte, and Aminolforte-e\u0026mdash;were used. The experiments were carried out under salinity conditions with concentrations of 0, 20, 40, and 60 mM NaCl. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the chemical composition of the biostimulants used in this study [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe compounds of amino acid, organic fertilizers\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBiostimulants\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFree amino acids (mg/L)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOrganic matters (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNitrogen\u003c/p\u003e \u003cp\u003e(%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eP2O5\u003c/p\u003e \u003cp\u003e(%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eK2O\u003c/p\u003e \u003cp\u003e(%)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eKadostim\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3750\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFosnutren\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3750\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHumiforte\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3750\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAminolforte\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3750\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAmount and type of amino acids\u0026thinsp;=\u0026thinsp;Glysin 11.2%, Valine 5.1%, Proline 8.3%, Alanin 13.2%, Aspartic acid 4.4%, Arginine 8.3%, Glutamic acid 0.9%, Lysine 5.1%, Lucine 16.4%, Isolucine 4.4%, Phenylalanin 5.1%, Methionine 4.2%, Serin 3.9%, Treonine 0.3%, Histidine 0.3%, Tyrosine 1.5%, Glutamine 0.9%, Systein 0.3%, Aspargine 0.4%, and Tryptophan 0.4%.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eMeasurement of Growth Parameters\u003c/h3\u003e\n\u003cp\u003eAt the start of flowering, simple growth metrics were measured. Crown diameter (mm) is measured with a caliper, while stem length (cm) is measured with a ruler. A caliper is used to measure the internode length (in centimeters). The number of internodes was counted from the stem's base to its tip. Number of lateral stems: The total number of branches or lateral stems from the plant's base was counted. A ruler was used to measure the lateral stem's length. Leaf width (mm): The leaf's width was measured with calipers [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. A ruler is used to measure the leaf length (mm). Number of leaves: Every plant's total number of leaves was meticulously tallied.\u003c/p\u003e \u003cp\u003eRoot length (cm): The root's length was measured from the tip to the root collar after the surrounding soil had been cleaned and removed. The shoot's fresh weight was measured using an analytical balance. Dry weight of shoots: A digital scale was used to measure the samples' dry weight after they had been dried for 48 hours at 70\u0026deg;C. The Moloudzadeh et al. approach was used to determine the relative water content, or RWC [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e].\u003c/p\u003e\n\u003ch3\u003eQuantification of soluble sugars\u003c/h3\u003e\n\u003cp\u003eWith a minor adjustment, we used the Dubois et al. method to assess the soluble sugars in a few chosen plant samples [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Using a digital scale, 0.1 g of the plant sample was initially weighed in this way. In order to liberate the soluble sugars in the solution, we made sure that the plant components were thoroughly mixed before homogenizing the sample in 10 milliliters of distilled water. After that, we filtered to produce a clear liquid extract. After that, we filtered the extract once again to get rid of any unwanted particles. One by one, we then moved 1 milliliter of the filtered extract to a sterile test tube and filled it with 1 milliliter of a 5% phenol solution.\u003c/p\u003e \u003cp\u003eWe dissolved a suitable quantity of phenol in distilled water to create the phenol solution. As you are aware, when sulfuric acid is present, phenol reacts with sugars to produce a color combination that is proportionate to the sugar content. Five milliliters of concentrated sulfuric acid (H2SO4) are now carefully added to the test tube. We must proceed cautiously and slowly because this reaction is exothermic, and we must be mindful that the exothermic reaction will cause the test tube to heat up significantly. Similarly, the hydrolysis of sugar molecules and the development of a yellowish-brown hue are significantly influenced by the quantity of concentrated sulfuric acid. We now leave the mixture of sulfuric acid in the test tube for ten to fifteen minutes at room temperature. As we saw, the phenol-sulfuric acid mixture now interacts and creates a colorful complex with the dissolved sugars. We must be mindful that the incubation period is crucial since too short a time may result in a weak or irregular color, while too long may produce a change in color intensity and lead to an incorrect diagnosis. Following a thorough incubation period and the proper amount of time, the absorbance of the resultant solution is measured using a spectrophotometer set at 485 nm. As you are aware, the concentration of soluble sugars in the sample directly correlates with the color's intensity.\u003c/p\u003e \u003cp\u003eA standard glucose solution was made beforehand, and the lab technician plotted the absorbance values of known glucose concentrations to create a calibration curve that would precisely indicate the amount of soluble sugars in the necessary samples. By comparing the sample's absorbance with the calibration curve, the concentration of soluble sugars in the plant sample was precisely determined. Following that, the outcome was expressed as glucose equivalents in milligrams per gram of fresh plant weight. It should be mentioned that precise standard curve preparation by the technician, precise reagent availability, and precise and suitable incubation period all affect measurement accuracy for determining plant solution sugar. Despite its effectiveness, this strategy necessitates close attention to every step in order to minimize errors. Furthermore, the spectrophotometric tube must be clean and the measurements must be made with the appropriate level of accuracy. To guarantee accuracy, the calibration curve must also be meticulously created for every set of data [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e].\u003c/p\u003e\n\u003ch3\u003eMeasurement of carotenoids in plant leaves\u003c/h3\u003e\n\u003cp\u003eThe carotenoid content of plant leaves was measured using the method of Lichtenthaler and Wellburn (1983) with slight modifications [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. First, 0.1 g of fresh leaves were thoroughly ground with 10 ml of 80% acetone until completely homogeneous.\u003c/p\u003e \u003cp\u003eNow it is time to transfer the desired mixture to the prepared centrifuge tubes and store them in a completely dark environment at 4\u0026deg;C for 24 hours according to the procedure. Now, we centrifuged the samples after one day for 10 minutes at 4000 rpm. Then, we carefully separated the supernatant and read them according to the instructions at wavelengths of 663, 645 and 470 nm for chlorophyll a, chlorophyll b and for total carotenoids. The concentrations of chlorophyll a, chlorophyll b and carotenoids were obtained using the exact equations of the instructions [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e].\u003c/p\u003e\n\u003ch3\u003eMeasurement of Proline in plant leaves\u003c/h3\u003e\n\u003cp\u003eThe Bates method was used to calculate the proline in leaves (9). To do this, 0.2 g of leaf tissue was weighed and thoroughly ground in 3 ml of 3% sulfosalicylic acid in a porcelain mortar. For fifteen minutes, the resultant homogenate was centrifuged at 18,000 rpm. Next, two milliliters of glacial acetic acid and two milliliters of ninhydrin reagent were added. The tubes were sealed at 100\u0026deg;C and then submerged in a hot water bath for an hour. Each tube was cooled, then filled with 4 cc of toluene and vortexed for 15 seconds. The red indicator containing proline dissolved in toluene was removed and placed in a spectrophotometer at the same time as the standard samples, and the absorbance of the samples was read at a wavelength of 520 nm. The proline concentration was determined in mg/g of fresh leaf tissue.