Predicting Photovoltaic-Thermal Panel Output in Urban Contexts Using Machine Learning Methods

Predicting Photovoltaic-Thermal Panel Output in Urban Contexts Using Machine Learning Methods | 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 comment Predicting Photovoltaic-Thermal Panel Output in Urban Contexts Using Machine Learning Methods Alireza Nazeri, Ali Taheri, Zahra Sadat Zomorodian This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5588685/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 In recent years, the use of data-driven methods for predicting photovoltaic (PV) panel electricity generation has grown significantly, with most studies relying on databases of actual PV panel performance. This study introduces a comprehensive methodology for predicting the performance of photovoltaic-thermal (PVT) panels, specifically focusing on electricity generation, hot water production, and carbon reduction. By leveraging artificial intelligence (AI) and machine learning (ML) methods, particularly Artificial Neural Networks (ANN) and Random Forest (RF), this research differentiates itself from prior studies by integrating predictive models for both electrical and thermal outputs. Additionally, the study examines the effect of different installation patterns on PVT panel output. A total of 1,575 different installation configurations were modeled across three urban districts in Tehran, and the results were used to train the two ML algorithms, which were then compared using Pearson correlation coefficient (R²), Root-mean-square deviation (RMSE), and Mean Absolute Error (MAE) metrics. The RF algorithm demonstrated superior performance, achieving an R² accuracy of 0.91 and shorter learning time. Finally, a framework is proposed based on the findings and simulation steps for predicting electricity generation, hot water production, and carbon reduction of PVT systems. Photovoltaic-Thermal (PVT) Systems Machine Learning in Renewable Energy Energy Efficiency Optimization AI-Driven Energy Prediction Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 1 Introduction Solar energy technologies, particularly photovoltaic (PV) and photovoltaic-thermal (PVT) systems, play a crucial role in transitioning towards sustainable energy solutions globally. PV systems convert sunlight into electricity, offering a renewable and clean energy source that reduces reliance on fossil fuels and mitigates greenhouse gas emissions [1]. Recent advancements in PV technology have significantly improved efficiency and reduced costs, making solar PV increasingly competitive and accessible across different regions. Additionally, PVT systems combine PV electricity generation with thermal energy capture, maximizing energy yield and enhancing overall system efficiency [2]. Studies highlight the environmental benefits of solar energy adoption, including reduced air pollution and enhanced energy security through decentralized energy production [2]. These technologies not only contribute to sustainable development goals but also support economic growth by creating jobs and fostering innovation in the renewable energy sector. Optimizing the installation patterns of photovoltaic (PV) systems on building envelopes is crucial for maximizing energy generation efficiency and system performance. Recent research highlights the significance of factors such as installation orientation, tilt angle optimization, and mitigation of shading effects. Studies emphasize that selecting the appropriate tilt angle based on geographical location can significantly enhance solar capture by minimizing angle-related losses [3]. Furthermore, strategies to minimize shading effects are essential for maintaining consistent energy production throughout the day [4]. Integrating PV systems into building facades or roofs not only optimizes energy generation but also contributes to sustainable urban development, aligning architectural and aesthetic considerations with renewable energy goals [5]. Recent advancements in artificial intelligence (AI) and machine learning (ML) have significantly advanced the optimization and prediction capabilities of photovoltaic-thermal (PVT) systems in urban environments. AI and machine learning (ML) have proven highly effective in predicting the performance of photovoltaic-thermal (PVT) systems. ML models outperform traditional methods in accurately forecasting both electricity and thermal outputs under varying conditions [6]. These advanced techniques enable better optimization and adaptation of PVT systems, particularly in dynamic urban environments, highlighting their growing relevance in enhancing renewable energy technologies. 2 Aim and Scope This study leverages artificial intelligence and machine learning methods, specifically Artificial Neural Networks (ANN) and Random Forest, to predict both electricity and hot water production from PVT systems in an urban context. Differentiating itself from prior research, which often focuses on single parameters or exclusively on PV electricity generation, this study integrates predictive models for both electrical and thermal outputs. Additionally, it considers the environmental impacts of PVT system deployment in urban areas, offering a comprehensive analysis that enhances our understanding of their performance and sustainability. By employing advanced AI and ML techniques, validated using metrics such as Root Mean Square Error (RMSE), R-squared (R²), and Mean Absolute Error (MAE), this research provides novel insights into optimizing PVT systems for energy efficiency and urban sustainability. This study aims to devise a model for PVT panel installation, leveraging artificial building blocks of varying heights to assess energy consumption and solar energy absorption potentials. The primary objective is to develop a software framework integrating database production and artificial intelligence. This software comprises two key components: predicting model performance and suggesting optimal models to users, streamlining decision-making processes and facilitating non-expert utilization. This paper is structured as follows: The initial section provides a review of the existing literature. Following that, the methodology employed in this study is outlined. Later, the development and optimization of the machine learning (ML) models are detailed. The subsequent section presents and discusses the results, accuracy of the models, and the proposed framework. Finally, the paper concludes with insights and recommendations for future research directions. 3 Literature review To identify studies that align with the research objectives, a combination of relevant keywords such as ‘machine learning,’ ‘artificial intelligence,’ ‘photovoltaic thermal,’ ‘energy production,’ and ‘urban context’ was used to conduct searches on Google Scholar and ScienceDirect. A total of 50 papers were initially collected. Studies published before 2019 were excluded from the review. The literature review included studies ranging from module-level to urban-level analyses, as well as those utilizing empirical or pre-simulated training datasets. Both single and ensemble machine learning methods were considered. Given the limited research on PVT modules, studies focusing on PV systems were also included. The final selection comprised 22 relevant papers, which are presented in Table 1 . The majority of the reviewed studies focused on the installation of PV and PVT panels on the rooftops of buildings, with power plants being the second most frequently examined context. Following this, research on individual PV modules was also prevalent. Additionally, a notable study by Suanpang and Jamjuntr explored the application of these technologies at the microgrid level [ 7 ] . In the literature, the most frequently considered variables were climate indicators, such as ambient temperature and solar irradiance. Additionally, panel and module temperatures were commonly analyzed. However, relatively few studies addressed factors such as cell types and building orientations. Normally most of the output results were based on the power generation of the PV and PVT modules which were installed. Very few studies were focused on the efficiency of the systems and on one of the works done by Rojek et al. reviewed CO2 reduction was also reviewed which was similar to purpose of this study that intended to do likewise. Most of the studies primarily focused on the power generation of installed PV and PVT modules. However, only a few studies concentrated on the efficiency of these systems. Notably, one study by Rojek et al. also examined CO2 reduction [ 8 ], aligning with the objective of this research, which similarly aims to assess environmental impact. The machine learning algorithms used for predictions can be categorized into two main groups: single models and ensemble models. Single models predict target values using a single ML model, whereas ensemble models make predictions based on the combined accuracy of multiple models. In this literature, ANN (Artificial Neural Networks), RF (Random Forest), and NN (Neural Networks) were the most frequently utilized algorithms, appearing 8, 5, and 4 times, respectively. The validation strategies employed in the majority of the studies involved splitting the dataset into training and testing sets, with varying proportions allocated to each. However, one study conducted by Mohana et al. utilized a more robust approach by implementing k-fold cross-validation as their validation strategy [ 9 ] . The most used accuracy metrics were RMSE (Root Mean Square Error), R² (R-squared), MAE (Mean Absolute Error), and MSE (Mean Squared Error). Additionally, some studies employed other metrics that were less frequently used, as detailed in Table 1 . Data were primarily obtained through measurements of the outputs from photovoltaic (PV) and photovoltaic-thermal (PVT) systems installed in their respective contexts. Additionally, a significant portion of the data was sourced from the datasets introduced in various studies. Notably, Shin et al. employed PVsyst and Solar Pro to simulate building-integrated photovoltaic (BIPV) systems in their research [ 10 ] . Table 1 Related research Reference Context Output Indicators Algorithm of ML Module type Modeling software Validation strategy Accuracy metric Best accuracy Data Type Variable [ 10 ] Building power generation ANN BIPV PVsyst, Solar Pro Train/test RMSE, MAE, R 2 0.92 (R 2 ) Simulated, Measured Solar irradiance [ 11 ] Building power generation GE, DE BIPV Train/test Erel 1.55 Measured Ambient Temperature, solar irradiation, relative outdoor humidity, wind speed [ 12 ] Building power generation ANN PVT Train/test MSE, NMSE, MAE, R 2 0.11 (NMSE) Measured solar irradiance, ambient temperature [ 13 ] Building total active power NN PV Train/test RMSE, MAE, Standard deviation 0.7 RMSE Measured Ambient Temperature, Horizontal irradiation [ 9 ] Building Power generation LASSO, RF, LR, PR, XGBoost, SVM, NN PV k-fold cross-validation MSE 0.9 Measured External temperature, wind speed, Humidity [ 14 ] Building electrical and thermal efficiencies ANN PVT Train/test MAE 0.0078% Measured solar irradiance and the module temperature [ 15 ] Urban power generation LR PV Train/test MAPE 1.40% Measured Ambient temperature, Relative Humidity [ 16 ] Building power generation MFFNN, CFNN, RBFNN, ENN PV Matlab Train/test R, MAE, RMSE 0.0021 (RMSE) Dataset Ambient temperature, relative Humidity, solar radiation, wind speed [ 7 ] Microgrid power generation LGBM, KNN PV Train/test R 2 , RMSE, MAE 0.84 R 2 Measured Solar irradiance, ambient temperature [ 17 ] Building electrical efficiency ANFIS, ANN, LS-SVR PVT Train/test AARD, MSE, R 2 0.95 R 2 Dataset radiation intensity, Coolant material [ 18 ] Module power generation SVM, GPR PV Train/test RMSE, MAE, R 2 0.98 R 2 Dataset Panel temperature, ambient temperature, relative humidity, [ 19 ] Module power generation NN PV Train/test MSE 0.01 Measured Radiation, Ambient temperature, Humidity, Wind speed, Evaporation [ 20 ] Building power generation KNR, LASSO, SVR, RF, ETR, GBR, XGBoost, ANN PV Train/test MAE, RMSE 0.60 (RMSE) Dataset Radiation, Ambient temperature, Humidity, Wind speed, Evaporation, Rooftop dimension [ 21 ] Module electrical efficiency MLP, RF, SVR PVT Train/test RMSE, R 2 0.76 (R 2 ) Measured mass flow rate, solar radiation, ambient temperature, wind speed, fluid inlet temperature, PVT surface area, pipe inner diameter [ 22 ] power plant power generation ELM, GA, SDA PV Train/test R 2 , MAE, nRMSE 0.59 (R 2 ) Dataset daily maximal, minimal and averaged temperature, daily averaged global horizontal radiation, daily averaged diffusive horizontal radiation [ 8 ] Building Power generation, CO2 reduction ANN PV Train/test RMSE 0.01 Dataset air temperature, wind speed, cloudiness, Current power direction [ 23 ] Module power generation DNN PVT Train/test MSE 3.34E-08 Measured Cell type [ 24 ] Building power generation RF, NN, SVM, LR PV Train/test RMSE, MAPE 1.76 (RMSE) Measured weather and solar generation data [ 25 ] power plant power generation MR, SVMR, GR PV Train/test MSE, MAE, R 2 0.88 (R 2 ) Measured solar radiation, ambient temperature, relative humidity [ 26 ] Building power generation ANN, DT, QSVM BIPV Train/test RMSE, MSE, R 2 , MAPE, MAE 0.88 (R 2 ) Measured Building orientations [ 27 ] power plant power generation LSTM, MLP PV Train/test MAE, MAPE, RMSE, R 2 0.77 (R 2 ) Dataset weather and solar generation data [ 28 ]time horizons power plant power generation ANN, XGBoost, RF, DT, KNN, LASSO, LR, RR PV Train/test RMSE, MAE, R 2 0.84 (R 2 ) Dataset ambient temperature, module temperature, irradiation 4 Methodology The study followed a systematic procedure: First, a dataset was generated using simulation-based software. Second, machine learning (ML) algorithms were applied to analyze this dataset and develop a predictive model. Subsequently, a new set of variables, not present in the original dataset, was introduced to assess the model’s performance with novel input data. This phase involved an iterative trial-and-error process to optimize the performance of the ML algorithms. Finally, a sensitivity analysis was performed to identify which features most significantly affected the calculated metrics. (Fig. 1 ) 4.1 context To create the dataset, the initial step involved selecting a context. Tehran, Iran, was chosen for this purpose, with three of its regions selected for analysis. Tehran is divided into 22 distinct urban areas (Fig. 2 ), each with unique characteristics. The selected regions are pivotal to this research, with the selection criterion focusing on variations in elevation and population density across the city. Zone 1 represents areas with tall building structures exceeding 27 meters in height. Zone 2 exemplifies regions with moderate building heights and a more dispersed urban layout. Finally, Region 16 is characterized by low-rise buildings and a densely packed urban fabric. These diverse zones were chosen to provide a comprehensive sample across different building heights and urban densities within Tehran. 