Bayesian Optimization of Biodegradable Polymers via Machine Learning Driven Features from Low-Field NMR Data

Bayesian Optimization of Biodegradable Polymers via Machine Learning Driven Features from Low-Field NMR Data | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Bayesian Optimization of Biodegradable Polymers via Machine Learning Driven Features from Low-Field NMR Data Ryo Fujita, Yoshifumi Amamoto, Jun Kikuchi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6364337/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 18 Jun, 2025 Read the published version in npj Materials Degradation → Version 1 posted 9 You are reading this latest preprint version Abstract Effective designs of biodegradable polymers are highly desirable for achieving a sustainable society by decreasing environmental burden and replacing petroleum-based resources with biomass. Low-field NMR is one of the candidate techniques because it provides information on the higher-order structure and dynamics of polymers quickly and conveniently. Although machine learning approaches such as Bayesian optimization (BO) and convolutional neural networks (CNNs) are significant, there have been almost no reports on effective material design based on low-field NMR data. This study proposes a method for optimizing polymer process conditions using CNN-based features extracted from relaxation curves. This approach identified important features related to material properties while reconstructing denoised relaxation curves of polylactic acid. BO of process conditions using these features achieved an optimization rate comparable to using material property values, suggesting that effective material design is possible without directly evaluating a large number of properties. This provides a framework to accelerate polymer development through low-field NMR with minimal property data. Physical sciences/Materials science Physical sciences/Materials science/Techniques and instrumentation Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 INTRODUCTION In recent years, several approaches (e.g., establishing resource recycling systems and using biomass as an alternative to petroleum) have been attracting attention in efforts to develop a sustainable society 1 . Among these, research and development of biodegradable polymers is regarded as a key strategy for societal implementation 2 – 4 . To expand the use of biodegradable polymers in recycling processes, it is necessary to examine material properties such as degradability and mechanical strength after degradation for specific applications. However, since degradation tests of biodegradable polymers require many days, there is concern that conventional trial-and-error processes based on empirical rules may prolong material development t 5 . In materials development, efficient property optimization approaches utilizing machine learning to handle complex polymer systems have drawn attention in recent years 6 – 9 . Such reverse-design approaches may be effective for biodegradable materials as well. Because polymer properties are influenced by a wide variety of factors, it is difficult to formulate explicit relationships between chemical structure or molding conditions and the resulting properties 10 – 12 . Traditionally, optimizing material properties has required exhaustive prototyping, measurement of properties, and identification of important factors based on empirical rules. On the other hand, Bayesian optimization (BO) is one of the important methods in materials informatics used to search for processing conditions that optimize material properties with a small number of trials 5 , 6 , 8 , 9 , 13 . However, as noted above, in the case of biodegradable polymers, degradation tests are time-consuming, making it difficult to apply an iterative BO process. Low-field NMR is a convenient tool that has been used in various fields, such as oil logging 14 , 15 , food analysis 16 , rubber quality control 17 , 18 and studies of polymer molecular mobility. The relaxation curves obtained by low-field NMR provide comprehensive information on material properties derived from molecular motion and higher-order structure 19 , and this technique is widely used in materials research 20 – 23 . Among several pulse sequencing, Magic Sandwich Echo (MSE) pulse sequencing can acquire a wide range of higher-order structural information along with dynamics from the rigid to mobile regions. In the case of biodegradable polymers, crystalline regions of polymers with densely folded molecular chains have low molecular mobility and exhibits fast NMR relaxation (Fig. 1 a colored with blue), strongly corresponding with stiffness. Interface regions exhibit medium molecular mobility and NMR relaxation (Fig. 1 a colored with purple). Non-crystalline regions where molecular chains are relatively weakly folded have high molecular mobility and exhibits slow NMR relaxation (Fig. 1 a colored with red), strongly corresponding with toughness and degradability (Fig. 1 a, left). Various physical properties, such as mechanical strength and biodegradability, are known to correspond to the molecular structure of polymers 24 – 26 . Therefore, comprehensive molecular-structure data(molecular-structural dataの方がいい༟) may contain descriptors for a wide variety of properties. Descriptors constructed from the dynamics of these molecular structures may provide an efficient trial-and-error