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eArtificial neural network (ANN) models\u003c/h2\u003e \u003cp\u003eArtificial neural networks are computational models made up of interconnected nodes or \"neurons\" that will simulate data processing and analysis. These neurons possess the inherent capacity to store, learn from, and interpret large sets of empirical data, thereby providing a robust framework for addressing complex real-world challenges. Key features of ANNs include their ability to efficiently process vast amounts of information, accurately map complex data relationships, tolerate noisy or incomplete data, adapt dynamically to varying inputs, generalize learned patterns across different contexts, and exhibit resilience under uncertain conditions. These attributes make ANNs an invaluable tool for predictive modeling, optimization, and performance enhancement in engineering and other domains. Their application allows for more precise solutions to intricate problems, contributing to significant reductions in both operational costs and time, and making them indispensable in solving modern, multifaceted engineering problems [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eMultilayer Perceptron Neural Network (MLPNN)\u003c/h3\u003e\n\u003cp\u003eThe MLPNN consists of three primary layers: an input layer, one or more hidden layers, and an output layer (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). These networks are composed of interconnected neurons, with each neuron characterized by a bias value, connection links, and associated weights for these links. The training process relies on input data paired with corresponding target outputs and utilizes specific learning algorithms to optimize the network. The mathematical behavior of a neuron (k) is described by equations (\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) and (\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e):\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{y}_{k}=f\\left({u}_{k}+{b}_{k}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{u}_{k}\\:=\\:\\sum\\:_{i=1}^{N}{w}_{ki}{x}_{i}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIt is important to note that in these equations, x1, x2, x3, \u0026hellip;, xn represent the input signals, while wk1, wk2, wk3, \u0026hellip;, wkn represent the weights of the neuron connections. uk describes the linear combination of the weighted inputs, bk is the bias, f is the activation function, and uk, as is well known, represents the output of the neuron.\u003c/p\u003e \u003cp\u003eMLPNNs are trained using the backpropagation algorithm, which employs an error-correction strategy. The network, generates predicted outputs based on input data and compares them to the target values to calculate the error. Weights and biases are iteratively adjusted to minimize this error. This process continues until the error falls below a predefined threshold.\u003c/p\u003e \u003cp\u003eAccording to Hashemi et al., the mean square error (MSE) is known as a performance measure for reducing errors during this optimization process [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e\n\u003ch3\u003eRadial Basis Function Neural Networks (RBFNN)\u003c/h3\u003e\n\u003cp\u003eRBFNNs, as you know, are widely used in various fields, including function approximation and pattern recognition. These networks are renowned for their simple architecture, exceptional resilience to input noise, and fast, efficient training procedures. Additionally, RBFNNs demonstrate superior generalization capabilities, enabling them to effectively handle patterns outside their training dataset. As you can see from Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, an RBFNN has three main layers, which are described below 1. Input layer, 2. Hidden layer, and 3. Output layer. The role of the input layer is to transfer data to the hidden layer, which uses radial basis functions to process the inputs, while the output layer calculates a linear combination of the responses of the hidden neurons to produce the final output. The output of an RBFNN is mathematically described by Eq.\u0026nbsp;\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{y}_{i}\\left(x\\right)=\\:\\sum\\:_{j=1}^{k}{w}_{ij}\\phi\\:\\left(‖x-{c}_{j}‖\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the formula you see, the symbol x represents the input vector, the symbol yi represents the i-th output of the network, the symbol K represents the number of neurons in the hidden layer, the symbol cj is the center associated with the j-th hidden neuron, and finally w\u003csub\u003eij\u003c/sub\u003e corresponds to the weight that connects the j-th hidden neuron to the i-th output neuron, and ||. || represents the Euclidean distance.The function φ serves as the radial basis function used by the hidden neurons, which quantifies the distance between the input vector and a designated center vector. Among the various types of radial basis functions discussed in research, the Gaussian function is the most prevalent. It is defined as:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:\\phi\\:\\:\\left(‖x-{c}_{j}‖\\right)=\\:{e}^{\\left(-{\\frac{‖x-{C}_{j}‖}{{2\\sigma\\:}_{j}^{2}}}^{2}\\right)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn this context, σ_j represents the width parameter of the j-th hidden neuron.\u003c/p\u003e \u003cp\u003eA key point in designing and training an RBF-NN is to accurately determine the centers, widths, and connection weights for the hidden neurons. The researchers proved that the number of hidden neurons required depends on the dimensionality and distribution of the input data. They also showed that, typically, reducing the dimensionality of the input data leads to a lower need for the number of hidden neurons [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eData partitioning and K-fold cross-validation\u003c/h2\u003e \u003cp\u003eCross-validation with K-fold data partitioning K-fold cross-validation was employed in this study to guarantee full representation of the data set in every iteration and to reduce the impact of random sample fluctuation. Pachouly et al. recently demonstrated that the data set is divided into subsets that do not overlap [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. The dataset is separated into non-overlapping subsets, as demonstrated by Pachouly et al. and Kamensky et al. In each cycle, we used one subset for testing and the other subsets for training. However, because this process was carried out k times, it was seen that every subset could be analyzed as the test set precisely once. Pachouly et al. shown that this approach provides the strongest evaluation of overfitting risk.\u003c/p\u003e \u003cp\u003eDespite being a widely used method for offline evaluation of machine learning algorithms, k-fold cross-validation can have problems with certain data types when samples within classes are gathered in close proximity to one another without being randomly assigned to the other class or classes. The training and test sets for time-series data, like EEG, contain examples from the same class that are highly correlated because of their temporal proximity. This is achieved by randomly splitting all samples into k divisions. This goes against the independence assumption, which is essential to k-fold cross-validation's efficacy [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. As a result, rather than identifying any actual class-related differences, the classifier may identify differences between the classes that are just connected to this temporal correlation of some data [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eWe used 5-fold cross-validation using the method of Phinzi et al [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. In this method, the data set is divided into five separate parts, four subsets of which will be selected for training and one subset as the test set. We carefully calculated the performance indicators of each iteration and also obtained the average results from all iterations to determine the overall evaluation of the model. We were able to accurately evaluate the exact performance. Recently, Ghafoorian Heidari et al., in addition to the above, considered data diversity and a reliable standard for evaluating the flexibility and conditional consistency of the model, which was fruitful [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. For computational analysis, we used MATLAB software (R2017b) in this study to develop RBF and MLP neural network models.\u003c/p\u003e \u003cp\u003eModel Performance Evaluation In the present study, we used MLP and RBF models to estimate the concentrations of three very important secondary metabolites in the medicinal plant (\u003cb\u003eD. moldavica)\u003c/b\u003e, which included the content of leaf amino acids, carotenoids and soluble sugars of the bark, and used three important and key statistical criteria: 1. Root mean square error (RMSE), 2. Mean absolute percentage error (MAPE) and finally 3. Coefficient of determination (R\u0026sup2;). These criteria are mathematically defined in equations.\u003c/p\u003e \u003cp\u003eIn the following formula (5), (6) and (7) respectively, and together they provide a general framework for examining the accuracy of the models. Specifically, the deviation between the predicted and observed values ​​(RMSE), as well as the percentage error relative to the actual observations (MAPE) and the proportion of variance in the dataset accurately explained by the model (R2) were investigated and also quantified.