4.2 Dataset creation To standardize calculations and ensure comparability of results, a specific type of thermal photovoltaic panel has been utilized in this study. The chosen model is the PV-MLE275HD2, manufactured by Mitsubishi. This panel is equipped with monocrystalline silicon photovoltaic cells, boasting 120 cells per panel. With a power output of 275 watts and a maximum voltage supply of 32.1 volts, these cells demonstrate an efficiency rating of 16.6%. Variable parameters crucial to panel installation have been identified, each encompassing a range of values and incremental steps. The cumulative variations within these parameters define the problem's potential states. Table 2 outlines the parameters investigated in this research, culminating in a total of 1575 calculated states. Table 2 Selected parameters and their values Variable Parameters Range of Variation Step of Variation Number of Cases Descriptions Horizontal Angle of panel −20° to 20° 10° 5 Vertical angle of panel 15° above and below the latitude 5° 7 Distance Between Panels 1 to 5 meters 1 meter 5 Panel elevation from roof 10 to 30 centimeters 10 centimeters Urban Block 3 In three different regions To initiate the three-dimensionalization of urban maps, GIS files encompassing the 22 regions were obtained from the Tehran Municipality. These files, comprising smaller units measuring 1 km by 1 km, collectively delineate an area of 1 square kilometer. Subsequently, utilizing the ArcGIS software, a shapefile file was generated for the designated area. This step is essential to advance to subsequent stages of the process. The shapefile format serves as a straightforward and indirect method for storing geometric and geographic feature information. In next step for solar radiation analysis, the Ladybug plugin within the Grasshopper software was utilized. This plugin, powered by the Energy Plus engine, was employed to perform calculations. The solar radiation analysis algorithm was designed using Tehran's epw file, providing essential meteorological data. Following, using the ladybug tools, pages with an average annual radiation exceeding 1500-kilowatt hours per square meter were identified and compiled into a list. This threshold is derived from the findings of [ 29 ]. Then the focus shifts to the installation of thermal photovoltaic panels on surfaces identified as optimal for radiation reception in previous stages. To facilitate this process, an algorithm was developed within the Grasshopper environment. To establish the boundaries of the panels, the sunshade surfaces were initially segmented at one-meter intervals. Subsequently, considering desired angles (as variables) and trigonometric principles, the width range of each panel (1 meter wide) was determined. The length of the panel was set to the maximum size, corresponding to the length of the sunshade surface. Additionally, distances between panels were determined, ranging from 1 to 4 meters. These values represent a crucial parameter (panel-to-panel distances) aimed at assessing shading effects. To ensure flexibility in panel installation angles, an algorithm was devised to allow vertical adjustment of the installed panels. Subsequently, the horizontal orientation and rotation of the panels are established to optimize their exposure to sunlight. Another crucial parameter to consider is the distance of the panels from the installation surface. This distance directly impacts cooling and, consequently, the efficiency of the system. It is modeled accordingly to account for its influence on system performance. In the probability generation phase, tailored algorithms were crafted for each desired parameter, effectively encompassing their respective steps and intervals. The subsequent step involves comprehensive testing of these parameters in conjunction. All 1575 states will be evaluated, and the optimal states will be identified as outcomes. The Colibri plugin is employed for this purpose. By iteratively considering all states within each parameter and multiplying them together, Colibri determines the total number of states for the problem. It subsequently generates the desired outputs—thermal and electrical—repeatedly to facilitate thorough analysis and decision-making. Upon specifying the desired parameters and installing the panels, the thermal and electrical outputs of each panel are calculated using Ladybug software plugins. Additionally, environmental outputs are generated to provide a comprehensive assessment of the system's performance and sustainability. For environmental assessment, carbon emissions are considered from various sources. The burning of each cubic meter of gas releases carbon into the environment, and the hot water output from the panels allows estimation of gas consumption and consequently carbon emissions on an annual basis. Furthermore, the production of electricity in power plants generates carbon emissions per kilowatt-hour. Additionally, the production of each thermal photovoltaic panel introduces carbon emissions into the cycle. By determining the number of panels utilized, the total carbon emissions associated with panel production can be calculated. In the subsequent step, considering that electricity production in power plants is correlated with carbon emissions, the amount of electricity generated by the panels is multiplied by the carbon emissions per kilowatt-hour produced by a power plant. This calculation, combined with the carbon emissions from panel production, characterizes the annual carbon emissions from the system. Figure 4 illustrates the steps of crating database. 4.3 ML algorithm development Following the simulation, 1575 distinct scenarios were generated based on the considered variables, and the results were quantified across six indicators spanning various domains. In this phase, the collected data is formatted and curated to serve as input for training machine learning algorithms. In this research, the employed machine learning algorithms encompass supervised learning and regression analysis. Specifically, two distinct algorithms, namely neural network (ANN) and random forest (RF), were utilized at this stage. Each algorithm is characterized by its unique set of parameters, also known as hyperparameters. Initially, a range was assigned to each hyperparameter, and through optimization, the highest achievable accuracy for estimating indicators was attained. Table 3 Type of algorithms and hyperparameters Type of algorithm hyperparameter Number of Scenarios ANN Number of Hidden Layers 1,2,3 Number of Neurons per Layer 1 to 200 in steps of 10 Activation Function RELU RF Number of Decision Trees 1 to 500 Max_depth 1 to 10 and None To enhance the learning process on the training data model, the introduced parameters were normalized using the method, ensuring that the range of all parameters fell between 0 and 1. This normalization method is instrumental in improving both the speed and accuracy of learning. The relationship utilized for normalization is as follows: $$\:{x}^{{\prime\:}}=\frac{x-\text{m}\text{i}\text{n}\left(x\right)}{\text{max}\left(x\right)-\text{m}\text{i}\text{n}\left(x\right)}$$ To prevent overfitting, a test set comprising 20% of the data not utilized in the processing or validation steps is created. The model is optimized using the remaining 80% of the data, with validation performed on the test set. This enables checking for signs of overfitting. By employing this method, the distribution of test sets remains consistent, reducing the likelihood of bias in the evaluation process. At this stage, the learning data is segmented by randomly dividing it into approximately 90% for model training and 10% for model evaluation. This division ensures that the model is trained on most of the data while retaining a smaller subset for evaluation to assess its performance accurately. 4.4 Accuracy measurement Accuracy measurement indices are vital for evaluating the performance and training of machine learning models. These indices compare the predicted values with the values obtained in the simulation. Common accuracy measurement indices include root mean square error (RMSE), percentage error (PE), recognition coefficient index (R 2 ), and mean square error (MSE) [ 30 ]. In this research, three error measurement indicators, RMSE, R 2 , and MAE are utilized. The calculation formulas for each are as follows: Root Mean Square Error (RMSE): $$\:RMSE=\:\sqrt{\frac{1}{N}\:\sum\:_{i=1}^{N}{\left({\widehat{y}}_{i}-\:{y}_{i}\right)}^{2}}$$ Recognition Coefficient Index (R 2 ): $$\:{R}^{2}=1-\:\frac{\sum\:_{i=1}^{N}{\left({\widehat{y}}_{i}-\:{y}_{i}\right)}^{2}}{\sum\:_{i=1}^{N}{\left({y}_{i}-\:{\stackrel{-}{y}}_{i}\right)}^{2}}$$ Mean Absolute Error (MAE): $$\:MAE=\:\frac{\sum\:\left|{y}_{i}-\:{\widehat{y}}_{i}\right|}{n}$$ 4.5 Sensitivity analysis in statistics involves comprehending the interrelationships among variables within a dataset and understanding how these relationships are influenced by other variables and to what extent. By closely examining the data and considering the correlations between variables, it can be inferred that the data changes linearly. Consequently, correlation calculation methods tailored for linear data with consistent performance are applicable. The most prevalent correlation calculation methods in this domain are the Pearson and Spearman methods [ 31 ]. In this research, the Pearson method was employed to analyze the sensitivity of the available data. Pearson correlation coefficient: $$\:r=\:\frac{\sum\:\left({x}_{i}-\:\stackrel{-}{x}\right)\left({y}_{i}-\:\stackrel{-}{y}\right)}{\sqrt{\sum\:{\left({x}_{i}-\:\stackrel{-}{x}\right)}^{2}\sum\:{\left({y}_{i}-\:\stackrel{-}{y}\right)}^{2}}}$$ 5 Results In the subsequent analysis, the characteristics of the output data for each considered indicator, encompassing both energy and environmental metrics, have been investigated. 5.1 Electricity production The highest numerical amount of electricity production was recorded in region 16, while the lowest was observed in region 1. In terms of average annual electricity production, panels in region 16 outperformed those in region 2 by approximately 38% and exceeded the production in region 1 by about 52%. A comparison of the results across these three regions reveals that shading in different urban areas has a significant impact on the performance of photovoltaic systems. Regions with lower buildings and less shading demonstrate higher electricity production compared to areas with taller buildings. 5.2 Hot water production Region 2 recorded the highest numerical hot water production, while Region 1 exhibited the lowest. In terms of average annual hot water production, the performance of panels in region 16 surpasses that of Region 2 by approximately 36% and exceeds that of Region 1 by about 50%. These results suggest that shading in different urban areas significantly affects the performance of thermal photovoltaic systems in hot water production. Specifically, regions with lower buildings and less shading demonstrate higher hot water production compared to areas with taller buildings. Furthermore, in regions characterized by more uniform building heights, such as Region 16, hot water production results are relatively consistent. In contrast, regions with varied building heights show significant differences in hot water production, underscoring the impact of building height variability on system performance. 5.3 Carbon reduction On average, the highest amount of carbon reduction occurred in region 16, primarily attributed to its higher production of hot water and electricity compared to the other two regions. Conversely, Region 1 exhibited the lowest average carbon reduction rate. Numerically, the highest amount of carbon reduction was observed in region 2, while the lowest was in region 1. Region 16 achieved a 56% higher carbon reduction compared to region 2, and approximately 90% higher compared to region 1. 5.4 Selecting optimal ML algorithm The optimization and validation of learning models should be conducted separately for each of the three investigated areas, using two machine learning algorithms, and for all target indicators. This process would require 30 iterations (3 areas × 2 algorithms × 5 indicators). Given that hyperparameter optimization is time-consuming, to save time, the two learning algorithms were evaluated only for one region (Region 1). Table 4 compares the two learning models based on the data from region 1, across various indicators and using the optimal hyperparameters. Table 4 Specifications of Machine Learning Model Hyperparameters Algorithm Target indicator Optimal Hyperparameter Random Forest n_estimators and max_depth Hot water none, 45 Electricity none, 100 Number of panels none, 45 CO2 reduction none, 100 ANN hidden-layer-sizes Hot water (100,200) Electricity (250,250) Number of panels (100,200) CO2 reduction (100,200,200) 5.5 Validation of learning models At this stage, each model was trained and validated using the optimal hyperparameters for region 1. The accuracy evaluation metrics for each target indicator are presented in Table 5 . Additionally, the time required for model training, as well as the target indicators for each model, have been compared. Table 5 Performance of Machine Learning Models Based on Data from Region 1 Algorithm Target indicator Learning Time (s) Validation RMSE MAE R-square Test Validation Test Validation Test Validation Random Forest Hot water 0.08 41643.7 2500.2 3229.2 576.04 0.99 0.99 Electricity 0.07 2098.4 9.473 137.6 3.5 0.99 0.99 Number of panels 0.05 0 0 0 0 1 1 CO2 reduction 0.1 8100.81 627.38 731.09 231.98 0.99 0.99 ANN Hot water 63.26 75972.91 41369.06 5771884562 1711399191 0.99 0.99 Electricity 25.64 32675.6 34486.9 30534.08 32395.7 0.93 0.91 Number of panels 37.6 51.6 26 20.03 17.4 0.99 0.99 CO2 reduction 50.28 14301.5 7901.5 6709.2 5916.8 0.99 0.99 Based on the comparison between the neural network and random forest models using the R 2 recognition coefficient index and the time required for learning, it's evident that the random forest model slightly outperforms the neural network model in terms of R 2 . Additionally, the random forest model demonstrates significantly better performance in terms of learning time compared to the neural network model. Therefore, based on these findings, the Random Forest algorithm is chosen to proceed further. At this stage, each of the models has been trained and validated with optimal hyperparameters for region 2. Each of the accuracy evaluation indicators for each of the target indicators is displayed in Table 6 . Also, the time required to learn the model has been measured in each target index. The duration of learning among the indicators varied from 0.05 to 0.09, and the recognition coefficient index among the target indicators was at least 0.99. Table 6 Performance of Machine Learning Models Based on Data from Region 2 Algorithm Target indicator Learning Time (s) Validation RMSE MAE R-square Test Validation Test Validation Test Validation Random Forest Hot water 0.06 403.85 1056.83 181.1 369.3 0.99 0.99 Electricity 0.05 31.3 20.9 16.1 8.7 0.99 0.99 Number of panels 0.08 0 0 0 0 1 1 CO2 reduction 0.09 218.92 263.41 131.79 131.41 0.99 0.99 At this stage, each of the models has been trained and validated with optimal hyperparameters for region 16. Each of the accuracy evaluation indicators for each of the target indicators is displayed in Table 7 . Also, the time required to learn the model has been measured in each target index. The duration of learning among the indicators was different from 0.05 to 0.95 and also the recognition coefficient index was at least 0.99 among the target indicators. Table 7 Performance of Machine Learning Models Based on Data from Region 16 Algorithm Target indicator Learning Time (s) Validation RMSE MAE R-square Test Validation Test Validation Test Validation Random Forest Hot water 0.09 752.53 1663.24 363.66 597.99 0.99 0.99 Electricity 0.07 38.27 23.31 17.94 4.5 0.99 0.99 Number of panels 0.05 0 0 0 0 1 1 CO2 reduction 0.06 345.43 425.25 219.88 238.9 0.99 0.99 5.6 Machine learning results The results of the simulation and the values predicted by the Random Forest algorithm for each of the target indicators for each region have been compared and are presented in Fig. 11 5.7 Sensitivity Analysis The correlation values between different data are visually represented in Fig. 12 , allowing for a clear understanding of the relationships between the variables. Each numerical value of the coefficients is clearly displayed, providing valuable insights into the strength and direction of the correlations observed in the data. According to Fig. 12 , the correlation values shed light on the factors influencing various aspects of the study: Hot Water Production: The most significant factor impacting hot water production is the distance between panels, with a coefficient of -0.75. This indicates that decreasing the distance between panels (increasing panel density) leads to higher hot water production. The density and height of buildings in the investigated area (coefficient: 0.42) also play a notable role. Additionally, the vertical angle of the panels (coefficient: 0.074) contributes to hot water production, while the horizontal angle and distance of panels from the ceiling have lesser impacts. Electricity Production: The investigated area (coefficient: 0.96) is the most influential factor in electricity production, followed by the vertical angle of the panels (coefficient: 0.093). Other factors, such as the horizontal angle, distance of panels from the ceiling, and distance between panels, also contribute to electricity production, albeit to a lesser extent. Number of Panels: The distance between panels has the highest impact on the number of panels, with a coefficient of -0.78, indicating that increasing panel density reduces the number of panels required. The investigated area (coefficient: 0.43) is the next significant factor, followed by the vertical angle of the panels. The horizontal angle and distance of panels from the ceiling have minimal effects on the number of panels. Amount of Carbon reduction: The distance between panels (coefficient: -0.75) has the greatest impact on carbon reduction, with higher panel density resulting in lower carbon reduction. The investigated area (coefficient: 0.48). Additionally, the vertical angle of the panels influences carbon reduction, while the horizontal angle and distance from the ceiling have minimal effects. 