approach to targeting(discovering?) promising materials. One of remaining tasks is how to obtain the superior dynamics descriptors when the relaxation curves include the noises, especially when the measurement time is limited or the difference between the relaxation curves are small. Convolutional neural network (CNN) is one of suitable ways to denoise the measurement data along with obtaining the features from input data. The convolutional layers in CNN catch the feature in local regions and subsequent hierarchically spatial structure. Therefore, CNN have been applied for denoising of various measurement data such as NMR, X-ray scattering data, and so on 27 , using autoencoder types models consisting of encoder and decoder. The encoder layer extracts information by convolution and projects it into a low-dimensional space called the latent space, while the decoder layer forms a denoising curve based on the information from latent space. The representation in the latent space is derived from the abstraction of the input data, which is information on molecular structure and material properties and can be extracted to apply the material design. 28 . Although CNNs are an effective method for one-dimensional time series data such as relaxation curves and are expected to provide effective noise reduction, to the best of our knowledge, there have been no reports of applying BO in the latent space of relaxation curves obtained from low-field NMR measurements. In this study, we demonstrate that, instead of using material properties as the objective variable, the latent space in the denoising CNN model of relaxation curves from low-field NMR can be used for Bayesian optimization (Fig. 1 a). The CNN denoising model achieves to distinguish even small difference in the relaxation curves of polylactic acid obtained by different molding conditions. The latent space features that most strongly correlated with the properties were used to visualize the important time regions in the relaxation curves and to optimize the process conditions (Fig. 1 b). Since the relaxation curves used in this denoising task can be obtained in 30 minutes to 1 hour of low-field NMR measurements, this method may provide a framework to speed up polymer understanding and design by optimizing process conditions and acquiring important dynamics information (Fig. 1 b). RESULTS AND DISCUSSION In this study, polylactic acid (PLA) was utilized as a representative biodegradable polymer. Sixty-four different films were prepared by changing molding or crystallization conditions of crystallization temperature (75 °C–120 °C), crystallization time (5 min–40 min), and nucleating agent concentration (0wt%–1.5wt%) of PLA (Table S1). These factors affect the molecular structure and properties of polymers. For example, Ma et al. demonstrated that crystallization temperature (100 °C–130 °C) influences the crystallinity, tensile strength, and molecular structure of PLA 29 . Therefore, it can be assumed that differences in the molding conditions of the samples prepared in this study will cause variations in the propriety and molecular structure of the polylactic acid film. The wide ranges of crystal structures, from almost amorphous to high degree of crystallinity, were confirmed in X-ray scattering/diffraction measurement and polarized optical microscopic observations (Fig. S1). Low-field NMR measurements were carried out to evaluate the chain dynamics of PLA, and enzymatic degradation tests and tensile tests were conducted to obtain mechanical properties. Low-field NMR captures changes in molecular mobility associated with differences in the polymer’s higher-order structure and state. In particular, using the MSE pulse sequence, the shape of the relaxation curve in the sub-millisecond time domain can be interpreted in terms of contributions from crystalline, intermediate, and non-crystalline regions. The low-field NMR relaxation curves for all samples are shown in Fig. 2a-b. With increasing the crystallization temperature, the difference in slower relaxation regions in the time after 0.05 ms was seemed to appear, suggesting that the difference in relaxation behavior is derived from the difference in crystalline structure of PLA. These differences were less pronounced when the dependence of nucleating agent concentration and crystallization time was plotted (Figs. S2 and S3). This may be due to the increase in crystal regions of PLA promotes faster T 2 relaxation, thereby reducing signals from the non-crystalline regions, which exhibit slower T2 relaxation. It should be noted the differencces were hardly observable in real scale, suggesiting the difference of dynamics in amorphos regions of PLA between the samples were lessly observed, because the chain mobility of PLA is frozen at room temperature due to high glass transition temperature ( T g ~ 60 °C). Furthermore, the samples crystallized at 90 °C–120 °C have a high noise level even in log scale, making it difficult to discern the relative magnitudes of the signals. The relaxation curves were denoised by CNN model. We constructed a custom architecture based on SE-ResNet as shown in Fig. S4 30,31 . Noiseless and noisy artificial data were created to mimic relaxation curves. The CNN model was trained with the artificial relaxation curves with noisy data (input) and denoised data (output). An example of denoising for a simulation