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:MAPE=\\:\\frac{1}{n}\\sum\\:_{i=1}^{n}\\left|\\frac{{\\left({Y}_{est}\\right)}_{i}-\\:{\\left({Y}_{meas}\\right)}_{i}}{{\\left({Y}_{meas}\\right)}_{i}}\\right|\\times\\:100\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(5)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}^{2}=1-\\:\\frac{{\\sum\\:_{i=1}^{n}\\left[{\\left({Y}_{est}\\right)}_{i}-\\:{\\left({Y}_{meas}\\right)}_{i}\\right]}^{2}}{\\sum\\:_{i=1}^{n}{\\left({Y}_{est}-\\stackrel{-}{Y}\\right)}_{i}^{2}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(6)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:RMSE=\\sqrt{\\frac{1}{n}\\:\\sum\\:_{i=1}^{n}{\\left[{\\left({Y}_{est}\\right)}_{i}-\\:{\\left({Y}_{meas}\\right)}_{i}\\right]}^{2}}\\:\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(7)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAs you can see, n represents the total number of data points in the dataset, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Y}_{est}\\)\u003c/span\u003e\u003c/span\u003eand\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{Y}_{meas}\\)\u003c/span\u003e \u003c/span\u003erepresent the predicted and actual observed concentrations, respectively, while \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Y\\)\u003c/span\u003e\u003c/span\u003e is the average of the observed values. As has been proven, the model performance is considered optimal when the MAPE and RMSE values ​​are minimized, and the coefficient of determination R\u0026sup2; reaches its maximum, which, according to Heidari et al., indicates the best fit between the predicted and observed values [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e"},{"header":"Results and Discussion","content":"\u003cp\u003eIn the present study, the levels of amino acid proline, carotenoids, and soluble sugar levels in the stem of \u003cem\u003eD. moldavica\u003c/em\u003e were investigated using two types of neural networks, MLP and RBF, for modeling. The data were obtained from a study designed to investigate the effect of applied stimuli on salinity stress with the permission of the author of the study, who is also present in this study. We selected 13 easily measured physiological and morphological traits here and used them as input variables. These 13 traits are stem length (cm), crown diameter (mm), internode length (cm), number of internodes, number of lateral stems, lateral stem length (cm), leaf width (mm), leaf length (mm), number of leaves, relative weight and root weight of stem (cm), relative weight of stem (cm), dry weight of branch (cm), dry stem length, and 3 very important traits that are very important during salt stress of plants and are measured in the laboratory by different and very difficult and expensive methods were considered as target output variables. These 3 traits include the very important amino acid proline, which is also known as the stress amino acid, carotenoids, and finally soluble sugars, which were vital biochemical indicators that we selected due to their physiological importance. The purpose of this research is to minimize the high laboratory costs, minimize the damage of chemicals and very high speed of operation, and efficiently estimate these vital traits.\u003c/p\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003eDesigning and optimizing RBF\u003c/h2\u003e \u003cp\u003eAfter data collection, the next step is to select an appropriate learning algorithm and design a neural network architecture suited to the problem at hand. The choice of learning algorithm depends on several factors, such as data size, problem type (classification, regression, etc.), and computational resources. Achieving optimal performance in the RBF model requires careful and methodical tuning of its parameters. These parameters include the selection of the transfer function, the spread value, and the method used for data normalization [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. The data are standardized in such a way that their distribution has a mean of zero and a standard deviation of one. To perform the optimization, various training functions for the RBF network were examined. Several RBF networks were trained using these functions, including the radial basis network (newrb), exact radial basis network (newrbe), generalized regression neural network (newgrnn), and probabilistic neural network (newpnn). A Among the configurations evaluated, the RBF model optimized with the newgrnn function exhibited superior predictive performance, achieving the lowest mean squared error (MSE) and the highest R\u0026sup2; value [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. To optimize the spread parameter, which plays a crucial role in determining the width of Gaussian basis functions in the RBF model and directly influences the balance between overfitting and underfitting, various values of this parameter were tested [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. The results indicated that the minimum RMSE was achieved at the optimal value of the spread, demonstrating the model's best generalization performance. This optimization was conducted by analyzing the RMSE curve as a function of the spread, where the optimal spread value was found to be 0.529, resulting in an RMSE of 0.484 (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003eDesigning and Optimizing the MLP Model\u003c/h2\u003e \u003cp\u003eIn this study, the MLP model was designed and optimized through a systematic approach for selecting the optimal number of layers and neurons. Due to the absence of a definitive method for determining the optimal number of neurons in the hidden layers, an iterative approach was employed in this study to systematically identify both the number of layers and the number of neurons per layer [ 23, 29]. Among the diverse computational approaches examined\u0026mdash;including Levenberg-Marquardt, Bayesian regularization, scaled conjugate gradient, steepest descent, elastic backpropagation, and Newton's method the Levenberg-Marquardt algorithm demonstrated superior performance and was consequently selected as the most effective learning algorithm, consistent with the results of Nait Amar et al. (2022). Additionally, the log-sigmoid activation function was selected for the hidden layer based on comparative analysis of various transfer functions [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003eEvaluation of Neural Network Models for Predicting Key Biochemical Molecules\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e offers a comprehensive evaluation of the MLP and RBF models' performance, utilizing 5-fold cross-validation to estimate carotenoid, proline, and shoot soluble sugar levels. The models were assessed based on R\u0026sup2;, RMSE, and MAPE, with calculations performed for the training set, test set, and overall dataset. This approach ensures a thorough analysis of the models' predictive ability to generalize across different data subsets.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePerformance comparison of RBFNN and MLPNN models for predicting carotenoid, proline, and shoot soluble sugar.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"13\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eModel types\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e \u003cp\u003eTrain\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c9\" namest=\"c7\"\u003e \u003cp\u003eTest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c13\" namest=\"c11\"\u003e \u003cp\u003eTotal\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMAPE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eMAP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003eMAPE\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eCarotenoid\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMLPNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.948\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.257\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.858\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.386\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e2.612\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.935\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0.299\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e2.291\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRBFNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.996\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.066\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.412\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.902\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.295\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.971\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.983\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0.148\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0.783\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eProline\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMLPNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.963\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.170\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.097\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.903\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.289\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.869\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.957\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0.199\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e1.371\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRBFNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.999\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.052\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.556\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.975\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.235\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.124\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.996\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0.115\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0.831\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eShoot soluble