6 Discussion This paper examines the parameters involved in installing a photovoltaic-thermal (PVT) system on buildings within an urban context. Additionally, it introduces a machine learning (ML) algorithm, selected from Artificial Neural Networks (ANN) and Random Forests (RF), based on the best accuracy. The literature review and accuracy metrics used in this study demonstrate the feasibility of ML methods for predicting the power generation and hot water production of PVT panels throughout the year in an urban environment. The accuracy of the ML algorithms, measured by the R² metric, ranged from 0.99 to 1 for the ANN algorithm, and from 0.91 to 1 for the RF algorithm, with the highest accuracy achieved in predicting electricity generation. Consequently, the RF algorithm was selected as the most accurate model for this context. Unlike many similar studies in this field, the dataset used to train and validate the ML algorithm was generated using the methods and software introduced earlier. The data was produced on a yearly basis and covered three different regions in Tehran, Iran, to account for various urban conditions. It is worth noting that while many studies in literature use climatic indicators as variables, this paper focuses on the installation conditions of the panels. This study has designed a framework using ML algorithms to predict electricity and hot water generation, as well as CO₂ reduction, from PVT panels. The results can be utilized to develop a data-driven framework that determines the most accurate and reliable prediction model for each target variable. The proposed algorithmic framework is presented in four steps: Defining the urban area by importing a GIS file or selecting a similar urban context from a database. Identifying suitable areas for installing PVT panels on buildings. Selecting the properties of the installed panels. Obtaining results for electricity and hot water generation, the number and area of panels, and CO₂ reduction using these panels. This proposed framework is illustrated in Fig.13 The present study is constrained by a defined set of design parameters with specific ranges as input features. For a more comprehensive framework, it is necessary to consider all possible input parameters and value ranges to increase the generalizability of the models and include more complex options, such as different PVT modules and the consideration of façades for panel installation. Additionally, this study was limited to calculations in three regions within a single city. To develop a more widely applicable framework, broader studies covering multiple cities and varying weather conditions are needed to generate more diverse training datasets. Future research should also explore and compare novel ML approaches, such as deep learning, to evaluate their prediction accuracy. 7 Conclusion Two ML algorithm were examined in this study and according to the results, both machine learning (ML) methods can effectively predict the power generation and CO 2 reduction of PVT panels in urban context, achieving R² values of up to 0.91, when using the Random Forest (RF) model. This approach could establish a framework capable of replacing traditional simulation-based methods, enabling the calculation of key metrics without the need for time-consuming computer simulations. However, the effectiveness of this approach hinges on a cost-benefit analysis that considers the ratio between the required input training data and the number of predictions needed. Since generating the training data still relies on conducting comprehensive computer simulations or real-world measurements, this method is more practical when a full parametric analysis of all combinations of design variables is available. The findings of this study have the potential to inform the development of a tool for early design stage analyses, eliminating the need for time-intensive simulations in existing platforms and programs. Abbreviations AARD absolute average relative deviation AI Artificial inteligence ANFIS adaptive neuro-fuzzy inference systems ANN Artificial Neural Network. BIPV Building Integrated Photovoltaic CFNN Cascade Feed-forward Neural Network DE Differential Evolution DNN deep neural network DT decision tree ELM extreme learning machine ENN Elman neural network ETR extra tree regressor GA genetic algorithm GBR gradient boosting regressor GE Grammatical Evolution GPR Gaussian process regression GR Gaussian regression KNN K nearest neighbors KNR k-neighbors regressor LASSO least absolute shrinkage and selection operator LGBM Light gradient boosting machine LR linear regression LS-SVR Least Squares Support Vector Regression LSTM Long Short-Term Memory MAPE Mean absolute percentage error MFFNN Multilayer Feed-Forward Neural Network ML Machine learning MLP multilayer perceptron MR multivariate regression MSE Mean Squared Error NMSE Normalized Mean Squared Error NN Neural Networks nRMSE normalized root mean square error PR polynomial regression PV Photovoltaic PVT Photovoltaic thermal QSVM quadratic support vector machine RBFNN Radial Basis Function Neural Network RELU Rectified Linear Unit RF random forest RMSE Root-mean-square deviation RR Ridge Regression SDA similar day analysis SVM support vector machine SVMR support vector machine regression SVR support vector regression XGBoost extreme gradient boosting Statements and Declarations Funding The authors declare that no funds, grants, or other support were received during the preparation of this manuscript. Competing Interests The authors have no relevant financial or non-financial interests to disclose. Author contributions Alireza Nazeri: Modeling and simulation, Machine learning model, data collection and analysis, Writing original draft. Ali Taheri: Modeling and simulation, Machine learning model, data collection and analysis Zahra Sadat Zomorodian: Methodology, Reviewing, Supervision. References M. Zhing, Y. L. Bai, T. Zhao, and M. Wang, “Energy harvesting properties of a flapping foil with blow aspirators: A numerical investigation,” Energy Reports , vol. 8, pp. 1803–1815, Nov. 2022, doi: 10.1016/j.egyr.2022.01.003. E. Ghirardi, G. Brumana, G. Franchini, and A. Perdichizzi, “The optimal share of PV and CSP for highly renewable power systems in the GCC region,” Renew Energy , vol. 179, pp. 1990–2003, 2021, doi: https://doi.org/10.1016/j.renene.2021.08.005. J. Jing, Y. Zhou, L. Wang, Y. Liu, and D. Wang, “The spatial distribution of China’s solar energy resources and the optimum tilt angle and power generation potential of PV systems,” Energy Convers Manag , vol. 283, p. 116912, 2023, doi: https://doi.org/10.1016/j.enconman.2023.116912. Z. Wang, J. Liu, Y. Zhang, H. Yuan, R. Zhang, and R. S. Srinivasan, “Practical issues in implementing machine-learning models for building energy efficiency: Moving beyond obstacles,” Renewable and Sustainable Energy Reviews , vol. 143, p. 110929, 2021, doi: https://doi.org/10.1016/j.rser.2021.110929. W. Chiang, I. Permana, F. Wang, H. Chen, and M. Erdenebayar, “Experimental investigation for an innovative hybrid photovoltaic/Thermal (PV/T) solar system,” Energy Reports , vol. 8, pp. 910–918, Nov. 2022, doi: 10.1016/j.egyr.2022.10.264. A. Dev, R. Kumar, and R. P. Saini, “Experimental evaluation of performance of a hybrid solar photovoltaic (PV/T) panel integrated with effective cooling solutions with water base nanofluids and phase change materials,” Energy Sources, Part A: Recovery, Utilization, and Environmental Effects , vol. 44, no. 3, pp. 7287–7302, Sep. 2022, doi: 10.1080/15567036.2022.2107732. P. Suanpang and P. Jamjuntr, “Machine Learning Models for Solar Power Generation Forecasting in Microgrid Application Implications for Smart Cities,” Sustainability , vol. 16, no. 14, p. 6087, Jul. 2024, doi: 10.3390/su16146087. I. Rojek, D. Mikołajewski, A. Mroziński, and M. Macko, “Machine Learning- and Artificial Intelligence-Derived Prediction for Home Smart Energy Systems with PV Installation and Battery Energy Storage,” Energies (Basel) , vol. 16, no. 18, Sep. 2023, doi: 10.3390/en16186613. M. Mohana, A. S. Saidi, S. Alelyani, M. J. Alshayeb, S. Basha, and A. E. Anqi, “Small-scale solar photovoltaic power prediction for residential load in saudi arabia using machine learning,” Energies (Basel) , vol. 14, no. 20, Oct. 2021, doi: 10.3390/en14206759. W. G. Shin, J. Y. Shin, H. M. Hwang, C. H. Park, and S. W. Ko, “Power Generation Prediction of Building-Integrated Photovoltaic System with Colored Modules Using Machine Learning,” Energies (Basel) , vol. 15, no. 7, Apr. 2022, doi: 10.3390/en15072589. L. Serrano-Luján, C. Toledo, J. M. Colmenar, J. Abad, and A. Urbina, “Accurate thermal prediction model for building-integrated photovoltaics systems using guided artificial intelligence algorithms,” Appl Energy , vol. 315, Jun. 2022, doi: 10.1016/j.apenergy.2022.119015. J. H. Yousif and H. A. Kazem, “Prediction and evaluation of photovoltaic-thermal energy systems production using artificial neural network and experimental dataset,” Case Studies in Thermal Engineering , vol. 27, Oct. 2021, doi: 10.1016/j.csite.2021.101297. M. H. Sulaiman, M. S. Jadin, Z. Mustaffa, H. Daniyal, and M. N. Mohd Azlan, “Short-term forecasting of rooftop retrofitted photovoltaic power generation using machine learning,” Journal of Building Engineering , vol. 94, Oct. 2024, doi: 10.1016/j.jobe.2024.109948. Y. Chaibi, M. Malvoni, T. El Rhafiki, T. Kousksou, and Y. Zeraouli, “Artificial neural-network based model to forecast the electrical and thermal efficiencies of PVT air collector systems,” Clean Eng Technol , vol. 4, Oct. 2021, doi: 10.1016/j.clet.2021.100132. A. Patel et al. , “A Practical Approach for Predicting Power in a Small-Scale Off-Grid Photovoltaic System using Machine Learning Algorithms,” International Journal of Photoenergy , vol. 2022, 2022, doi: 10.1155/2022/9194537. Y. Kassem and A. A. Othman, “Selection of most relevant input parameters for predicting photovoltaic output power using machine learning and quadratic models,” Model Earth Syst Environ , vol. 8, no. 4, pp. 4661–4686, Nov. 2022, doi: 10.1007/s40808-022-01413-7. Y. Cao, E. Kamrani, S. Mirzaei, A. Khandakar, and B. Vaferi, “Electrical efficiency of the photovoltaic/thermal collectors cooled by nanofluids: Machine learning simulation and optimization by evolutionary algorithm,” Energy Reports , vol. 8, pp. 24–36, Nov. 2022, doi: 10.1016/j.egyr.2021.11.252. B. Zazoum, “Solar photovoltaic power prediction using different machine learning methods,” Energy Reports , vol. 8, pp. 19–25, Apr. 2022, doi: 10.1016/j.egyr.2021.11.183. S. Zhang, J. Wang, H. Liu, J. Tong, and Z. Sun, “Prediction of energy photovoltaic power generation based on artificial intelligence algorithm,” Neural Comput Appl , vol. 33, no. 3, pp. 821–835, Feb. 2021, doi: 10.1007/s00521-020-05249-z. V. H. S. Pham and H. D. Tran, “Research on applying machine learning models to predict the electricity generation capacity of rooftop solar energy systems on buildings,” Asian Journal of Civil Engineering , vol. 24, no. 8, pp. 3413–3423, Dec. 2023, doi: 10.1007/s42107-023-00722-1. H. Gharaee, M. Erfanimatin, and A. M. Bahman, “Machine learning development to predict the electrical efficiency of photovoltaic-thermal (PVT) collector systems,” Energy Convers Manag , vol. 315, Sep. 2024, doi: 10.1016/j.enconman.2024.118808. Y. Zhou, N. Zhou, L. Gong, and M. Jiang, “Prediction of photovoltaic power output based on similar day analysis, genetic algorithm and extreme learning machine,” Energy , vol. 204, Aug. 2020, doi: 10.1016/j.energy.2020.117894. H. Alghamdi, C. Maduabuchi, A. Albaker, A. Almalaq, T. Alsuwian, and I. Alatawi, “Machine Learning Performance Prediction of a Solar Photovoltaic-Thermoelectric System with Various Crystalline Silicon Cell Types,” Int J Energy Res , vol. 2023, 2023, doi: 10.1155/2023/1990593. C. Scott, M. Ahsan, and A. Albarbar, “Machine learning for forecasting a photovoltaic (PV) generation system,” Energy , vol. 278, Sep. 2023, doi: 10.1016/j.energy.2023.127807. A. K. Tripathi et al. , “Advancing solar PV panel power prediction: A comparative machine learning approach in fluctuating environmental conditions,” Case Studies in Thermal Engineering , vol. 59, Jul. 2024, doi: 10.1016/j.csite.2024.104459. R. Kabilan et al. , “Short-Term Power Prediction of Building Integrated Photovoltaic (BIPV) System Based on Machine Learning Algorithms,” International Journal of Photoenergy , vol. 2021, 2021, doi: 10.1155/2021/5582418. M. Elsaraiti and A. Merabet, “Solar Power Forecasting Using Deep Learning Techniques,” IEEE Access , vol. 10, pp. 31692–31698, 2022, doi: 10.1109/ACCESS.2022.3160484. S. T. Asiedu, F. K. A. Nyarko, S. Boahen, F. B. Effah, and B. A. Asaaga, “Machine learning forecasting of solar PV production using single and hybrid models over different time horizons,” Heliyon , vol. 10, no. 7, Apr. 2024, doi: 10.1016/j.heliyon.2024.e28898. E. Biyik et al. , “A key review of building integrated photovoltaic (BIPV) systems,” Engineering Science and Technology, an International Journal , vol. 20, no. 3, pp. 833–858, 2017, doi: 10.1016/j.jestch.2017.01.009. C. J. Willmott and K. Matsuura, “Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance,” Clim Res , vol. 30, no. 1, pp. 79–82, 2005, [Online]. Available: https://www.int-res.com/abstracts/cr/v30/n1/p79-82/ J. E. Gonçalves, T. van Hooff, and D. Saelens, “Understanding the behaviour of naturally-ventilated BIPV modules: A sensitivity analysis,” Renew Energy , vol. 161, pp. 133–148, 2020, doi: https://doi.org/10.1016/j.renene.2020.06.086. Additional Declarations No competing interests reported. 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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-5588685","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"comment","associatedPublications":[],"authors":[{"id":389078501,"identity":"9517b5f4-85bc-465c-858d-66494211451d","order_by":0,"name":"Alireza 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the hot water production for training data in different regions\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-5588685/v1/e76e494656b26a7d451d5f7c.png"},{"id":71237300,"identity":"eba165b1-d085-4684-839b-5c41c4ecbad7","added_by":"auto","created_at":"2024-12-12 12:09:08","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":18922,"visible":true,"origin":"","legend":"\u003cp\u003eBox plot of the simulation results of the hot water production for test data in different regions\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-5588685/v1/8cf9ed0f722bc259dafccc95.png"},{"id":71237290,"identity":"70735ffc-7747-4f92-8aaf-461278702e74","added_by":"auto","created_at":"2024-12-12 12:09:08","extension":"png","order_by":9,"title":"Figure 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12:09:07","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":180048,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of Simulation and Predicted Results in Region 1,2,16\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-5588685/v1/a01f86cc535d12742b0188ac.png"},{"id":71237586,"identity":"13e80ebc-c0ba-4e2e-b62b-a9a5923d0ec3","added_by":"auto","created_at":"2024-12-12 12:17:07","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":100740,"visible":true,"origin":"","legend":"\u003cp\u003eOverall sensitivity analysis\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-5588685/v1/40464398c49465ced9b7d730.png"},{"id":71237303,"identity":"d7f99126-4b71-4cd4-94b0-b65bdf616c2f","added_by":"auto","created_at":"2024-12-12 12:09:08","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":155194,"visible":true,"origin":"","legend":"\u003cp\u003eProposed framework for evaluation of PVT panels in urban context\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-5588685/v1/733b739ed91df9204349c4c8.png"},{"id":71238526,"identity":"57be6fd7-f835-498a-9967-82282fb8493f","added_by":"auto","created_at":"2024-12-12 12:25:13","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1586071,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5588685/v1/58ef17c7-98db-443d-9677-7c531250a098.