curve is shown in Fig. S5. The noises in relaxation curves were reduced through the CNN, indicating the CNN model worked effectively for the denoising task. After training, real data of polylactic acid relaxation curves was inputted for denoising. The denoising for the real data of low-field NMR measurements of PLA by the CNN model was attempted as show in Fig. 3a-b. The denoised curves showed a linear decay on the logarithmic axis in the slow time region, suggesting high noise rejection performance in the measured data. In addition, the separation of the relaxation curves by molding conditions such as crystallization temperature was clearly visualized, suggesting improved interpretability of differences in molecular dynamics between samples. Similarly, the moderate differences in nucleating agent concentration and crystallization time were also distinguishable (Figs. S6 and S7). These results indicate that denoising the relaxation curves even when differences are subtle can assist in correlating relaxation behavior with the crystal structure of PLA. Furthermore, this suggests that the latent representation of the relaxation curves learned by the denoising model may correspond to material property information. The material properties of PLA were predicted by random forest regression (RFR). As the material properties, enzymatic degradation rates ( r enzyme ), strain at break, and Young's modulus were evaluated for all films. For strain at break and Young’s modulus, the films were pre-treated by enzymatic degradation and/or light irradiation before the tensile tests (Y2-Y9, Table 1). All data points from the relaxation curves (either denoised or raw) were used as explanatory variables, and the property values were used as objective variables. Fig. 4 shows the root mean square error (RMSE) of each property predicted by RFR. The RFR showed a similar RMSE trend for train data with and without noise removal (Fig. 4a). However, the prediction using the test data of the non-denoised curves showed an increase in RMSE, suggesting that the regression performance of the RFR was reduced by noise especially in unseen or test data (Figs. 4c-d and S8). A similar trend was observed in the coefficient of determination ( R 2 ) for most propertoes (Table 1), indicating that the predictions from the denoised relaxation curves show stable accuracy for both train and test. The improvement of prediction performance of material properties by denoising may be due to the clarification of the difference in relaxation curves by property, as shown in Fig. 3. In other words, noise in the relaxation curves likely caused overfitting on the training data, reducing predictive performance on unseen test data. Although there have been many attempts to predict properties and extract descriptors of polymers 23,32,33 , this study successfully predicted a wide variety of properties while using only low-field NMR relaxation curves as explanatory variables, which are a relatively easy method to obtain the information of chain dynamics as well as higher order sturcutre. Our approach demonstrates the feasibility of a prediction approach of material properties based on simple low-field NMR measurements. Table 1 . Kind of material’s properties and results on machine learning. Nine materials properties labelled as Y1-Y9 were evaluated in this study. The enzymatic degradation rate ( r enzyme ), strain at break, and Young’ modulus were indicated as materials properties. In the last two case, after the films were treated by enzymatic degradation (deg) and/or light irradiation (light), tensile tests were carried out. The R 2 and r correspond to coefficient of determination and correlation coefficient, respectively. The train and test mean the predicted values for train and test data, respectively. The ‘denoised’ and ‘no denoise ’indicate the relaxation curves with and without denoising, respectively. ‘latent’ in r latent-property is the GAP values with highest correlation coefficient to the properties. Properties r enzyme Strain at break Young's modulus - - deg light deg+ light - deg light deg+ light label Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 R 2 train, denoised 0.964 0.935 0.898 0.928 0.937 0.923 0.897 0.829 0.922 R 2 test, denoised 0.927 0.618 0.649 0.872 0.601 0.616 0.472 -1.171 0.518 R 2 train, no denoise 0.941 0.923 0.915 0.926 0.931 0.923 0.903 0.842 0.925 R 2 test, no denoise 0.561 0.123 0.408 0.410 0.413 0.553 0.541 -0.515 0.489 r l atent -properties 0.510 0.428 0.569 0.515 0.514 0.617 0.572 0.341 0.662 The important time regions in relaxation curves, before and after denoising, were evaluated using feature Importance of RFR. In the case of prediction of Y1, the feature importance from the denoising curve is high around the 0.1 ~ 0.15 msec region, while that without denoising shows localized distributions (Fig. 5). The feature Importance distributions for other properties showed a similar trend (Figs. S9 and S10). While the averaging of multiple weak decision trees in RFR provides robustness to noise, the result of RFR were affected by the noise. These results consistently show the improvements in RFR performance due to noise removal by CNN. Since RFR is one of the effective approaches to NMR analysis 21,34–36 , the improved performance and interpretability achieved through denoising could assist in extracting effective descriptors from relaxation curves