sugar\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMLPNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.944\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.166\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.338\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.876\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.619\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.965\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.937\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1.276\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e1.463\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRBFNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.999\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.178\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.206\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.941\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.948\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.229\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.992\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0.455\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0.411\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003eCarotenoid Prediction\u003c/h2\u003e \u003cp\u003eThe results of this study for carotenoid content in this plant showed that the RBFNN model is more suitable for superior prediction performance compared to MLPNN. It was also observed that in the RBFNN model, the entire dataset changed to an overall R\u0026sup2; of 0.983, RMSE of 0.148 and MAPE of 0.783, while it changed to an R\u0026sup2; of 0.935, RMSE of 0.299 and MAPE of 2.291 in the MLPNN model. It is worth noting that in the important traits tested, RBFNN showed higher accuracy and better performance than the MLPNN model. Therefore, it can be said that according to our results, the RBFNN model performed more robustly and better for predicting carotenoid content, and consistently showed lower prediction errors and higher accuracy measures in all evaluation criteria. This observation aligns with findings from various studies that have highlighted the efficacy of RBFNN models in capturing complex, non-linear relationships in plant biochemistry [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. Specifically, the RBFNN model's superior performance in terms of lower RMSE and MAPE values, and higher R\u0026sup2; values across all datasets, suggests its enhanced capacity for generalization and accuracy in predicting carotenoid levels under varying experimental conditions. In agreement with our results, previous research has demonstrated the advantages of RBFNN over other neural network architectures in predicting biochemical traits. For instance, Li et al. [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e] proposed a generalized residual shelf-life prediction model for post-harvest table grapes. By employing an optimized radial basis function (RBF) neural network, their model demonstrated significantly higher accuracy compared to traditional shelf life (SL) prediction methods. Guardado Yordi et al. [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e] emphasized the potential of machine learning algorithms, particularly the Random Forest model, in accurately predicting antioxidant properties based on the structural-topological features of flavonoids. Their findings highlight the effectiveness of integrating artificial intelligence methods with chemical structure analysis to enhance predictive accuracy in biochemical research, aligning with our approach to estimating secondary metabolites in medicinal plants [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. RBFNN's ability to model complex patterns in plant biochemical data can be attributed to its unique structure, which allows for effective representation of the relationships between input features and output biochemical traits. Unlike MLPNN, which uses multiple hidden layers to learn data representations, RBFNN relies on radial basis functions to map input data directly to output variables in a less computationally intensive manner. These results are in line with the research of Gonz\u0026aacute;lez-Camacho et al., who showed that the RBFNN model is particularly suitable for predicting the amount of plant metabolites that are very important and significant, as well as for nonlinear and multifaceted relationships [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e], Machine learning and deep learning, when combined with hyperspectral imaging, offer a promising solution for early disease detection and monitoring large agricultural areas with minimal labor. These technologies not only enable faster disease diagnosis but also aid in identifying gene regulatory networks and developing disease-resistant crops, revolutionizing modern plant science [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. Recently, Jurinjak Tusek et al. [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e] evaluated various modeling techniques, including linear and nonlinear regression and ANN, for predicting the physical and chemical properties of aqueous extracts from nine medicinal plants: dandelion, chamomile, lavender, lemon balm, marigold, mint, nettle, plantain, and yarrow. The chemical properties analyzed were total phenolic content and antioxidant activity, while the physical properties included total dissolved solids and extraction yield. The results showed that while regression models were useful, the ANN model outperformed others, achieving higher accuracy (R\u0026sup2; \u0026gt; 0.9) in predicting both physical and chemical properties simultaneously. These findings contribute to the growing body of literature suggesting that RBFNN models offer significant advantages for predicting biochemical compounds in medicinal and aromatic plants.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003eProline Prediction\u003c/h2\u003e \u003cp\u003eFor proline prediction, the RBFNN model showed better performance compared to the MLPNN model. In this study, the RBFNN model was shown to have an outstanding overall R\u0026sup2; of 0.996, RMSE of 0.115, and MAPE of 0.831 on the entire dataset and also significantly outperformed MLPNN which recorded an overall R\u0026sup2; of 0.957, RMSE of 0.199, and MAPE of 1.371. Finally, in the experimental data of this study, the RBFNN showed further superiority with R\u0026sup2; of 0.975, RMSE of 0.235, and MAPE of 1.124, surpassing the MLPNN performance criteria of R\u0026sup2; = 0.903, RMSE\u0026thinsp;=\u0026thinsp;0.289, and MAPE\u0026thinsp;=\u0026thinsp;1.869. Our research is consistent with the research of Zhang and Wang, who showed better performance of the RBFNN model for estimating secondary metabolites in medicinal plants than other methods [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eResearchers have shown that secondary metabolites such as proline are very important and efficient during environmental stress. Also, the application of machine learning models such as RBFNN has been promising in accurately predicting the amount of this amino acid with high accuracy. In our project, the RBFNN model was better than the MLPNN model with lower RMSE and MAPE in both the complete and experimental datasets of this amino acid, showing its potential for reliable and accurate predictions of the data. In contrast, the MLPNN model showed relatively lower accuracy. In addition, the work of Jamir and HP [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e] also showed in a project the prediction of plant secondary metabolites targeting therapeutic outcomes, such as α-glucosidase inhibition and considered the role of machine learning to be very important in the advancement of medicinal plant research. In addition, Nazarenko et al. [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e] also considered the application of machine learning in the analytical control of medicinal plant preparations and emphasized its investigation for the prediction and accurate analysis of plant compounds. These advances indicate that the integration of RBFNN with multi-source data in the future can significantly increase the predictive power of secondary metabolites in medicinal plants, including proline, carotenoids, and sugars.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003eShoot Soluble Sugar Prediction\u003c/h2\u003e \u003cp\u003eFor soluble sugar in the branch, the RBFNN model also showed significantly more accurate prediction with an overall R\u0026sup2; of 0.992, RMSE of 0.455 and MAPE of 0.411 for the complete dataset, as for the amino acid proline. The MLPNN model, however, showed slightly lower overall performance measures with R\u0026sup2; of 0.937, RMSE of 1.276 and MAPE of 1.463. In the dataset of this project, RBFNN showed R\u0026sup2; of 0.941, RMSE of 0.948, and MAPE of 1.229. While MLPNN showed R\u0026sup2; of 0.876, RMSE of 1.619 and MAPE of 1.965.