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Predicting Photovoltaic-Thermal Panel Output in Urban Contexts Using Machine Learning Methods","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eSolar energy technologies, particularly photovoltaic (PV) and photovoltaic-thermal (PVT) systems, play a crucial role in transitioning towards sustainable energy solutions globally. PV systems convert sunlight into electricity, offering a renewable and clean energy source that reduces reliance on fossil fuels and mitigates greenhouse gas emissions [1]. Recent advancements in PV technology have significantly improved efficiency and reduced costs, making solar PV increasingly competitive and accessible across different regions. Additionally, PVT systems combine PV electricity generation with thermal energy capture, maximizing energy yield and enhancing overall system efficiency [2]. Studies highlight the environmental benefits of solar energy adoption, including reduced air pollution and enhanced energy security through decentralized energy production [2]. These technologies not only contribute to sustainable development goals but also support economic growth by creating jobs and fostering innovation in the renewable energy sector.\u003c/p\u003e\n\u003cp\u003eOptimizing the installation patterns of photovoltaic (PV) systems on building envelopes is crucial for maximizing energy generation efficiency and system performance. Recent research highlights the significance of factors such as installation orientation, tilt angle optimization, and mitigation of shading effects. Studies emphasize that selecting the appropriate tilt angle based on geographical location can significantly enhance solar capture by minimizing angle-related losses [3]. Furthermore, strategies to minimize shading effects are essential for maintaining consistent energy production throughout the day [4]. Integrating PV systems into building facades or roofs not only optimizes energy generation but also contributes to sustainable urban development, aligning architectural and aesthetic considerations with renewable energy goals [5].\u003c/p\u003e\n\u003cp\u003eRecent advancements in artificial intelligence (AI) and machine learning (ML) have significantly advanced the optimization and prediction capabilities of photovoltaic-thermal (PVT) systems in urban environments. \u0026nbsp;AI and machine learning (ML) have proven highly effective in predicting the performance of photovoltaic-thermal (PVT) systems. ML models outperform traditional methods in accurately forecasting both electricity and thermal outputs under varying conditions [6]. These advanced techniques enable better optimization and adaptation of PVT systems, particularly in dynamic urban environments, highlighting their growing relevance in enhancing renewable energy technologies.\u003c/p\u003e"},{"header":"2 Aim and Scope","content":"\u003cp\u003eThis study leverages artificial intelligence and machine learning methods, specifically Artificial Neural Networks (ANN) and Random Forest, to predict both electricity and hot water production from PVT systems in an urban context. Differentiating itself from prior research, which often focuses on single parameters or exclusively on PV electricity generation, this study integrates predictive models for both electrical and thermal outputs. Additionally, it considers the environmental impacts of PVT system deployment in urban areas, offering a comprehensive analysis that enhances our understanding of their performance and sustainability. By employing advanced AI and ML techniques, validated using metrics such as Root Mean Square Error (RMSE), R-squared (R\u0026sup2;), and Mean Absolute Error (MAE), this research provides novel insights into optimizing PVT systems for energy efficiency and urban sustainability.\u003c/p\u003e \u003cp\u003eThis study aims to devise a model for PVT panel installation, leveraging artificial building blocks of varying heights to assess energy consumption and solar energy absorption potentials. The primary objective is to develop a software framework integrating database production and artificial intelligence. This software comprises two key components: predicting model performance and suggesting optimal models to users, streamlining decision-making processes and facilitating non-expert utilization.\u003c/p\u003e \u003cp\u003eThis paper is structured as follows: The initial section provides a review of the existing literature. Following that, the methodology employed in this study is outlined. Later, the development and optimization of the machine learning (ML) models are detailed. The subsequent section presents and discusses the results, accuracy of the models, and the proposed framework. Finally, the paper concludes with insights and recommendations for future research directions.\u003c/p\u003e"},{"header":"3 Literature review","content":"\u003cp\u003eTo identify studies that align with the research objectives, a combination of relevant keywords such as \u0026lsquo;machine learning,\u0026rsquo; \u0026lsquo;artificial intelligence,\u0026rsquo; \u0026lsquo;photovoltaic thermal,\u0026rsquo; \u0026lsquo;energy production,\u0026rsquo; and \u0026lsquo;urban context\u0026rsquo; was used to conduct searches on Google Scholar and ScienceDirect.\u003c/p\u003e \u003cp\u003eA total of 50 papers were initially collected. Studies published before 2019 were excluded from the review. The literature review included studies ranging from module-level to urban-level analyses, as well as those utilizing empirical or pre-simulated training datasets. Both single and ensemble machine learning methods were considered. Given the limited research on PVT modules, studies focusing on PV systems were also included. The final selection comprised 22 relevant papers, which are presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThe majority of the reviewed studies focused on the installation of PV and PVT panels on the rooftops of buildings, with power plants being the second most frequently examined context. Following this, research on individual PV modules was also prevalent. Additionally, a notable study by Suanpang and Jamjuntr explored the application of these technologies at the microgrid level [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] .\u003c/p\u003e \u003cp\u003eIn the literature, the most frequently considered variables were climate indicators, such as ambient temperature and solar irradiance. Additionally, panel and module temperatures were commonly analyzed. However, relatively few studies addressed factors such as cell types and building orientations.\u003c/p\u003e \u003cp\u003eNormally most of the output results were based on the power generation of the PV and PVT modules which were installed. Very few studies were focused on the efficiency of the systems and on one of the works done by Rojek et al. reviewed CO2 reduction was also reviewed which was similar to purpose of this study that intended to do likewise.\u003c/p\u003e \u003cp\u003eMost of the studies primarily focused on the power generation of installed PV and PVT modules. However, only a few studies concentrated on the efficiency of these systems. Notably, one study by\u003c/p\u003e \u003cp\u003eRojek et al. also examined CO2 reduction [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], aligning with the objective of this research, which similarly aims to assess environmental impact.\u003c/p\u003e \u003cp\u003eThe machine learning algorithms used for predictions can be categorized into two main groups: single models and ensemble models. Single models predict target values using a single ML model, whereas ensemble models make predictions based on the combined accuracy of multiple models. In this literature, ANN (Artificial Neural Networks), RF (Random Forest), and NN (Neural Networks) were the most frequently utilized algorithms, appearing 8, 5, and 4 times, respectively.\u003c/p\u003e \u003cp\u003eThe validation strategies employed in the majority of the studies involved splitting the dataset into training and testing sets, with varying proportions allocated to each. However, one study conducted by Mohana et al. utilized a more robust approach by implementing k-fold cross-validation as their validation strategy [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] .\u003c/p\u003e \u003cp\u003eThe most used accuracy metrics were RMSE (Root Mean Square Error), R\u0026sup2; (R-squared), MAE (Mean Absolute Error), and MSE (Mean Squared Error). Additionally, some studies employed other metrics that were less frequently used, as detailed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eData were primarily obtained through measurements of the outputs from photovoltaic (PV) and photovoltaic-thermal (PVT) systems installed in their respective contexts. Additionally, a significant portion of the data was sourced from the datasets introduced in various studies. Notably, Shin et al. employed PVsyst and Solar Pro to simulate building-integrated photovoltaic (BIPV) systems in their research [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\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\u003eRelated research\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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eReference\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eContext\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOutput Indicators\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAlgorithm of ML\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eModule type\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eModeling software\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eValidation strategy\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eAccuracy metric\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eBest accuracy\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c12\" namest=\"c10\"\u003e \u003cp\u003eData Type\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c13\"\u003e \u003cp\u003eVariable\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 citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBuilding\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003epower generation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eANN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBIPV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003ePVsyst, Solar Pro\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTrain/test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eRMSE, MAE, R\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.92 (R\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c11\" namest=\"c10\"\u003e \u003cp\u003eSimulated, Measured\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c13\" namest=\"c12\"\u003e \u003cp\u003eSolar irradiance\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBuilding\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003epower generation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGE, DE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBIPV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTrain/test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eErel\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c11\" namest=\"c10\"\u003e \u003cp\u003eMeasured\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c13\" namest=\"c12\"\u003e \u003cp\u003eAmbient Temperature, solar irradiation, relative outdoor humidity, wind speed\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBuilding\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003epower generation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eANN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePVT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTrain/test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eMSE, NMSE, MAE, R\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.11 (NMSE)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c11\" namest=\"c10\"\u003e \u003cp\u003eMeasured\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c13\" namest=\"c12\"\u003e \u003cp\u003esolar irradiance, ambient temperature\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBuilding\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003etotal active power\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTrain/test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eRMSE, MAE, Standard deviation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.7 RMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eMeasured\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c13\" namest=\"c11\"\u003e \u003cp\u003eAmbient Temperature, Horizontal irradiation\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBuilding\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePower generation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLASSO, RF, LR, PR, XGBoost, SVM, NN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003ek-fold cross-validation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eMeasured\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c13\" namest=\"c11\"\u003e \u003cp\u003eExternal temperature, wind speed, Humidity\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBuilding\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eelectrical and thermal efficiencies\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eANN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePVT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTrain/test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.0078%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eMeasured\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c13\" namest=\"c11\"\u003e \u003cp\u003esolar irradiance and the module temperature\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUrban\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003epower generation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTrain/test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eMAPE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.40%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eMeasured\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c13\" namest=\"c11\"\u003e \u003cp\u003eAmbient temperature, Relative Humidity\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBuilding\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003epower generation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMFFNN, CFNN, RBFNN, ENN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eMatlab\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTrain/test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eR, MAE, RMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.0021 (RMSE)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eDataset\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c13\" namest=\"c11\"\u003e \u003cp\u003eAmbient temperature, relative Humidity, solar radiation, wind speed\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMicrogrid\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003epower generation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLGBM, KNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTrain/test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e, RMSE, MAE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.84 R\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eMeasured\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c13\" namest=\"c11\"\u003e \u003cp\u003eSolar irradiance, ambient temperature\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBuilding\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eelectrical efficiency\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eANFIS, ANN, LS-SVR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePVT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTrain/test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eAARD, MSE, R\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.95 