for property prediction. The features of the relaxation curves were also extracted from latent space in CNN. In the current study, the global average pooling (GAP) layer was treated as the latent space in denoising CNN model (Fig. S3). The correlation coefficients between each node values of GAP layers (GAP values) and each physical properties were calculated, and the one latent space with the strongest correlation with each material property was identified (Table 1, r latent-properties ). A notable correlation was observed for all properties except Y8, consistent with the poor RFR prediction accuracy for that property (Fig. 4a). Linear relationships between the GAP values and material properties were identified, as shown in Fig. 6a-b. These correlations suggest that the latent space of the CNN denoising model extract the information of dynamics, which related to the property. In addition, clusters corresponding to the crysallization temperature were observed in the scatter plot (Figs 6 and S10), suggesting the extraction of crystal structure information from the relaxation curves in the latent space. These results indicate the effectiveness of the noise reduction model in extracting features from the relaxation curves. It has been pointed out that material properties of polymers can correspond to the latent space of neural networks 28,37 . Attempts have been made to analyze correspondence between latent space and glass transition temperature, to visualize the latent space by PCA analysis, and to map the polymer properties to the properties using RFR 37–40 . In these attempts, training data are generally expressed as strings in SMILES format, etc., to construct large-scale chemical language models. In contrast, our study used lightweight training dataset with 310 data points and artificial 50,000 numbers of mimic relaxation curves, to form polymer fingerprints corresponding to various physical properties of mechanical strength and biodegradability before and after degradation. Since the relaxation curve shape reflects the physical and chemical state of the nucleus, the approach using pattern recognition architecture may lead to essential and efficient information extraction. Visualization of important regions from relaxation curves using machine learning has been attempted by Okada et al. 21 , but this study extends this approach by synthesizing variables that correspond linearly to physical properties from the relaxation curves to construct effective indicators as objective variables in the material properties. Each latent space in the encoder-decoder structure include any information in input and/or output data, which can be dealt with important feature in the original dimentsion. We therefore visualized the feature maps in the last convolutional layers corresponding to the selected GAP latent variables. Fig. 7 the feature maps corresponding to the GAP variables highly correlated with Y1 and Y9. Since the GAP value is calculated as the average of the feature maps, regions with large absolute values in the feature maps are considered to be regions with a strong contribution to the latent space-material property correspondence representing important patterns of the input data 41 . The regions in the relatively early relaxation time were recognized as the important regins in the relaxation curve (Figs. 7 and S11). This behavior showed a different tendency for the feature importance of RFR (Fig. 5b). Because the kernel in CNN is suitable to extract the information in attenuation of the relaxation curve, more fluctuated regions were recognized as the important descriptors of low-field NMR for the properties. Generally, the entire latent space is often targeted as a black box in model validation ,as seen in teqniques such as in Grad-CAM or non-linear analysis 39,42,43 . On the other hand, in this study, by calculating the correlation of properties for each latent space and specifying the latent space corresponding to the properties, the feature map was visualized as a heat map highlighting the regions with strong influence on that property. We then performed BO using the latent space to identify effective process conditions. The BO is an algorithm that finds the x that y maximizes for an unknown function y=f(x) with a small number of trials, and it is widely applied in the process of searching for conditions to optimize material properties. To evaluate the contribution of the latent space to the optimization of the molding process, optimizations of the crystallization conditions with GAP values as the objective variable was performed, along with Bayesian optimization for conventional material properties and random search for comparisons. In order to reduce the influence of randomness on the interpretation of the results, a series of optimization processes were performed 200 times for each property. In the most cases, the BO for GAP values and material properties showed higher performances compared with the random searches (Figs. 8 and S12). The number of trials required to achieve 80% of the maximum value of a property was tested for significant differences between the optimization processes, and the magnitude of the difference in the number of trials was determined numerically using Cohen's d (Table 2). BO using GAP values significantly outperformed random search for Y6~Y9, and Cohen's d also indicated a high-performance difference. The