\u003c/p\u003e \u003cp\u003eThis further underscores the superiority of the RBFNN model in capturing complex relationships between input features and output variables. Recent research highlights the influential role of ML in improving the modeling and optimization of secondary metabolite production in plants. Tan et al. [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e] applied RBFNN to optimize metabolite synthesis in \u003cem\u003eSpirodela polyrhiza\u003c/em\u003e, achieving accurate predictions and significant improvements. These findings demonstrate the potential of ML-driven approaches to advance secondary metabolite research and applications in plant biochemistry. Their work emphasizes how machine learning approaches can be employed to predict a variety of plant secondary metabolites, including soluble sugars, with high accuracy. The application of machine learning models such as RBFNN has also been increasingly acknowledged for its superiority in capturing the underlying relationships in complex biological data [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. This is consistent with findings from Zhang and Wang [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e] and Jamir and HP [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e], who highlighted the effectiveness of RBFNN in predicting various secondary metabolites in medicinal plants. The ability of RBFNN to model complex data and predict secondary metabolites, such as soluble sugars, amino acids, and carotenoids, reflects its growing role in advancing the field of medicinal plant research. The RBFNN model also provided the best and most accurate prediction for plant sugar content, which is very important for the timing of environmental stress and plant growth and response to stresses. Nazarenko et al. [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e] on the use of machine learning for quality control in medicinal plant preparations emphasized the importance of learning these models in ensuring the stability and reliability of plant-based products. The current results contribute to this broader trend and emphasize that machine learning can be an essential tool for sustainable production and quality control of medicinal plants and reducing the use of chemicals. Figures\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e and \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e compare the regression relationships between predicted and measured values for carotenoid, shoot proline, and shoot soluble sugar using the RBF and MLP neural network models, respectively. The RBF model (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e) demonstrates superior predictive accuracy, with R\u0026sup2; values of 0.983, 0.996, and 0.992 for carotenoid, proline, and shoot soluble sugar, respectively.\u003c/p\u003e \u003cp\u003eIn comparison, the MLP model (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e) achieves R\u0026sup2; values of 0.935, 0.957, and 0.937 for the same traits. While the MLP model also exhibits strong predictive performance, the RBF model slightly outperforms it, particularly for carotenoid and shoot soluble sugar predictions, indicating its higher overall reliability for this dataset.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section2\"\u003e \u003ch2\u003eComparative Evaluation of Neural Network Models for Predicting Carotenoid, Proline, and Shoot Soluble Sugar\u003c/h2\u003e \u003cp\u003eThis investigation compared the performance of two neural network models, MLP and RBF, in predicting carotenoid levels, shoot proline, and shoot soluble sugar concentrations. The models were evaluated using three critical metrics: RMSE, MAPE, and R\u0026sup2;, with the results presented in Figs.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e, \u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e, and \u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e, which focused specifically on the test dataset to ensure a thorough analysis of prediction accuracy.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e displays the RMSE values for both models across all measured variables. It is evident that the RBF model consistently achieved lower RMSE values compared to the MLP, suggesting it outperformed the MLP in terms of accuracy and error reduction. This consistent trend across all three variables emphasizes the RBF's superior capability to effectively capture and predict complex biochemical characteristics with higher precision.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e showcases the MAPE values for both models, where the RBF consistently outperformed the MLP model, exhibiting significantly lower error percentages across all variables. Notably, this advantage was most pronounced in the prediction of shoot soluble sugar, where the RBF achieved a substantial reduction in prediction error compared to the MLP. Furthermore, Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e presents the R\u0026sup2; values for both models, reflecting their efficacy in explaining the variance within the measured data. The RBF model demonstrated consistently higher R\u0026sup2; values, signifying a stronger alignment between its predictions and the actual values. This further underscores the RBF's capability to effectively capture the underlying relationships in the dataset. In conclusion, the comparative evaluation confirms that the RBF model outperformed the MLP in predicting carotenoid, shoot Proline, and shoot soluble sugar concentrations. This is evidenced by its superior performance in terms of lower RMSE and MAPE values and higher R\u0026sup2; scores, establishing the RBF as a more reliable and precise tool for predicting biochemical properties.\u003c/p\u003e \u003cp\u003eResearchers have shown that RBF networks are suitable for predicting biochemical traits in plants due to their ability to handle nonlinear relationships [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]. In contrast, while MLP networks can also model non-linearities, they often require more data and fine-tuning to achieve comparable accuracy, especially for tasks involving intricate biochemical interactions [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e]. This aligns with the findings in the present study, where the RBF model consistently outperformed the MLP in all three prediction scenarios.\u003c/p\u003e \u003cp\u003eAdditionally, RBF networks have been widely applied in plant science, where they have demonstrated strong predictive capabilities for estimating various physiological and biochemical traits under different environmental conditions [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. Studies have shown that RBF's inherent flexibility in adjusting to the complexity of plant biochemical responses under stress conditions (e.g., salinity, drought) enhances its accuracy in prediction [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e]. These advantages make RBF an appealing choice for applications in plant biotechnology and agronomy, where accurate prediction of biochemical traits is crucial for crop improvement and sustainability.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec20\" class=\"Section2\"\u003e \u003ch2\u003eEvaluation of Predicted and Actual Data Using the Optimized RBF Model\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows all the statistical properties including sum, mean, standard deviation, minimum and maximum values ​​for both actual and predicted data sets. It can be stated that the accuracy and consistency of the RBF model for all three variables of this study were proven and their minimum deviation was shown in the statistical parameters.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of observed and predicted values for carotenoid, proline, and shoot soluble sugar using the final RBF model.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eElement\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePhases\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eData\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSum\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eAverage\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eStandard deviation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eMinimum\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eMaximum\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"5\" rowspan=\"6\"\u003e \u003cp\u003eCarotenoid\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eTotal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eActual\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e539.407\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8.990\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.178\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e6.822\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e11.540\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePredicted\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e540.836\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e9.014\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.197\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e6.841\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e11.390\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eTrain\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eActual\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e428.075\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8.918\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.247\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e6.822\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e11.540\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePredicted\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e428.066\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8.918\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.238\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e6.841\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e11.390\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eTest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eActual\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e111.332\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e9.278\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.786\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e7.943\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e10.622\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePredicted\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e112.770\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e9.397\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.925\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e7.899\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e11.275\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"5\" rowspan=\"6\"\u003e \u003cp\u003eProline\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eTotal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eActual\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e387.041\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6.451\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.939\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e2.272\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e10.302\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePredicted\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e386.940\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6.449\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.932\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e2.301\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e10.254\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eTrain\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eActual\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e299.823\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6.246\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e2.050\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e2.272\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e10.302\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePredicted\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e299.816\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6.246\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e2.047\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e2.301\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e10.254\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eTest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eActual\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e87.218\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e7.268\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.075\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e5.704\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e9.412\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePredicted\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e87.124\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e7.260\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.041\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e5.748\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e9.077\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"5\" rowspan=\"6\"\u003e \u003cp\u003esoluble sugar\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eTotal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eActual\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3660.866\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e61.014\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e5.175\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e49.214\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e69.420\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePredicted\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3652.846\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e60.881\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e5.104\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e49.610\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e69.318\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eTrain\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eActual\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2893.552\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e60.282\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e5.327\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e49.214\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e69.420\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePredicted\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2893.414\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e60.279\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e5.313\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e49.610\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e69.318\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eTest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eActual\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e767.314\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e63.943\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e3.108\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e58.600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e69.218\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePredicted\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e759.433\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e63.286\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e3.180\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e56.312\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e69.248\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec21\" class=\"Section2\"\u003e \u003ch2\u003eCarotenoids\u003c/h2\u003e \u003cp\u003eIn this study, for the entire carotenoid pigment dataset, the predicted mean value was 9.014 and the observed mean was 8.990, with standard deviations of 1.197 and 1.178, respectively. This close alignment demonstrated the ability of the RBF model to replicate the true distribution of carotenoid concentrations, which is consistent with the consistency of predictions in the training and test subsets.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec22\" class=\"Section2\"\u003e \u003ch2\u003eProline\u003c/h2\u003e \u003cp\u003eIn this study, for the amino acid proline, the accuracy of the results, which was consistently observed in both the training and testing subsets, demonstrated the reliability of the RBF model in predicting proline levels with higher accuracy. The predicted mean (6.449) for the entire dataset was very close to the actual mean (6.451) and was almost identical, with the minimum difference observed in the standard deviations (1.932 vs. 1.939).\u003c/p\u003e \u003cdiv id=\"Sec23\" class=\"Section3\"\u003e \u003ch2\u003eShoot Soluble Sugar\u003c/h2\u003e \u003cp\u003eIn this study, the soluble sugar in the shoot also followed a similar trend as proline, with the predicted mean (60.881) being very close to the actual mean (61.014), with only minor differences in standard deviations (5.104 vs. 5.175), which can be seen in both the training and experimental subsets, emphasizing the robustness of the model in accurately predicting the soluble sugar concentration in the shoot.\u003c/p\u003e \u003cp\u003eTherefore, the close alignment between the predicted values ​​in this study and the actual values, as well as the minimal deviation in statistical criteria, emphasizes the effectiveness of the optimized RBF model in capturing important biochemical traits in this valuable medicinal plant.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis project evaluated two neural network models, MLP and RBF, for predicting the levels of key biochemically important metabolites in \u003cem\u003eD. moldavica\u003c/em\u003e, especially under plant stress. The results were carefully examined and observed, and consistently for all three secondary metabolites, the performance of the RBF model was superior, as demonstrated by its lower RMSE and MAPE values ​​and higher R\u0026sup2; scores across all datasets. This superiority reflects the RBF model\u0026rsquo;s capability to capture complex, non-linear interactions between morphological and biochemical variables, making it a robust and reliable predictive tool. The practical implications of these results are significant, particularly in precision agriculture and plant biochemical research. In this study, we were able to accurately model the relationships between easily measurable growth parameters and key biochemical characteristics (carotenoids, proline, and soluble sugar levels). We concluded that the best model was the RBF model, which can be an efficient tool for strategic management of medicinal plants, reducing chemical consumption, reducing environmental pollution, reducing costs, and ultimately developing sustainable agriculture. It can also predict the performance of medicinal plants efficiently and be an effective step towards the sustainable development of agricultural sciences, pharmaceuticals, and the food and medical industries.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eClinical trial number\u003c/strong\u003e: not applicable\u003cstrong\u003e.