R\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eDataset\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c13\" namest=\"c11\"\u003e \u003cp\u003eradiation intensity, Coolant material\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eModule\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003epower generation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSVM, GPR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTrain/test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eRMSE, MAE, R\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.98 R\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eDataset\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c13\" namest=\"c11\"\u003e \u003cp\u003ePanel temperature, ambient temperature, relative humidity,\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eModule\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003epower generation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTrain/test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eMeasured\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c13\" namest=\"c11\"\u003e \u003cp\u003eRadiation, Ambient temperature, Humidity, Wind speed, Evaporation\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBuilding\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003epower generation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eKNR, LASSO, SVR, RF, ETR, GBR, XGBoost, ANN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTrain/test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eMAE, RMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.60 (RMSE)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eDataset\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c13\" namest=\"c11\"\u003e \u003cp\u003eRadiation, Ambient temperature, Humidity, Wind speed, Evaporation, Rooftop dimension\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eModule\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eelectrical efficiency\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMLP, RF, SVR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePVT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTrain/test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eRMSE, R\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.76 (R\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eMeasured\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c13\" namest=\"c11\"\u003e \u003cp\u003emass flow rate, solar radiation, ambient temperature, wind speed, fluid inlet temperature, PVT surface area, pipe inner diameter\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003epower plant\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003epower generation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eELM, GA, SDA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTrain/test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e, MAE, nRMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.59 (R\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eDataset\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c13\" namest=\"c11\"\u003e \u003cp\u003edaily maximal, minimal and averaged temperature, daily averaged global horizontal radiation, daily\u003c/p\u003e \u003cp\u003eaveraged diffusive horizontal radiation\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBuilding\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePower generation, CO2 reduction\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eANN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTrain/test\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\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eDataset\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c13\" namest=\"c11\"\u003e \u003cp\u003eair temperature, wind speed, cloudiness, Current power direction\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eModule\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003epower generation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDNN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePVT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTrain/test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e3.34E-08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eMeasured\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c13\" namest=\"c11\"\u003e \u003cp\u003eCell type\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBuilding\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003epower generation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRF, NN, SVM, LR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTrain/test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eRMSE, MAPE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.76 (RMSE)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eMeasured\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c13\" namest=\"c11\"\u003e \u003cp\u003eweather and solar generation data\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003epower plant\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003epower generation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMR, SVMR, GR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTrain/test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eMSE, MAE, R\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.88 (R\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eMeasured\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c13\" namest=\"c11\"\u003e \u003cp\u003esolar radiation, ambient temperature, relative humidity\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBuilding\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003epower generation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eANN, DT, QSVM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBIPV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTrain/test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eRMSE, MSE, R\u003csup\u003e2\u003c/sup\u003e, MAPE, MAE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.88 (R\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eMeasured\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c13\" namest=\"c11\"\u003e \u003cp\u003eBuilding orientations\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003epower plant\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003epower generation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLSTM, MLP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTrain/test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eMAE, MAPE, RMSE, R\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.77 (R\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eDataset\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c13\" namest=\"c11\"\u003e \u003cp\u003eweather and solar generation data\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]time horizons\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003epower plant\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003epower generation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eANN, XGBoost, RF, DT, KNN, LASSO, LR, RR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTrain/test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eRMSE, MAE, R\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.84 (R\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eDataset\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c13\" namest=\"c11\"\u003e \u003cp\u003eambient temperature, module temperature, irradiation\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"4 Methodology","content":"\u003cp\u003eThe study followed a systematic procedure: First, a dataset was generated using simulation-based software. Second, machine learning (ML) algorithms were applied to analyze this dataset and develop a predictive model. Subsequently, a new set of variables, not present in the original dataset, was introduced to assess the model\u0026rsquo;s performance with novel input data. This phase involved an iterative trial-and-error process to optimize the performance of the ML algorithms. Finally, a sensitivity analysis was performed to identify which features most significantly affected the calculated metrics. (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e)\u003c/p\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n \u003ch2\u003e4.1 context\u003c/h2\u003e\n \u003cp\u003eTo create the dataset, the initial step involved selecting a context. Tehran, Iran, was chosen for this purpose, with three of its regions selected for analysis. Tehran is divided into 22 distinct urban areas (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e), each with unique characteristics. The selected regions are pivotal to this research, with the selection criterion focusing on variations in elevation and population density across the city.\u003c/p\u003e\n \u003cp\u003eZone 1 represents areas with tall building structures exceeding 27 meters in height. Zone 2 exemplifies regions with moderate building heights and a more dispersed urban layout. Finally, Region 16 is characterized by low-rise buildings and a densely packed urban fabric. These diverse zones were chosen to provide a comprehensive sample across different building heights and urban densities within Tehran.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n \u003ch2\u003e4.2 Dataset creation\u003c/h2\u003e\n \u003cp\u003eTo standardize calculations and ensure comparability of results, a specific type of thermal photovoltaic panel has been utilized in this study. The chosen model is the PV-MLE275HD2, manufactured by Mitsubishi. This panel is equipped with monocrystalline silicon photovoltaic cells, boasting 120 cells per panel. With a power output of 275 watts and a maximum voltage supply of 32.1 volts, these cells demonstrate an efficiency rating of 16.6%.\u003c/p\u003e\n \u003cp\u003eVariable parameters crucial to panel installation have been identified, each encompassing a range of values and incremental steps. The cumulative variations within these parameters define the problem\u0026apos;s potential states. Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e outlines the parameters investigated in this research, culminating in a total of 1575 calculated states.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eSelected parameters and their values\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eVariable Parameters\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRange of Variation\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eStep of Variation\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eNumber of Cases\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eDescriptions\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHorizontal Angle of panel\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026minus;20\u0026deg; to 20\u0026deg;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10\u0026deg;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eVertical angle of panel\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e15\u0026deg; above and below the latitude\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u0026deg;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDistance Between Panels\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1 to 5 meters\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1 meter\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePanel elevation from roof\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10 to 30 centimeters\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10 centimeters\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eUrban Block\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIn three different regions\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eTo initiate the three-dimensionalization of urban maps, GIS files encompassing the 22 regions were obtained from the Tehran Municipality. These files, comprising smaller units measuring 1 km by 1 km, collectively delineate an area of 1 square kilometer.\u003c/p\u003e\n \u003cp\u003eSubsequently, utilizing the ArcGIS software, a shapefile file was generated for the designated area. This step is essential to advance to subsequent stages of the process. The shapefile format serves as a straightforward and indirect method for storing geometric and geographic feature information.\u003c/p\u003e\n \u003cp\u003eIn next step for solar radiation analysis, the Ladybug plugin within the Grasshopper software was utilized. This plugin, powered by the Energy Plus engine, was employed to perform calculations. The solar radiation analysis algorithm was designed using Tehran\u0026apos;s epw file, providing essential meteorological data.\u003c/p\u003e\n \u003cp\u003eFollowing, using the ladybug tools, pages with an average annual radiation exceeding 1500-kilowatt hours per square meter were identified and compiled into a list. This threshold is derived from the findings of [\u003cspan class=\"CitationRef\"\u003e29\u003c/span\u003e]. Then the focus shifts to the installation of thermal photovoltaic panels on surfaces identified as optimal for radiation reception in previous stages. To facilitate this process, an algorithm was developed within the Grasshopper environment.\u003c/p\u003e\n \u003cp\u003eTo establish the boundaries of the panels, the sunshade surfaces were initially segmented at one-meter intervals. Subsequently, considering desired angles (as variables) and trigonometric principles, the width range of each panel (1 meter wide) was determined. The length of the panel was set to the maximum size, corresponding to the length of the sunshade surface.\u003c/p\u003e\n \u003cp\u003eAdditionally, distances between panels were determined, ranging from 1 to 4 meters. These values represent a crucial parameter (panel-to-panel distances) aimed at assessing shading effects.\u003c/p\u003e\n \u003cp\u003eTo ensure flexibility in panel installation angles, an algorithm was devised to allow vertical adjustment of the installed panels. Subsequently, the horizontal orientation and rotation of the panels are established to optimize their exposure to sunlight. Another crucial parameter to consider is the distance of the panels from the installation surface. This distance directly impacts cooling and, consequently, the efficiency of the system. It is modeled accordingly to account for its influence on system performance.\u003c/p\u003e\n \u003cp\u003eIn the probability generation phase, tailored algorithms were crafted for each desired parameter, effectively encompassing their respective steps and intervals. The subsequent step involves comprehensive testing of these parameters in conjunction. All 1575 states will be evaluated, and the optimal states will be identified as outcomes.\u003c/p\u003e\n \u003cp\u003eThe Colibri plugin is employed for this purpose. By iteratively considering all states within each parameter and multiplying them together, Colibri determines the total number of states for the problem. It subsequently generates the desired outputs\u0026mdash;thermal and electrical\u0026mdash;repeatedly to facilitate thorough analysis and decision-making.\u003c/p\u003e\n \u003cp\u003eUpon specifying the desired parameters and installing the panels, the thermal and electrical outputs of each panel are calculated using Ladybug software plugins. Additionally, environmental outputs are generated to provide a comprehensive assessment of the system\u0026apos;s performance and sustainability.\u003c/p\u003e\n \u003cp\u003eFor environmental assessment, carbon emissions are considered from various sources. The burning of each cubic meter of gas releases carbon into the environment, and the hot water output from the panels allows estimation of gas consumption and consequently carbon emissions on an annual basis.\u003c/p\u003e\n \u003cp\u003eFurthermore, the production of electricity in power plants generates carbon emissions per kilowatt-hour. Additionally, the production of each thermal photovoltaic panel introduces carbon emissions into the cycle. By determining the number of panels utilized, the total carbon emissions associated with panel production can be calculated.\u003c/p\u003e\n \u003cp\u003eIn the subsequent step, considering that electricity production in power plants is correlated with carbon emissions, the amount of electricity generated by the panels is multiplied by the carbon emissions per kilowatt-hour produced by a power plant. This calculation, combined with the carbon emissions from panel production, characterizes the annual carbon emissions from the system. Figure \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e illustrates the steps of crating database.