only other case of Y1 showed slightly worse performance than the random search, resulting in Cohen's d of -0.2389, suggesting that the effect was small. The comparison of optimization from physical properties and optimization from GAP also showed no significant difference for Y1~Y5 and Y8, while optimization from GAP had a weaker effect than optimization from physical properties for Y6 and Y9, and a moderate effect for Y7. Overall, BO using latent-space objectives achieved improvements comparable to those achieved by conventional BO using actual property values, and both approaches performed better than random search. Previous studies include Bayesian optimization of the degradability of polylactic acid using NMR spectral data as the objective variable 44 , materials property optimization combining evaluation of physical properties by a neural network that has been pre-trained with a large amount of real data and candidate submission by a genetic algorithm 45 , and data derived from biological samples. The correspondence between latent space and qualitative scores of image classification models of biological samples has been studied 46 . Our study combines elements of these approaches, emphasizing both the use of readily obtainable experimental data and the ease of constructing an analytical model. The denoising model can be easily trained with artificial data, and once trained, its latent space encodes material property information extracted from measured low-field NMR data. It was shown that Bayesian optimization using the latent space can optimize various properties of polymers as well as real data, suggesting the feasibility of a property optimization process based on data that can be obtained more quickly and inexpensively than before. Table 2 . Statical test to confirm difference in Bayesian optimization and random search. The random search (Random), property optimization (Pro. opt.) and GAP optimization (GAP opt.) were compared by t-test (p-value) and Cohen’s d. Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Random vs Pro. opt. p- value 0.023 0.041 0.183 0.002 0.085 < 0.001 < 0.001 0.052 < 0.001 Cohen's d -0.228 0.205 0.133 0.328 0.173 1.332 0.751 0.195 0.730 Random vs GAP opt. p-value 0.017 0.135 0.245 0.082 0.051 < 0.001 < 0.001 < 0.001 < 0.001 Cohen's d -0.239 0.150 0.116 0.175 0.196 1.066 1.345 0.339 0.585 Pro. opt. vs GAP opt. p- value 0.991 0.561 0.183 0.068 0.716 0.001 < 0.001 0.163 0.123 Cohen's d 0.001 -0.058 -0.015 -0.183 0.036 -0.323 0.510 0.140 -0.154 This study demonstrates the feasibility of using a CNN latent space obtained from a denoising task, instead of direct material property values, for optimizing biodegradable polymer processing. The denoising model developed in this study removed noise components from the signal and visualized small differences in the relaxation curves reflecting molecular dynamics. Noise removal also improved the accuracy of property regression and contributed to the visualization of important components. Furthermore, the specific latent space that correlate with material properties were identified among many latent spaces of the denoised model, suggesting the possibility of extracting information relating to material properties of biodegradable polymers. BO using these latent features as the objective variable for optimizing molding conditions showed performance comparable to using actual measured properties as the objective. Hence, this method is applicable to optimize the material design of biodegradable polymers without high experimental costs of degradations. The application of the noise reduction model to the optimization of material properties in this study suggests the feasibility of a material property optimization process that omits the process of obtaining material properties. Since relaxation curves reflect molecular dynamics of polymers, some latent spaces in the denoising model linearly correlated with the material property. This may enable the integrated replacement of multiple measurements for material properties with simple and high-throughput low-field NMR measurements, which is expected to contribute to the efficiency of material property optimization. In general, noise reduction models can be created relatively easily by constructing data sets by creating artificial data using random numbers or by adding white noise to measured data. Thus, this method is useful for the materials with high experimental costs to evaluate the properties. Furthermore, noise reduction models have the potential to extract effective features form wide range of NMR measurement such as solution NMR, which extracts exhaustive information at frequencies that reflect the exhaustive information of the chemicals and materials as well as low-field NMR 47,48 . Thus, the latent space utilization of the noise reduction model treated in this study is expected to be applied to diverse fields not limited to polymers and low-field NMR. METHODS Molding of polylactic acid and evaluation of material properties Poly lactic acid pellets were obtained by TEIJIN LIMITTED. After melting pellets of polylactic acid at 200 °C, isothermal crystallizations were carried out using hot press machine (Imoto Machinery CO., Ltd.) in sixty-four different molding conditions corresponding to all combinations by changing each condition one by one, with crystallization temperatures of 75, 90, 105, 120 °C, crystallization times of 5, 10, 20, and 40 minutes, and nucleating agent concentrations of 0, 0.167, 0.5, and 1.5%. The molding conditions of the polylactic acid are summarized in Table S1. The obtained films were subjected to three types of treatments: enzymatic degradation, light irradiation, and enzymatic degradation plus light irradiation. The strain at break and Young's modulus were obtained by uniaxial elongation a tensile-testing machine (Imoto Machinery CO., Ltd.) at 10 mm/min and room temperature with the dumbbell-shape of a 2 ´ 12 mm 2 . Enzymatic degradation rates were carried out by immersing the films in Proteinase K solution (1 mg/mL, 1 mL, pH 7.4) for 2 d at 37 °C. The degradation rate ( r enzyme ) was calculated from the weights of the film before and after degradation ( w before and w after , respectively) as: r enzyme = w after / w before . Low-field NMR measurement Sheets of polylactic acid films were cut to 1 cm height and placed in a 10 mm tube for low-field NMR measurements (Bruker mq20 Minispec, Milton, ON, Canada). A Magic Sandwich Echo (MSE) was used for pulse sequencing. Relaxation curves of low-field NMR measurements were obtained at 25 °C for each sample before degradation treatment. The relaxation curves were normalized by dividing them by the maximum intensity. Convolutional neural network (CNN) The CNN model was constructed by artificial data of relaxation curves, and used to denoise the experimental data, where the GAP values were obtained as values in latent spaces. As the artificial data, relaxation curves were randomly obtained by sampling from three exponential curves with T 2 parameters in the range of (0.0200,0.035), (0.031,0.07), (0.07,0.145), (0.145,0.195), respectively with Weibull coefficients in the range of 1~2 for the component with the shortest T 2 among the four components. The structure of CNN was indicated in Fig. S4. The noise-added relaxation curves were inputted in CNN to train for minimizing the squared error between the output and the curve before adding the noise. The mean squared error between the artificial curve before adding the noise and the curve generated by the CNN model during training was estimated to be 3.96 × 10 -6 and 3.33 × 10 -6 for train data and test data, respectively, indicating high noise-rejection performance of the model for the dataset. Random forest regressor (RFR) RFR was constructed using scikit-learn library (1.5.2) 49 in Python language with the number of trees as 300, fixed seed and dividing the data set into 70% train data and 30% test data. The explanatory variables were 310 data points of the relaxation curve of low-field NMR, and the objective variable was one of the material properties Y1-Y9. Default values were used for the hyperparameters except for the number of trees. The feature importance of RFR in NMR relaxation curves were obtained by feature_importances_ functions. Bayesian optimization Python library Bayesian-optimization (2.0.3) was used to implement Bayesian optimization, and hyperparameters were set to default values. BO was carried out for two types of objectives: (1) each material property Y1–Y9, and (2) the single GAP latent variable most strongly correlated with each property (selected from 256 candidates).The explanatory variable in both cases was the molding condition. A random search was also performed as a control by randomly choosing molding conditions to check whether the optimization algorithm works effectively. All optimization processes, including random search, were run 200 times in each property to make sure optimization performance without randomness by bootstrap sampling or sampling with replacement from the original dataset. BO and random search are performed in real number space. However, since the molding conditions of real data are discrete, when the model actually specifies the molding conditions in the search process, the explanatory variable of the sample molded with the closest conditions was selected. Declarations DATA AVAILABILITY All data and code used in this study is publicly available. The datasets and source code be accessed on GitHub (URL: https://github.com/neko166/Python-Code-for-NMR-denoising-and-analysis/tree/main) . ACKNOWLEDGEMENTS We would like to express our gratitude to Yuuri Tsuboi (RIKEN), for her contribution to the acquisition of NMR Relaxation data. CREATIVE COMMONS Open Access This airticle is licenced under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptaion, distribution, reproduction in any medium or format, as long as you give appropriate credit to the oridinal authors and the source provide a link to the Creative Commons license, and indicated if change were made. The image or other third party material in this article are included in the airticle’s Creative Commons license, unless indicated otherwisein a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit URL AUTHOR CONTRIBUTIONS Y.A. performed the experiments. R.F. analyzed the data. J.K. supervised the research. R.F. drafted the manuscript, and the others reviewed it. COMPETING INTERESTS The authors declare no competing interests. References Mohanty, A. K. et al. Sustainable polymers. Nature Reviews Methods Primers 2 , 46 (2022). Gbadeyan, O. J., Linganiso, L. Z. & Deenadayalu, N. Thermomechanical characterization of bioplastic films produced using a combination of polylactic acid and bionano calcium carbonate. Sci Rep 