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u0026apos; Contributions\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSh Najafian:\u003c/strong\u003e Writing \u0026ndash; original draft, Visualization, Investigation, Data curation. \u003cstrong\u003eShahnaz Fathi and Roya\u003c/strong\u003e \u003cstrong\u003eMovlodzadeh:\u003c/strong\u003e Resources, Methodology. \u003cstrong\u003eSajad Heidari:\u003c/strong\u003e Conceptualization, Formal analysis, Methodology, Software, original draft, Editing. \u003cstrong\u003e\u0026nbsp;Shahnaz Fathi\u003c/strong\u003e review \u0026amp; editing, Project administration, funding acquisition.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics declarations\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eEthical approval and consent to participate.\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompliance with ethical standards\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe presented manuscript represents the honest research work of the authors.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research received no external funding.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data used in this study is openly available, and the data used is available upon request from the corresponding authors SH.N.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Details\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e1. Department of Medicinal and aromatic Plants, Shahid Bakeri High Education Center of Miandoab, Urmia University, Urmia, Iran\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e2. Department of Biosystems Engineering, Shiraz University, Shiraz, Iran\u003c/p\u003e\n\u003cp\u003e3. Department of Natural Resources and Environment Engineering, School of Agriculture, Shiraz University, Shiraz, IR Iran.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eXu, Y., Liang, D., Wang, G. T., Wen, J. \u0026amp; Wang, R. J. Nutritional and functional properties of wild food medicine plants from the coastal region of South China. \u003cem\u003eJ. Evid-Based Integr. Med.\u003c/em\u003e \u003cb\u003e25\u003c/b\u003e, 1\u0026ndash;13 (2020).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAćimović, M., Stanković, J., Cvetković, M., Todosijević, M. \u0026amp; Rat, M. The chemical composition of the essential oil of \u003cem\u003eDracocephalum moldavica\u003c/em\u003e L. from Vojvodina Province (Serbia). \u003cem\u003eBiol. Nyssana\u003c/em\u003e. \u003cb\u003e10\u003c/b\u003e, 23\u0026ndash;28 (2019).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAćimović, M. et al. \u003cem\u003eDracocephalum moldavica\u003c/em\u003e: Cultivation, chemical composition and biological activity. \u003cem\u003eJ. Agron. Technol. Eng. Manag\u003c/em\u003e. \u003cb\u003e2\u003c/b\u003e, 153\u0026ndash;167 (2019).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKeikhaie, R. K., Jahantigh, H. R., Bagheri, R. \u0026amp; Kehkhaie, R. A. The effect of the ethanol extract of \u003cem\u003eDracocephalum moldavica\u003c/em\u003e (Badrashbu) against strains of antibiotic-resistant \u003cem\u003eEscherichia coli\u003c/em\u003e and \u003cem\u003eKlebsiella pneumoniae\u003c/em\u003e. \u003cem\u003eInt. J. Infect.\u003c/em\u003e \u003cb\u003e5\u003c/b\u003e, 65295 (2018).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFallah, S., Rostaei, M., Lorigooini, Z. \u0026amp; Sukri, A. A. Chemical compositions of essential oil and antioxidant activity of dragonhead (\u003cem\u003eDracocephalum moldavica\u003c/em\u003e) in sole crop and dragonhead-soybean (Glycine max) intercropping system under organic manure and chemical fertilizers. \u003cem\u003eInd. Crops Prod.\u003c/em\u003e \u003cb\u003e115\u003c/b\u003e, 158\u0026ndash;165 (2018).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMafakheri, S. \u0026amp; Asghari, B. Optimization of growth and biochemical production in \u003cem\u003eDracocephalum moldavica\u003c/em\u003e L. through biochar and salicylic acid application in a pot experiment. \u003cem\u003eJ. Med. Plants By-Prod\u003c/em\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRaza, A. et al. Assessment of proline function in higher plants under extreme temperatures. \u003cem\u003ePlant. Biol.\u003c/em\u003e ; 380\u0026ndash;395. (2023).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSwapnil, P., Meena, M., Singh, S. K., Dhuldhaj, U. P. \u0026amp; Harish, Marwal, A. Vital roles of carotenoids in plants and humans to deteriorate stress with its structure, biosynthesis, metabolic engineering and functional aspects. \u003cem\u003eCurr. Plant. Biol.\u003c/em\u003e \u003cb\u003e26\u003c/b\u003e, 100203 (2021).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSoltis, P. S., Nelson, G., Zare, A. \u0026amp; Meineke, E. K. Plants meet machines: prospects in machine learning for plant biology. \u003cem\u003eAppl. Plant. Sci.\u003c/em\u003e \u003cb\u003e8\u003c/b\u003e, e11371 (2020).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFenu, G. \u0026amp; Malloci, F. M. Forecasting plant and crop disease: an explorative study on current algorithms. \u003cem\u003eBig Data Cogn. Comput.\u003c/em\u003e \u003cb\u003e5\u003c/b\u003e (2), 1\u0026ndash;16 (2021).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRico-Ch\u0026aacute;vez, A. K. et al. Machine learning for plant stress modeling: A perspective towards hormesis management. \u003cem\u003ePlants\u003c/em\u003e \u003cb\u003e11\u003c/b\u003e, 970 (2022).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMoloudzadeh, R., Fathi, S., Yari, F., Najafian, S. \u0026amp; Seyedi, A. The potential of coated iron nanoparticles for modulating negative effects of salinity stress in Ajowan. \u003cem\u003eHortic. Environ. Biotechnol.\u003c/em\u003e \u003cb\u003e65\u003c/b\u003e, 747\u0026ndash;760 (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDubois, M., Gilles, K. A., Hamilton, J. K., Rebers, P. A. \u0026amp; Smith, F. Colorimetric method for the determination of sugars and related substances. \u003cem\u003eAnal. Chem.\u003c/em\u003e \u003cb\u003e28\u003c/b\u003e (3), 350\u0026ndash;356 (1956).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLichtenthaler, H. K. \u0026amp; Wellburn, A. R. Determinations of total carotenoids and chlorophylls a and b of leaf extracts in different solvents. \u003cem\u003eBiochem. Soc. Trans.\u003c/em\u003e \u003cb\u003e11\u003c/b\u003e, 591\u0026ndash;592 (1983).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGholamzadeh, E., Ghaemi, A., Shokri, A. \u0026amp; Heydari, B. Investigation of boiler energy consumption in the gas refinery units using RSM ANN and Aspen HYSYS. \u003cem\u003eHeliyon\u003c/em\u003e ; e41450. (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGhritlahre, H. K. \u0026amp; Prasad, R. K. Exergetic performance prediction of solar air heater using MLP, GRNN and RBF models of artificial neural network technique. \u003cem\u003eJ. Environ. Manag\u003c/em\u003e. \u003cb\u003e223\u003c/b\u003e, 566\u0026ndash;575 (2018).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHashemi Fath, A., Madanifar, F. \u0026amp; Abbasi, M. Implementation of multilayer perceptron (MLP) and radial basis function (RBF) neural networks to predict solution gas-oil ratio of crude oil systems. Petroleum. ; 6:80\u0026ndash;91. (2020).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePachouly, J., Ahirrao, S., Kotecha, K., Selvachandran, G. \u0026amp; Abraham, A. A systematic literature review on software defect prediction using artificial intelligence: Datasets, data validation methods, approaches, and tools. \u003cem\u003eEng. Appl. Artif. Intell.\u003c/em\u003e \u003cb\u003e111\u003c/b\u003e, 104773 (2022).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRoberts, D. R. et al. Cross-validation strategies for data with temporal, spatial, hierarchical, or phylogenetic structure. \u003cem\u003eEcography\u003c/em\u003e \u003cb\u003e40\u003c/b\u003e, 913\u0026ndash;929 (2017).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWhite, J. \u0026amp; Power, S. D. K-Fold cross-validation can significantly overestimate true classification accuracy in common EEG-based passive BCI experimental designs: An empirical investigation. \u003cem\u003eSensors\u003c/em\u003e \u003cb\u003e23\u003c/b\u003e (13), 6077 (2023).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePhinzi, K., Abriha, D. \u0026amp; Szab\u0026oacute;, S. Classification efficacy using k-fold cross-validation and bootstrapping resampling techniques on the example of mapping complex gully systems. \u003cem\u003eRemote Sens.\u003c/em\u003e \u003cb\u003e13\u003c/b\u003e, 2980 (2021).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGhafoorian Heidari, S. I., Safehian, M., Moodi, F. \u0026amp; Shadroo, S. Predictive modeling of the long-term effects of combined chemical admixtures on concrete compressive strength using machine learning algorithms. \u003cem\u003eCase Stud. Chem. Environ. Eng.\u003c/em\u003e \u003cb\u003e10\u003c/b\u003e, 101008 (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHeidari, S., Mirzaee-Ghaleh, E., Rabbani, H. \u0026amp; Vesali, F. Development of an Android app for estimating the water quality parameters in fish pond. \u003cem\u003eEnviron. Sci. Pollut Res.\u003c/em\u003e \u003cb\u003e28\u003c/b\u003e, 34501\u0026ndash;34510 (2021).