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\n \u003ch2\u003e4.3 ML algorithm development\u003c/h2\u003e\n \u003cp\u003eFollowing the simulation, 1575 distinct scenarios were generated based on the considered variables, and the results were quantified across six indicators spanning various domains. In this phase, the collected data is formatted and curated to serve as input for training machine learning algorithms.\u003c/p\u003e\n \u003cp\u003eIn this research, the employed machine learning algorithms encompass supervised learning and regression analysis. Specifically, two distinct algorithms, namely neural network (ANN) and random forest (RF), were utilized at this stage. Each algorithm is characterized by its unique set of parameters, also known as hyperparameters. Initially, a range was assigned to each hyperparameter, and through optimization, the highest achievable accuracy for estimating indicators was attained.\u0026nbsp;\u003c/p\u003e\n \u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eType of algorithms and hyperparameters\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eType of algorithm\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ehyperparameter\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eNumber of Scenarios\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eANN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNumber of Hidden Layers\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1,2,3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNumber of Neurons per Layer\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1 to 200 in steps of 10\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eActivation Function\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRELU\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003eRF\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNumber of Decision Trees\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1 to 500\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMax_depth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1 to 10 and None\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003eTo enhance the learning process on the training data model, the introduced parameters were normalized using the method, ensuring that the range of all parameters fell between 0 and 1. This normalization method is instrumental in improving both the speed and accuracy of learning. The relationship utilized for normalization is as follows:\u003c/p\u003e\n \u003cdiv id=\"Equa\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e$$\\:{x}^{{\\prime\\:}}=\\frac{x-\\text{m}\\text{i}\\text{n}\\left(x\\right)}{\\text{max}\\left(x\\right)-\\text{m}\\text{i}\\text{n}\\left(x\\right)}$$\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eTo prevent overfitting, a test set comprising 20% of the data not utilized in the processing or validation steps is created. The model is optimized using the remaining 80% of the data, with validation performed on the test set. This enables checking for signs of overfitting. By employing this method, the distribution of test sets remains consistent, reducing the likelihood of bias in the evaluation process.\u003c/p\u003e\n \u003cp\u003eAt this stage, the learning data is segmented by randomly dividing it into approximately 90% for model training and 10% for model evaluation. This division ensures that the model is trained on most of the data while retaining a smaller subset for evaluation to assess its performance accurately.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n \u003ch2\u003e4.4 Accuracy measurement\u003c/h2\u003e\n \u003cp\u003eAccuracy measurement indices are vital for evaluating the performance and training of machine learning models. These indices compare the predicted values with the values obtained in the simulation. Common accuracy measurement indices include root mean square error (RMSE), percentage error (PE), recognition coefficient index (R\u003csup\u003e2\u003c/sup\u003e), and mean square error (MSE) [\u003cspan class=\"CitationRef\"\u003e30\u003c/span\u003e].\u003c/p\u003e\n \u003cp\u003eIn this research, three error measurement indicators, RMSE, R\u003csup\u003e2\u003c/sup\u003e, and MAE are utilized. The calculation formulas for each are as follows:\u003c/p\u003e\n \u003cp\u003eRoot Mean Square Error (RMSE):\u003c/p\u003e\n \u003cdiv id=\"Equb\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e$$\\:RMSE=\\:\\sqrt{\\frac{1}{N}\\:\\sum\\:_{i=1}^{N}{\\left({\\widehat{y}}_{i}-\\:{y}_{i}\\right)}^{2}}$$\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eRecognition Coefficient Index (R\u003csup\u003e2\u003c/sup\u003e):\u003c/p\u003e\n \u003cdiv id=\"Equc\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e$$\\:{R}^{2}=1-\\:\\frac{\\sum\\:_{i=1}^{N}{\\left({\\widehat{y}}_{i}-\\:{y}_{i}\\right)}^{2}}{\\sum\\:_{i=1}^{N}{\\left({y}_{i}-\\:{\\stackrel{-}{y}}_{i}\\right)}^{2}}$$\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eMean Absolute Error (MAE):\u003c/p\u003e\n \u003cdiv id=\"Equd\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e$$\\:MAE=\\:\\frac{\\sum\\:\\left|{y}_{i}-\\:{\\widehat{y}}_{i}\\right|}{n}$$\u003c/div\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\n \u003ch2\u003e4.5 Sensitivity analysis\u003c/h2\u003e\n \u003cp\u003ein statistics involves comprehending the interrelationships among variables within a dataset and understanding how these relationships are influenced by other variables and to what extent. By closely examining the data and considering the correlations between variables, it can be inferred that the data changes linearly. Consequently, correlation calculation methods tailored for linear data with consistent performance are applicable.\u003c/p\u003e\n \u003cp\u003eThe most prevalent correlation calculation methods in this domain are the Pearson and Spearman methods [\u003cspan class=\"CitationRef\"\u003e31\u003c/span\u003e]. In this research, the Pearson method was employed to analyze the sensitivity of the available data.\u003c/p\u003e\n \u003cp\u003ePearson correlation coefficient:\u003c/p\u003e\n \u003cdiv id=\"Eque\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Eque\" name=\"EquationSource\"\u003e$$\\:r=\\:\\frac{\\sum\\:\\left({x}_{i}-\\:\\stackrel{-}{x}\\right)\\left({y}_{i}-\\:\\stackrel{-}{y}\\right)}{\\sqrt{\\sum\\:{\\left({x}_{i}-\\:\\stackrel{-}{x}\\right)}^{2}\\sum\\:{\\left({y}_{i}-\\:\\stackrel{-}{y}\\right)}^{2}}}$$\u003c/div\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"5 Results","content":"\u003cp\u003eIn the subsequent analysis, the characteristics of the output data for each considered indicator, encompassing both energy and environmental metrics, have been investigated.\u003c/p\u003e\n\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\n \u003ch2\u003e5.1 Electricity production\u003c/h2\u003e\n \u003cp\u003eThe highest numerical amount of electricity production was recorded in region 16, while the lowest was observed in region 1. In terms of average annual electricity production, panels in region 16 outperformed those in region 2 by approximately 38% and exceeded the production in region 1 by about 52%.\u003c/p\u003e\n \u003cp\u003eA comparison of the results across these three regions reveals that shading in different urban areas has a significant impact on the performance of photovoltaic systems. Regions with lower buildings and less shading demonstrate higher electricity production compared to areas with taller buildings.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\n \u003ch2\u003e5.2 Hot water production\u003c/h2\u003e\n \u003cp\u003eRegion 2 recorded the highest numerical hot water production, while Region 1 exhibited the lowest. In terms of average annual hot water production, the performance of panels in region 16 surpasses that of Region 2 by approximately 36% and exceeds that of Region 1 by about 50%.\u003c/p\u003e\n \u003cp\u003eThese results suggest that shading in different urban areas significantly affects the performance of thermal photovoltaic systems in hot water production. Specifically, regions with lower buildings and less shading demonstrate higher hot water production compared to areas with taller buildings.\u003c/p\u003e\n \u003cp\u003eFurthermore, in regions characterized by more uniform building heights, such as Region 16, hot water production results are relatively consistent. In contrast, regions with varied building heights show significant differences in hot water production, underscoring the impact of building height variability on system performance.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\n \u003ch2\u003e5.3 Carbon reduction\u003c/h2\u003e\n \u003cp\u003eOn average, the highest amount of carbon reduction occurred in region 16, primarily attributed to its higher production of hot water and electricity compared to the other two regions. Conversely, Region 1 exhibited the lowest average carbon reduction rate. Numerically, the highest amount of carbon reduction was observed in region 2, while the lowest was in region 1. Region 16 achieved a 56% higher carbon reduction compared to region 2, and approximately 90% higher compared to region 1.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\n \u003ch2\u003e5.4 Selecting optimal ML algorithm\u003c/h2\u003e\n \u003cp\u003eThe optimization and validation of learning models should be conducted separately for each of the three investigated areas, using two machine learning algorithms, and for all target indicators. This process would require 30 iterations (3 areas \u0026times; 2 algorithms \u0026times; 5 indicators). Given that hyperparameter optimization is time-consuming, to save time, the two learning algorithms were evaluated only for one region (Region 1).\u003c/p\u003e\n \u003cp\u003eTable \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e compares the two learning models based on the data from region 1, across various indicators and using the optimal hyperparameters.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab4\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eSpecifications of Machine Learning Model Hyperparameters\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAlgorithm\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eTarget indicator\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eOptimal Hyperparameter\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"4\"\u003e\n \u003cp\u003eRandom Forest\u003c/p\u003e\n \u003cp\u003en_estimators and max_depth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHot water\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003enone, 45\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eElectricity\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003enone, 100\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNumber of panels\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003enone, 45\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCO2 reduction\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003enone, 100\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"4\"\u003e\n \u003cp\u003eANN\u003c/p\u003e\n \u003cp\u003ehidden-layer-sizes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHot water\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e(100,200)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eElectricity\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e(250,250)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNumber of panels\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e(100,200)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCO2 reduction\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e(100,200,200)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\n \u003ch2\u003e5.5 Validation of learning models\u003c/h2\u003e\n \u003cp\u003eAt this stage, each model was trained and validated using the optimal hyperparameters for region 1. The accuracy evaluation metrics for each target indicator are presented in Table \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e. Additionally, the time required for model training, as well as the target indicators for each model, have been compared.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab5\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003ePerformance of Machine Learning Models Based on Data from Region 1\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eAlgorithm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eTarget indicator\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eLearning Time (s)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"6\"\u003e\n \u003cp\u003eValidation\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eRMSE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eMAE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eR-square\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eValidation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eValidation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eValidation\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"4\"\u003e\n \u003cp\u003eRandom Forest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHot water\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e41643.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2500.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3229.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e576.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eElectricity\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2098.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.473\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e137.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNumber of panels\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCO2 reduction\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8100.81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e627.38\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e731.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e231.98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"4\"\u003e\n \u003cp\u003eANN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHot water\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e63.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e75972.91\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e41369.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5771884562\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1711399191\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eElectricity\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e25.64\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e32675.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e34486.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e30534.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e32395.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.91\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNumber of panels\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e37.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e51.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e17.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCO2 reduction\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e50.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14301.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7901.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6709.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5916.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eBased on the comparison between the neural network and random forest models using the R\u003csup\u003e2\u003c/sup\u003e recognition coefficient index and the time required for learning, it\u0026apos;s evident that the random forest model slightly outperforms the neural network model in terms of R\u003csup\u003e2\u003c/sup\u003e. Additionally, the random forest model demonstrates significantly better performance in terms of learning time compared to the neural network model. Therefore, based on these findings, the Random Forest algorithm is chosen to proceed further.