12 , 15538 (2022). Guicherd, M. et al. An engineered enzyme embedded into PLA to make self-biodegradable plastic. Nature 631 , 884–890 (2024). Samir, A., Ashour, F. H., Hakim, A. A. A. & Bassyouni, M. Recent advances in biodegradable polymers for sustainable applications. npj Materials Degradation vol. 6 68 Preprint at https://doi.org/10.1038/s41529-022-00277-7 (2022). Diwale, S. et al. Bayesian optimization for material discovery processes with noise. Mol Syst Des Eng 7 , 622–636 (2022). Noguchi, S. & Inoue, J. Bayesian inverse inference of material properties from microstructure images. Comput Mater Sci 245 , 113306 (2024). Ramprasad, R., Batra, R., Pilania, G., Mannodi-Kanakkithodi, A. & Kim, C. Machine learning in materials informatics: Recent applications and prospects. npj Computational Materials vol. 3 54 Preprint at https://doi.org/10.1038/s41524-017-0056-5 (2017). Chitturi, S. R. et al. Targeted materials discovery using Bayesian algorithm execution. NPJ Comput Mater 10 , 156 (2024). Herbol, H. C., Poloczek, M. & Clancy, P. Cost-effective materials discovery: Bayesian optimization across multiple information sources. Mater Horiz 7 , 2113–2123 (2020). Pai, S. M. et al. Machine learning applied to the design and optimization of polymeric materials: A review. Next Materials 7 , 100449 (2025). Patra, T. K. Data-Driven Methods for Accelerating Polymer Design. ACS Polymers Au 2 , 8–26 (2022). Amamoto, Y. Data-driven approaches for structure-property relationships in polymer science for prediction and understanding. Polymer Journal vol. 54 957–967 Preprint at https://doi.org/10.1038/s41428-022-00648-6 (2022). Fukazawa, T., Ikegami, T., Kawata, M. & Miyake, T. Materials Secure Computation with Secret Sharing: A Bayesian Optimization Scheme and Its Performance. J Physical Soc Japan 94 , 013801 (2025). Luo, S. H. et al. A machine learning framework for low-field NMR data processing. Pet Sci 19 , 581–593 (2022). Luo, G., Xiao, L., Luo, S., Liao, G. & Shao, R. A study on multi-exponential inversion of nuclear magnetic resonance relaxation data using deep learning. Journal of Magnetic Resonance 346 , 107358 (2023). Nakashima, Y. & Shiba, N. Nondestructive measurement of intramuscular fat content of fresh beef meat by a hand-held magnetic resonance sensor. Int J Food Prop 24 , 1722–1736 (2021). da Silva Ruiz, N. M. et al. Time domain NMR evaluation of thermal and thermochemical aging of nitrile rubber on crosslinking and mechanical properties. Polym Degrad Stab 224 , 110727 (2024). B. Blu¨ mich, S. A. K. K. S. S. V. H. and A. S. Unilateral Nuclear Magnetic Resonance for Quality Control: The NMR-MOUSE. Spectroscopy 18 , 24–54 (2003). Yamada, S., Kurotani, A., Chikayama, E. & Kikuchi, J. Signal deconvolution and noise factor analysis based on a combination of time–frequency analysis and probabilistic sparse matrix factorization. Int J Mol Sci 21 , 2978 (2020). Besghini, D., Mauri, M. & Simonutti, R. Time domain NMR in polymer science: From the laboratory to the industry. Applied Sciences (Switzerland) vol. 9 1801 Preprint at https://doi.org/10.3390/app9091801 (2019). Okada, M., Amamoto, Y. & Kikuchi, J. Designing Sustainable Hydrophilic Interfaces via Feature Selection from Molecular Descriptors and Time-Domain Nuclear Magnetic Resonance Relaxation Curves. Polymers (Basel) 16 , 824 (2024). Matlahov, I. & van der Wel, P. C. A. Hidden motions and motion-induced invisibility: Dynamics-based spectral editing in solid-state NMR. Methods vol. 148 123–135 Preprint at https://doi.org/10.1016/j.ymeth.2018.04.015 (2018). Hara, K., Yamada, S., Kurotani, A., Chikayama, E. & Kikuchi, J. Materials informatics approach using domain modelling for exploring structure–property relationships of polymers. Sci Rep 12 , 10558 (2022). Srikanth, M., Sandeep, T. S. R. S., Sucharitha, K. & Godi, S. Biodegradation of plastic polymers by fungi: a brief review. Bioresources and Bioprocessing vol. 9 42 Preprint at https://doi.org/10.1186/s40643-022-00532-4 (2022). Mierzwa-Hersztek, M., Gondek, K. & Kopeć, M. Degradation of Polyethylene and Biocomponent-Derived Polymer Materials: An Overview. J Polym Environ 27 , 600–611 (2019). Plota, A. & Masek, A. Lifetime prediction methods for degradable polymeric materials—a short review. Materials vol. 13 1–25 Preprint at https://doi.org/10.3390/ma13204507 (2020). Zhou, Z. et al. A machine learning model for textured X-ray scattering and diffraction image denoising. NPJ Comput Mater 9 , 58 (2023). Gómez-Bombarelli, R. et al. Automatic Chemical Design Using a Data-Driven Continuous Representation of Molecules. ACS Cent Sci 4 , 268–276 (2018). Ma, B. et al. Effect of poly(lactic acid) crystallization on its mechanical and heat resistance performances. Polymer (Guildf) 212 , 123280 (2021). Hu, J., Shen, L., Albanie, S., Sun, G. & Wu, E. Squeeze-and-Excitation Networks. (2017). He, K., Zhang, X., Ren, S. & Sun, J. Deep Residual Learning for Image Recognition. (2015). Wang, J. et al. Estimating the Relative Crystallinity of Biodegradable Polylactic Acid and Polyglycolide Polymer Composites by Machine Learning Methodologies. Polymers (Basel) 14 , 527 (2022). Omigbodun, F. T., Osa-Uwagboe, N., Udu, A. G. & Oladapo, B. I. Leveraging Machine Learning for Optimized Mechanical Properties and 3D Printing of PLA/cHAP for Bone Implant. Biomimetics 9 , 587 (2024). Yamada, S., Tsuboi, Y., Yokoyama, D. & Kikuchi, J. Polymer composition