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYan, Z. et al. A multi-energy load prediction of a building using the multi-layer perceptron neural network method with different optimization algorithms. \u003cem\u003eEnergy Explor. Exploit.\u003c/em\u003e \u003cb\u003e41\u003c/b\u003e, 273\u0026ndash;305 (2023).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eShoaib, M. et al. A. stochastic numerical analysis based on hybrid NAR-RBFs networks nonlinear SITR model for novel COVID-19 dynamics. \u003cem\u003eComput. Methods Programs Biomed.\u003c/em\u003e \u003cb\u003e202\u003c/b\u003e, 105973 (2021).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNoroozian, M., Ghaemi, A. \u0026amp; Heidari, Z. Potential of artificial intelligence and response surface methodology to predict CO₂ capture by KOH-modified activated alumina. \u003cem\u003eCase Stud. Chem. Environ. Eng.\u003c/em\u003e \u003cb\u003e8\u003c/b\u003e, 100442 (2023).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMessikh, N., Bougdah, N., Bousba, S. \u0026amp; Djazi, F. Modeling the adsorption of chlorobenzene on modified bentonite using an artificial neural network. \u003cem\u003eCurr. Res. Green. Sustain. Chem.\u003c/em\u003e \u003cb\u003e3\u003c/b\u003e, 100026 (2020).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZheng, L., Jiang, L., Zheng, K. \u0026amp; Yu, M. Estimation of explosion limits of gas mixture using a single spread GRNN. 2nd Int Conf Artif Intell Manag Sci Electron Commer (AIMSEC). \u003cem\u003eIEEE\u003c/em\u003e ; 1113\u0026ndash;1115. (2021).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKumar, M., Mehta, U. \u0026amp; Cirrincione, G. Enhancing neural network classification using fractional-order activation functions. \u003cem\u003eAI Open.\u003c/em\u003e \u003cb\u003e5\u003c/b\u003e, 10\u0026ndash;22 (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNait Amar, M., Jahanbani Ghahfarokhi, A. \u0026amp; Shang Wui Ng, C. Predicting wax deposition using robust machine learning techniques. \u003cem\u003ePetroleum\u003c/em\u003e \u003cb\u003e8\u003c/b\u003e, 167\u0026ndash;173 (2022).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGonz\u0026aacute;lez-Camacho, J. M. et al. Genome-enabled prediction of genetic values using radial basis function neural networks. \u003cem\u003eTheor. Appl. Genet.\u003c/em\u003e \u003cb\u003e125\u003c/b\u003e, 759\u0026ndash;771 (2012).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYunan, I., Yassin, I. M., Syed Adnan, S. F. \u0026amp; Fazalul Rahiman, M. H. Identification of essential oil extraction system using Radial Basis Function (RBF) neural network. \u003cem\u003eProc. IEEE 8th Int. Colloq. Signal. Process. Appl.\u003c/em\u003e ; 6194779. (2012).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLi, Y., Chu, X., Fu, Z., Feng, J. \u0026amp; Mu, W. Shelf-life prediction model of postharvest table grape using optimized radial basis function (RBF) neural network. \u003cem\u003eBr. Food J.\u003c/em\u003e ; (2019).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGuardado Yordi, E. et al. Artificial intelligence applied to flavonoid data in food matrices. Foods. 2019; 8(11):573. (2019).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGonz\u0026aacute;lez-Camacho, J. M. et al. Genome-enabled prediction of genetic values using radial basis function neural networks. \u003cem\u003eTheor. Appl. Genet.\u003c/em\u003e \u003cb\u003e125\u003c/b\u003e, 759\u0026ndash;771 (2012).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDas, S., Pattanayak, S. \u0026amp; Behera, P. R. Application of machine learning: a recent advancement in plant diseases detection. J Plant Prot Res. 2022; 62:122\u0026ndash;135. (2022).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJurinjak Tušek, A. et al. Application of multivariate regression and artificial neural network modelling for prediction of physical and chemical properties of medicinal plants aqueous extracts. \u003cem\u003eJ. Appl. Res. Med. Aromat. Plants\u003c/em\u003e. \u003cb\u003e16\u003c/b\u003e, 100229 (2022).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang, Y. \u0026amp; Wang, Y. Recent trends of machine learning applied to multi-source data of medicinal plants. \u003cem\u003eJ. Pharm. Anal.\u003c/em\u003e \u003cb\u003e13\u003c/b\u003e (5), 675\u0026ndash;689 (2023).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJamir, L. HP P. Employing Machine Learning Models to Predict Potential α-Glucosidase Inhibitory Plant Secondary Metabolites Targeting Type-2 Diabetes and Their In Vitro Evaluation. J Chem Inf Model.2024; 64(2):221\u0026ndash;233. (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNazarenko, D. V., Rodin, I. A. \u0026amp; Shpigun, O. A. The use of machine learning in the analytical control of the preparations of medicinal plants. Inorg Mater.2019; 55(6):619\u0026ndash;624. (2019).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTan, W. H., Tong, C. Y., Chua, M. X. \u0026amp; Derek, C. J. C. Modelling and optimizing secondary metabolites production in \u003cem\u003eSpirodela polyrhiza\u003c/em\u003e using machine learning. J Clean Prod. 2024; 478:143986. (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhao, Y., Zheng, S., Pei, J. \u0026amp; Yang, X. Multiple discriminants pr eserving support subspace RBFNNs with graph similarity learning. \u003cem\u003eInf. Sci.\u003c/em\u003e \u003cb\u003e619\u003c/b\u003e, 421\u0026ndash;438 (2023).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLee, W. J. \u0026amp; Lee, E. H. Runoff prediction based on the discharge of pump stations in an urban stream using a modified multi-layer perceptron combined with meta-heuristic optimization. \u003cem\u003eWater\u003c/em\u003e \u003cb\u003e14\u003c/b\u003e (1), 99 (2022).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZarbakhsh, S. \u0026amp; Shahsavar, A. R. Artificial neural network-based model to predict the effect of γ-aminobutyric acid on salinity and drought-responsive morphological traits in pomegranate. \u003cem\u003eSci. Rep.\u003c/em\u003e \u003cb\u003e12\u003c/b\u003e, 16662 (2022).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Biochemical, Cleaner production, Ecological sustainability, Secondary metabolites, Dracocephalum moldavica, Machine learning, Proline accumulation","lastPublishedDoi":"10.21203/rs.3.rs-6105806/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6105806/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eBackground\u003c/h2\u003e \u003cp\u003eThe aim of this project was to predict, for the first time, the levels of important secondary metabolites during stress in medicinal plants, including carotenoids, amino acid proline, and soluble sugars, without the use of expensive and dangerous chemicals for humans. For this project, artificial neural network models including radial basis function (RBF) and multilayer perceptron (MLP) were used.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e \u003cp\u003eThe effectiveness of the models was generally evaluated on experimental datasets through a 5-fold cross-validation method to obtain reliable performance measures. Among the performances were R-squared (R2), mean point error (MAPE), and root mean square error (RMSE). In our study, the RBF model was functionally and optimally better than the MLP model with R2 values ​​of 0.90, 0.975, and 0.941 for soluble sugar, carotenoid pigment, and the highly important amino acid proline, respectively. The associated RMSEs were 0.29, 0.235, and 0.98, while the associated MAPEs were 1.971, 1.124, and 1. 229.The research results demonstrated the RBF model's exceptional ability to effectively represent nonlinear relationships between input variables and biological characteristics. While the MLP model generated plausible forecasts, it was ineffective at estimating the levels of soluble sugars, carotenoids, and proline in the plant. We concluded that the best model was the RBF model, which can be an efficient tool for strategic management of medicinal plants, reducing chemical consumption, reducing environmental pollution, reducing costs, and ultimately developing sustainable agriculture. It can also predict the performance of medicinal plants efficiently and be an effective step towards the sustainable development of agricultural sciences, pharmaceuticals, and the food and medical industries.\u003c/p\u003e\u003ch2\u003eConclusions\u003c/h2\u003e \u003cp\u003eThis study emphasizes the value of using computer modeling in agriculture, which is essential for evaluating important aspects of this field, especially with regard to different plant species and environmental conditions.\u003c/p\u003e","manuscriptTitle":"Application of machine learning models to predict secondary metabolites for the first time in the valuable medicinal plant (Dracocephalum moldavica L.)","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-03-17 08:51:11","doi":"10.21203/rs.3.rs-6105806/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"325346f5-f858-4ab2-bd75-a7f356429271","owner":[],"postedDate":"March 17th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":45615538,"name":"Biological sciences/Biochemistry"},{"id":45615539,"name":"Biological sciences/Biotechnology"}],"tags":[],"updatedAt":"2025-11-17T06:39:27+00:00","versionOfRecord":[],"versionCreatedAt":"2025-03-17 08:51:11","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6105806","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6105806","identity":"rs-6105806","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}