\u003c/p\u003e\n \u003cp\u003eAt this stage, each of the models has been trained and validated with optimal hyperparameters for region 2. Each of the accuracy evaluation indicators for each of the target indicators is displayed in Table \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e. Also, the time required to learn the model has been measured in each target index. The duration of learning among the indicators varied from 0.05 to 0.09, and the recognition coefficient index among the target indicators was at least 0.99.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003ctable id=\"Tab6\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003ePerformance of Machine Learning Models Based on Data from Region 2\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eAlgorithm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eTarget indicator\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eLearning Time (s)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"6\"\u003e\n \u003cp\u003eValidation\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eRMSE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eMAE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eR-square\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eValidation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eValidation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eValidation\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"4\"\u003e\n \u003cp\u003eRandom Forest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHot water\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e403.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1056.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e181.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e369.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eElectricity\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e31.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e16.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNumber of panels\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCO2 reduction\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e218.92\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e263.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e131.79\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e131.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eAt this stage, each of the models has been trained and validated with optimal hyperparameters for region 16. Each of the accuracy evaluation indicators for each of the target indicators is displayed in Table \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e. Also, the time required to learn the model has been measured in each target index. The duration of learning among the indicators was different from 0.05 to 0.95 and also the recognition coefficient index was at least 0.99 among the target indicators.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003ctable id=\"Tab7\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003ePerformance of Machine Learning Models Based on Data from Region 16\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eAlgorithm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eTarget indicator\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eLearning Time (s)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"6\"\u003e\n \u003cp\u003eValidation\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eRMSE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eMAE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eR-square\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eValidation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eValidation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eValidation\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"4\"\u003e\n \u003cp\u003eRandom Forest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHot water\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e752.53\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1663.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e363.66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e597.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eElectricity\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e38.27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e23.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e17.94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNumber of panels\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCO2 reduction\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e345.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e425.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e219.88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e238.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e\n \u003ch2\u003e5.6 Machine learning results\u003c/h2\u003e\n \u003cp\u003eThe results of the simulation and the values predicted by the Random Forest algorithm for each of the target indicators for each region have been compared and are presented in Fig.\u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec17\" class=\"Section2\"\u003e\n \u003ch2\u003e5.7 Sensitivity Analysis\u003c/h2\u003e\n \u003cp\u003eThe correlation values between different data are visually represented in Fig. \u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003e, allowing for a clear understanding of the relationships between the variables. Each numerical value of the coefficients is clearly displayed, providing valuable insights into the strength and direction of the correlations observed in the data.\u003c/p\u003e\n \u003cp\u003eAccording to Fig. \u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003e, the correlation values shed light on the factors influencing various aspects of the study:\u003c/p\u003e\n \u003cp\u003eHot Water Production: The most significant factor impacting hot water production is the distance between panels, with a coefficient of -0.75. This indicates that decreasing the distance between panels (increasing panel density) leads to higher hot water production. The density and height of buildings in the investigated area (coefficient: 0.42) also play a notable role. Additionally, the vertical angle of the panels (coefficient: 0.074) contributes to hot water production, while the horizontal angle and distance of panels from the ceiling have lesser impacts.\u003c/p\u003e\n \u003cp\u003eElectricity Production: The investigated area (coefficient: 0.96) is the most influential factor in electricity production, followed by the vertical angle of the panels (coefficient: 0.093). Other factors, such as the horizontal angle, distance of panels from the ceiling, and distance between panels, also contribute to electricity production, albeit to a lesser extent.\u003c/p\u003e\n \u003cp\u003eNumber of Panels: The distance between panels has the highest impact on the number of panels, with a coefficient of -0.78, indicating that increasing panel density reduces the number of panels required. The investigated area (coefficient: 0.43) is the next significant factor, followed by the vertical angle of the panels. The horizontal angle and distance of panels from the ceiling have minimal effects on the number of panels.\u003c/p\u003e\n \u003cp\u003eAmount of Carbon reduction: The distance between panels (coefficient: -0.75) has the greatest impact on carbon reduction, with higher panel density resulting in lower carbon reduction. The investigated area (coefficient: 0.48). Additionally, the vertical angle of the panels influences carbon reduction, while the horizontal angle and distance from the ceiling have minimal effects.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"6 Discussion","content":"\u003cp\u003eThis paper examines the parameters involved in installing a photovoltaic-thermal (PVT) system on buildings within an urban context. Additionally, it introduces a machine learning (ML) algorithm, selected from Artificial Neural Networks (ANN) and Random Forests (RF), based on the best accuracy. The literature review and accuracy metrics used in this study demonstrate the feasibility of ML methods for predicting the power generation and hot water production of PVT panels throughout the year in an urban environment.\u003c/p\u003e\n\u003cp\u003eThe accuracy of the ML algorithms, measured by the R\u0026sup2; metric, ranged from 0.99 to 1 for the ANN algorithm, and from 0.91 to 1 for the RF algorithm, with the highest accuracy achieved in predicting electricity generation. Consequently, the RF algorithm was selected as the most accurate model for this context.\u003c/p\u003e\n\u003cp\u003eUnlike many similar studies in this field, the dataset used to train and validate the ML algorithm was generated using the methods and software introduced earlier. The data was produced on a yearly basis and covered three different regions in Tehran, Iran, to account for various urban conditions. It is worth noting that while many studies in literature use climatic indicators as variables, this paper focuses on the installation conditions of the panels.\u003c/p\u003e\n\u003cp\u003eThis study has designed a framework using ML algorithms to predict electricity and hot water generation, as well as CO₂ reduction, from PVT panels. The results can be utilized to develop a data-driven framework that determines the most accurate and reliable prediction model for each target variable. The proposed algorithmic framework is presented in four steps:\u003c/p\u003e\n\u003col start=\"1\" type=\"1\"\u003e\n \u003cli\u003eDefining the urban area by importing a GIS file or selecting a similar urban context from a database.\u003c/li\u003e\n \u003cli\u003eIdentifying suitable areas for installing PVT panels on buildings.\u003c/li\u003e\n \u003cli\u003eSelecting the properties of the installed panels.\u003c/li\u003e\n \u003cli\u003eObtaining results for electricity and hot water generation, the number and area of panels, and CO₂ reduction using these panels. This proposed framework is illustrated in Fig.13\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003eThe present study is constrained by a defined set of design parameters with specific ranges as input features. For a more comprehensive framework, it is necessary to consider all possible input parameters and value ranges to increase the generalizability of the models and include more complex options, such as different PVT modules and the consideration of fa\u0026ccedil;ades for panel installation. Additionally, this study was limited to calculations in three regions within a single city. To develop a more widely applicable framework, broader studies covering multiple cities and varying weather conditions are needed to generate more diverse training datasets. Future research should also explore and compare novel ML approaches, such as deep learning, to evaluate their prediction accuracy.\u003c/p\u003e"},{"header":"7 Conclusion","content":"\u003cp\u003eTwo ML algorithm were examined in this study and according to the results, both machine learning (ML) methods can effectively predict the power generation and CO\u003csub\u003e2\u003c/sub\u003e reduction of PVT panels in urban context, achieving R\u0026sup2; values of up to 0.91, when using the Random Forest (RF) model.\u003c/p\u003e \u003cp\u003eThis approach could establish a framework capable of replacing traditional simulation-based methods, enabling the calculation of key metrics without the need for time-consuming computer simulations. However, the effectiveness of this approach hinges on a cost-benefit analysis that considers the ratio between the required input training data and the number of predictions needed. Since generating the training data still relies on conducting comprehensive computer simulations or real-world measurements, this method is more practical when a full parametric analysis of all combinations of design variables is available.\u003c/p\u003e \u003cp\u003eThe findings of this study have the potential to inform the development of a tool for early design stage analyses, eliminating the need for time-intensive simulations in existing platforms and programs.\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"618\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eAARD\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"bottom\" style=\"width: 430px;\"\u003e\n \u003cp\u003eabsolute average relative deviation\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eAI\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"bottom\" style=\"width: 430px;\"\u003e\n \u003cp\u003eArtificial inteligence\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eANFIS\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"bottom\" style=\"width: 430px;\"\u003e\n \u003cp\u003eadaptive neuro-fuzzy inference systems\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eANN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"bottom\" style=\"width: 430px;\"\u003e\n \u003cp\u003eArtificial Neural Network.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eBIPV\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"bottom\" style=\"width: 430px;\"\u003e\n \u003cp\u003eBuilding Integrated Photovoltaic\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eCFNN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"bottom\" style=\"width: 430px;\"\u003e\n \u003cp\u003eCascade Feed-forward Neural Network\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eDE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"bottom\" style=\"width: 430px;\"\u003e\n \u003cp\u003eDifferential Evolution\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eDNN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"bottom\" style=\"width: 430px;\"\u003e\n \u003cp\u003edeep neural network\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eDT\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"bottom\" style=\"width: 430px;\"\u003e\n \u003cp\u003edecision tree\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eELM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003eextreme learning machine\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eENN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003eElman neural network\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eETR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003eextra tree regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eGA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003egenetic algorithm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eGBR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003egradient boosting regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eGE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003eGrammatical Evolution\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eGPR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003eGaussian process regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eGR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003eGaussian regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eKNN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003eK nearest neighbors\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eKNR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003ek-neighbors regressor\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eLASSO\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003eleast absolute shrinkage and selection\u003cbr\u003e\u0026nbsp;operator\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eLGBM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003eLight gradient boosting machine\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eLR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003elinear regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eLS-SVR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003eLeast Squares Support Vector Regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eLSTM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003eLong Short-Term Memory\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eMAPE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003eMean absolute percentage error\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eMFFNN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003eMultilayer Feed-Forward Neural Network\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eML\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003eMachine learning\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eMLP\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003emultilayer perceptron\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eMR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003emultivariate regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eMSE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003eMean Squared Error\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eNMSE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003eNormalized Mean Squared Error\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eNN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003eNeural Networks\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003enRMSE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003enormalized root mean square error\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003ePR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003epolynomial regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003ePV\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003ePhotovoltaic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003ePVT\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003ePhotovoltaic thermal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eQSVM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003equadratic support vector machine\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eRBFNN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 370px;\"\u003e\n \u003cp\u003eRadial Basis Function Neural Network\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eRELU\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 370px;\"\u003e\n \u003cp\u003eRectified Linear Unit\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eRF\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003erandom forest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eRMSE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003eRoot-mean-square deviation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eRR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003eRidge Regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eSDA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003esimilar day analysis\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eSVM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003esupport vector machine\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eSVMR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003esupport vector machine regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eSVR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003esupport vector regression\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 188px;\"\u003e\n \u003cp\u003eXGBoost\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 370px;\"\u003e\n \u003cp\u003eextreme gradient boosting\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 59px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e"},{"header":"Statements and Declarations","content":"\u003cp\u003eFunding\u003c/p\u003e\n\u003cp\u003eThe authors declare that no funds, grants, or other support were received during the preparation of this manuscript.\u003c/p\u003e\n\u003cp\u003eCompeting Interests\u003c/p\u003e\n\u003cp\u003eThe authors have no relevant financial or non-financial interests to disclose.\u003c/p\u003e\n\u003cp\u003eAuthor contributions\u003c/p\u003e\n\u003cp\u003eAlireza Nazeri: Modeling and simulation, Machine learning model, data collection and analysis, Writing original draft.\u003c/p\u003e\n\u003cp\u003eAli Taheri: Modeling and simulation, Machine learning model, data collection and analysis\u003c/p\u003e\n\u003cp\u003eZahra Sadat Zomorodian: Methodology, Reviewing, Supervision.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eM. Zhing, Y. L. Bai, T. Zhao, and M. Wang, \u0026ldquo;Energy harvesting properties of a flapping foil with blow aspirators: A numerical investigation,\u0026rdquo; \u003cem\u003eEnergy Reports\u003c/em\u003e, vol. 8, pp. 1803\u0026ndash;1815, Nov. 2022, doi: 10.1016/j.egyr.2022.01.003.\u003c/li\u003e\n \u003cli\u003eE. Ghirardi, G. Brumana, G. Franchini, and A. Perdichizzi, \u0026ldquo;The optimal share of PV and CSP for highly renewable power systems in the GCC region,\u0026rdquo; \u003cem\u003eRenew Energy\u003c/em\u003e, vol. 179, pp. 1990\u0026ndash;2003, 2021, doi: https://doi.org/10.1016/j.renene.2021.08.005.\u003c/li\u003e\n \u003cli\u003eJ. Jing, Y. Zhou, L. Wang, Y. Liu, and D. Wang, \u0026ldquo;The spatial distribution of China\u0026rsquo;s solar energy resources and the optimum tilt angle and power generation potential of PV systems,\u0026rdquo; \u003cem\u003eEnergy Convers Manag\u003c/em\u003e, vol. 283, p. 116912, 2023, doi: https://doi.org/10.1016/j.enconman.2023.116912.\u003c/li\u003e\n \u003cli\u003eZ. Wang, J. Liu, Y. Zhang, H. Yuan, R. Zhang, and R. S. Srinivasan, \u0026ldquo;Practical issues in implementing machine-learning models for building energy efficiency: Moving beyond obstacles,\u0026rdquo; \u003cem\u003eRenewable and Sustainable Energy Reviews\u003c/em\u003e, vol. 143, p. 110929, 2021, doi: https://doi.org/10.1016/j.rser.2021.110929.\u003c/li\u003e\n \u003cli\u003eW. Chiang, I. Permana, F. Wang, H. Chen, and M. Erdenebayar, \u0026ldquo;Experimental investigation for an innovative hybrid photovoltaic/Thermal (PV/T) solar system,\u0026rdquo; \u003cem\u003eEnergy Reports\u003c/em\u003e, vol. 8, pp. 910\u0026ndash;918, Nov. 2022, doi: 10.1016/j.egyr.2022.10.264.\u003c/li\u003e\n \u003cli\u003eA. Dev, R. Kumar, and R. P. Saini, \u0026ldquo;Experimental evaluation of performance of a hybrid solar photovoltaic (PV/T) panel integrated with effective cooling solutions with water base nanofluids and phase change materials,\u0026rdquo; \u003cem\u003eEnergy Sources, Part A: Recovery, Utilization, and Environmental Effects\u003c/em\u003e, vol. 44, no. 3, pp. 7287\u0026ndash;7302, Sep. 2022, doi: 10.1080/15567036.2022.2107732.\u003c/li\u003e\n \u003cli\u003eP. Suanpang and P. Jamjuntr, \u0026ldquo;Machine Learning Models for Solar Power Generation Forecasting in Microgrid Application Implications for Smart Cities,\u0026rdquo; \u003cem\u003eSustainability\u003c/em\u003e, vol. 16, no. 14, p. 6087, Jul. 2024, doi: 10.3390/su16146087.\u003c/li\u003e\n \u003cli\u003eI. Rojek, D. Mikołajewski, A. Mroziński, and M. Macko, \u0026ldquo;Machine Learning- and Artificial Intelligence-Derived Prediction for Home Smart Energy Systems with PV Installation and Battery Energy Storage,\u0026rdquo; \u003cem\u003eEnergies (Basel)\u003c/em\u003e, vol. 16, no. 18, Sep. 2023, doi: 10.3390/en16186613.\u003c/li\u003e\n \u003cli\u003eM. Mohana, A. S. Saidi, S. Alelyani, M. J. Alshayeb, S. Basha, and A. E. Anqi, \u0026ldquo;Small-scale solar photovoltaic power prediction for residential load in saudi arabia using machine learning,\u0026rdquo; \u003cem\u003eEnergies (Basel)\u003c/em\u003e, vol. 14, no. 20, Oct. 2021, doi: 10.3390/en14206759.\u003c/li\u003e\n \u003cli\u003eW. G. Shin, J. Y. Shin, H. M. Hwang, C. H. Park, and S. W. Ko, \u0026ldquo;Power Generation Prediction of Building-Integrated Photovoltaic System with Colored Modules Using Machine Learning,\u0026rdquo; \u003cem\u003eEnergies (Basel)\u003c/em\u003e, vol. 15, no. 7, Apr. 2022, doi: 10.3390/en15072589.\u003c/li\u003e\n \u003cli\u003eL. Serrano-Luj\u0026aacute;n, C. Toledo, J. M. Colmenar, J. Abad, and A. Urbina, \u0026ldquo;Accurate thermal prediction model for building-integrated photovoltaics systems using guided artificial intelligence algorithms,\u0026rdquo; \u003cem\u003eAppl Energy\u003c/em\u003e, vol. 315, Jun. 2022, doi: 10.1016/j.apenergy.2022.119015.\u003c/li\u003e\n \u003cli\u003eJ. H. Yousif and H. A. Kazem, \u0026ldquo;Prediction and evaluation of photovoltaic-thermal energy systems production using artificial neural network and experimental dataset,\u0026rdquo; \u003cem\u003eCase Studies in Thermal Engineering\u003c/em\u003e, vol. 27, Oct. 2021, doi: 10.1016/j.csite.2021.101297.\u003c/li\u003e\n \u003cli\u003eM. H. Sulaiman, M. S. Jadin, Z. Mustaffa, H. Daniyal, and M. N. Mohd Azlan, \u0026ldquo;Short-term forecasting of rooftop retrofitted photovoltaic power generation using machine learning,\u0026rdquo; \u003cem\u003eJournal of Building Engineering\u003c/em\u003e, vol. 94, Oct. 2024, doi: 10.1016/j.jobe.2024.109948.\u003c/li\u003e\n \u003cli\u003eY. Chaibi, M. Malvoni, T. El Rhafiki, T. Kousksou, and Y. Zeraouli, \u0026ldquo;Artificial neural-network based model to forecast the electrical and thermal efficiencies of PVT air collector systems,\u0026rdquo; \u003cem\u003eClean Eng Technol\u003c/em\u003e, vol. 4, Oct. 2021, doi: 10.1016/j.clet.2021.100132.\u003c/li\u003e\n \u003cli\u003eA. Patel \u003cem\u003eet al.\u003c/em\u003e, \u0026ldquo;A Practical Approach for Predicting Power in a Small-Scale Off-Grid Photovoltaic System using Machine Learning Algorithms,\u0026rdquo; \u003cem\u003eInternational Journal of Photoenergy\u003c/em\u003e, vol. 2022, 2022, doi: 10.1155/2022/9194537.\u003c/li\u003e\n \u003cli\u003eY. Kassem and A. A. Othman, \u0026ldquo;Selection of most relevant input parameters for predicting photovoltaic output power using machine learning and quadratic models,\u0026rdquo; \u003cem\u003eModel Earth Syst Environ\u003c/em\u003e, vol. 8, no. 4, pp. 4661\u0026ndash;4686, Nov. 2022, doi: 10.1007/s40808-022-01413-7.\u003c/li\u003e\n \u003cli\u003eY. Cao, E. Kamrani, S. Mirzaei, A. Khandakar, and B. Vaferi, \u0026ldquo;Electrical efficiency of the photovoltaic/thermal collectors cooled by nanofluids: Machine learning simulation and optimization by evolutionary algorithm,\u0026rdquo; \u003cem\u003eEnergy Reports\u003c/em\u003e, vol. 8, pp. 24\u0026ndash;36, Nov. 2022, doi: 10.1016/j.egyr.2021.11.252.\u003c/li\u003e\n \u003cli\u003eB. Zazoum, \u0026ldquo;Solar photovoltaic power prediction using different machine learning methods,\u0026rdquo; \u003cem\u003eEnergy Reports\u003c/em\u003e, vol. 8, pp. 19\u0026ndash;25, Apr. 2022, doi: 10.1016/j.egyr.2021.11.183.\u003c/li\u003e\n \u003cli\u003eS. Zhang, J. Wang, H. Liu, J. Tong, and Z. Sun, \u0026ldquo;Prediction of energy photovoltaic power generation based on artificial intelligence algorithm,\u0026rdquo; \u003cem\u003eNeural Comput Appl\u003c/em\u003e, vol. 33, no. 3, pp. 821\u0026ndash;835, Feb. 2021, doi: 10.1007/s00521-020-05249-z.\u003c/li\u003e\n \u003cli\u003eV. H. S. Pham and H. D. Tran, \u0026ldquo;Research on applying machine learning models to predict the electricity generation capacity of rooftop solar energy systems on buildings,\u0026rdquo; \u003cem\u003eAsian Journal of Civil Engineering\u003c/em\u003e, vol. 24, no. 8, pp. 3413\u0026ndash;3423, Dec. 2023, doi: 10.1007/s42107-023-00722-1.\u003c/li\u003e\n \u003cli\u003eH. Gharaee, M. Erfanimatin, and A. M. Bahman, \u0026ldquo;Machine learning development to predict the electrical efficiency of photovoltaic-thermal (PVT) collector systems,\u0026rdquo; \u003cem\u003eEnergy Convers Manag\u003c/em\u003e, vol. 315, Sep. 2024, doi: 10.1016/j.enconman.2024.118808.\u003c/li\u003e\n \u003cli\u003eY. Zhou, N. Zhou, L. Gong, and M. Jiang, \u0026ldquo;Prediction of photovoltaic power output based on similar day analysis, genetic algorithm and extreme learning machine,\u0026rdquo; \u003cem\u003eEnergy\u003c/em\u003e, vol. 204, Aug. 2020, doi: 10.1016/j.energy.2020.117894.\u003c/li\u003e\n \u003cli\u003eH. Alghamdi, C. Maduabuchi, A. Albaker, A. Almalaq, T. Alsuwian, and I. Alatawi, \u0026ldquo;Machine Learning Performance Prediction of a Solar Photovoltaic-Thermoelectric System with Various Crystalline Silicon Cell Types,\u0026rdquo; \u003cem\u003eInt J Energy Res\u003c/em\u003e, vol. 2023, 2023, doi: 10.1155/2023/1990593.\u003c/li\u003e\n \u003cli\u003eC. Scott, M. Ahsan, and A. Albarbar, \u0026ldquo;Machine learning for forecasting a photovoltaic (PV) generation system,\u0026rdquo; \u003cem\u003eEnergy\u003c/em\u003e, vol. 278, Sep. 2023, doi: 10.1016/j.energy.2023.127807.\u003c/li\u003e\n \u003cli\u003eA. K. Tripathi \u003cem\u003eet al.\u003c/em\u003e, \u0026ldquo;Advancing solar PV panel power prediction: A comparative machine learning approach in fluctuating environmental conditions,\u0026rdquo; \u003cem\u003eCase Studies in Thermal Engineering\u003c/em\u003e, vol. 59, Jul. 2024, doi: 10.1016/j.csite.2024.104459.\u003c/li\u003e\n \u003cli\u003eR. Kabilan \u003cem\u003eet al.\u003c/em\u003e, \u0026ldquo;Short-Term Power Prediction of Building Integrated Photovoltaic (BIPV) System Based on Machine Learning Algorithms,\u0026rdquo; \u003cem\u003eInternational Journal of Photoenergy\u003c/em\u003e, vol. 2021, 2021, doi: 10.1155/2021/5582418.\u003c/li\u003e\n \u003cli\u003eM. Elsaraiti and A. Merabet, \u0026ldquo;Solar Power Forecasting Using Deep Learning Techniques,\u0026rdquo; \u003cem\u003eIEEE Access\u003c/em\u003e, vol. 10, pp. 31692\u0026ndash;31698, 2022, doi: 10.1109/ACCESS.2022.3160484.\u003c/li\u003e\n \u003cli\u003eS. T. Asiedu, F. K. A. Nyarko, S. Boahen, F. B. Effah, and B. A. Asaaga, \u0026ldquo;Machine learning forecasting of solar PV production using single and hybrid models over different time horizons,\u0026rdquo; \u003cem\u003eHeliyon\u003c/em\u003e, vol. 10, no. 7, Apr. 2024, doi: 10.1016/j.heliyon.2024.e28898.\u003c/li\u003e\n \u003cli\u003eE. Biyik \u003cem\u003eet al.\u003c/em\u003e, \u0026ldquo;A key review of building integrated photovoltaic (BIPV) systems,\u0026rdquo; \u003cem\u003eEngineering Science and Technology, an International Journal\u003c/em\u003e, vol. 20, no. 3, pp. 833\u0026ndash;858, 2017, doi: 10.1016/j.jestch.2017.01.009.\u003c/li\u003e\n \u003cli\u003eC. J. Willmott and K. Matsuura, \u0026ldquo;Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance,\u0026rdquo; \u003cem\u003eClim Res\u003c/em\u003e, vol. 30, no. 1, pp. 79\u0026ndash;82, 2005, [Online]. Available: https://www.int-res.com/abstracts/cr/v30/n1/p79-82/\u003c/li\u003e\n \u003cli\u003eJ. E. Gon\u0026ccedil;alves, T. van Hooff, and D. Saelens, \u0026ldquo;Understanding the behaviour of naturally-ventilated BIPV modules: A sensitivity analysis,\u0026rdquo; \u003cem\u003eRenew Energy\u003c/em\u003e, vol. 161, pp. 133\u0026ndash;148, 2020, doi: https://doi.org/10.1016/j.renene.2020.06.086.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"Photovoltaic-Thermal (PVT) Systems, Machine Learning in Renewable Energy, Energy Efficiency Optimization, AI-Driven Energy Prediction","lastPublishedDoi":"10.21203/rs.3.rs-5588685/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5588685/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn recent years, the use of data-driven methods for predicting photovoltaic (PV) panel electricity generation has grown significantly, with most studies relying on databases of actual PV panel performance. This study introduces a comprehensive methodology for predicting the performance of photovoltaic-thermal (PVT) panels, specifically focusing on electricity generation, hot water production, and carbon reduction. By leveraging artificial intelligence (AI) and machine learning (ML) methods, particularly Artificial Neural Networks (ANN) and Random Forest (RF), this research differentiates itself from prior studies by integrating predictive models for both electrical and thermal outputs. Additionally, the study examines the effect of different installation patterns on PVT panel output. A total of 1,575 different installation configurations were modeled across three urban districts in Tehran, and the results were used to train the two ML algorithms, which were then compared using Pearson correlation coefficient (R²), Root-mean-square deviation (RMSE), and Mean Absolute Error (MAE) metrics. The RF algorithm demonstrated superior performance, achieving an R² accuracy of 0.91 and shorter learning time. Finally, a framework is proposed based on the findings and simulation steps for predicting electricity generation, hot water production, and carbon reduction of PVT systems.\u003c/p\u003e","manuscriptTitle":"Predicting Photovoltaic-Thermal Panel Output in Urban Contexts Using Machine Learning Methods","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-12-12 12:08:48","doi":"10.21203/rs.3.rs-5588685/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":"980cd324-b7b9-490c-b06d-8dfa62b9c68e","owner":[],"postedDate":"December 12th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-12-12T12:08:49+00:00","versionOfRecord":[],"versionCreatedAt":"2024-12-12 12:08:48","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5588685","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5588685","identity":"rs-5588685","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}