optimization approach based on feature extraction of bound and free water using time-domain nuclear magnetic resonance. Journal of Magnetic Resonance 351 , 107438 (2023). Takamura, A., Tsukamoto, K., Sakata, K. & Kikuchi, J. Integrative measurement analysis via machine learning descriptor selection for investigating physical properties of biopolymers in hairs. Sci Rep 11 , 24359 (2021). Leniak, A., Pietruś, W., Świderska, A. & Kurczab, R. From NMR to AI: Do We Need 1H NMR Experimental Spectra to Obtain High-Quality logD Prediction Models? J Chem Inf Model 65 , 2924–2939 (2025). Casado, U. M., Altuna, F. I. & Miccio, L. A. Towards Sustainable Material Design: A Comparative Analysis of Latent Space Representations in AI Models. Sustainability (Switzerland) 16 , 10681 (2024). Kuenneth, C. & Ramprasad, R. polyBERT: a chemical language model to enable fully machine-driven ultrafast polymer informatics. Nat Commun 14 , 4099 (2023). Gurnani, R. et al. PolyG2G: A Novel Machine Learning Algorithm Applied to the Generative Design of Polymer Dielectrics. Chemistry of Materials 33 , 7008–7016 (2021). Hu, J., Li, Z., Lin, J. & Zhang, L. Prediction and Interpretability of Glass Transition Temperature of Homopolymers by Data-Augmented Graph Convolutional Neural Networks. ACS Appl Mater Interfaces 15 , 54006–54017 (2023). Azam, S. et al. Using feature maps to unpack the CNN ‘Black box’ theory with two medical datasets of different modality. Intelligent Systems with Applications 18 , 200233 (2023). Batra, R. et al. Polymers for Extreme Conditions Designed Using Syntax-Directed Variational Autoencoders. Chemistry of Materials 32 , 10489–10500 (2020). Szandała, T. Unlocking the black box of CNNs: Visualising the decision-making process with PRISM. Inf Sci (N Y) 642 , 119162 (2023). Yamawaki, R., Tei, A., Ito, K. & Kikuchi, J. Decomposition factor analysis based on virtual experiments throughout bayesian optimization for compost-degradable polymers. Applied Sciences (Switzerland) 11 , 2820 (2021). Atasi, C., Kern, J. & Ramprasad, R. Design of Recyclable Plastics with Machine Learning and Genetic Algorithm. J Chem Inf Model 64 , 9249–9259 (2024). Rotem, O. et al. Visual interpretability of image-based classification models by generative latent space disentanglement applied to in vitro fertilization. Nat Commun 15 , 7390 (2024). Asakura, T., Date, Y. & Kikuchi, J. Application of ensemble deep neural network to metabolomics studies. Anal Chim Acta 1037 , 230–236 (2018). Date, Y. & Kikuchi, J. Application of a Deep Neural Network to Metabolomics Studies and Its Performance in Determining Important Variables. Anal Chem 90 , 1805–1810 (2018). Pedregosa FABIANPEDREGOSA, F. et al. Scikit-Learn: Machine Learning in Python Gaël Varoquaux Bertrand Thirion Vincent Dubourg Alexandre Passos PEDREGOSA, VAROQUAUX, GRAMFORT ET AL. Matthieu Perrot . Journal of Machine Learning Research vol. 12 http://scikit-learn.sourceforge.net. (2011). Additional Declarations No competing interests reported. Supplementary Files Supplimentalinformation.docx Cite Share Download PDF Status: Published Journal Publication published 18 Jun, 2025 Read the published version in npj Materials Degradation → Version 1 posted Editorial decision: Revision requested 24 Apr, 2025 Reviews received at journal 23 Apr, 2025 Reviews received at journal 16 Apr, 2025 Reviewers agreed at journal 05 Apr, 2025 Reviewers agreed at journal 04 Apr, 2025 Reviewers invited by journal 04 Apr, 2025 Editor assigned by journal 03 Apr, 2025 Submission checks completed at journal 03 Apr, 2025 First submitted to journal 02 Apr, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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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-6364337","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":447295298,"identity":"974a29e8-0364-425f-8080-564aec5115a3","order_by":0,"name":"Ryo Fujita","email":"","orcid":"","institution":"Yokohama City University","correspondingAuthor":false,"prefix":"","firstName":"Ryo","middleName":"","lastName":"Fujita","suffix":""},{"id":447295299,"identity":"704a28ff-0975-4822-9688-e59cbbe4cf48","order_by":1,"name":"Yoshifumi Amamoto","email":"","orcid":"","institution":"RIKEN Center for Sustainable Resource Science","correspondingAuthor":false,"prefix":"","firstName":"Yoshifumi","middleName":"","lastName":"Amamoto","suffix":""},{"id":447295300,"identity":"de07a5b3-ac59-4d9a-a85a-7ad36b7bab14","order_by":2,"name":"Jun Kikuchi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2klEQVRIiWNgGAWjYBACxgYQNkhgYJBgbHzAAGIwMCQQraXZgCgtUG0gLQxsEsSoZmCekXuAcUZBWmL/7Oa26oqCNDlzBoZnD/DaMCMvgXGDQU7ijDsH226eMcgxtmxgSDfAryXHgPGBQUXiBonEtpsNIMYBhjQJorUUArXUE6cF5DCQFmDQ5SQYENTS88bg4AyDNOMZNxKbJRsM0gw3HCbgF8P2HMOHPX+SZftnpD/82PAnWd7geE/aA7xaGhgYDqAKMfOk4dPBII9FjP0YXi2jYBSMglEw4gAAp19ONNGnUyQAAAAASUVORK5CYII=","orcid":"","institution":"RIKEN Center for Sustainable Resource Science","correspondingAuthor":true,"prefix":"","firstName":"Jun","middleName":"","lastName":"Kikuchi","suffix":""}],"badges":[],"createdAt":"2025-04-02 22:08:10","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6364337/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6364337/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41529-025-00613-7","type":"published","date":"2025-06-18T15:57:10+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":81373027,"identity":"b4f4cd6d-eed8-46c4-a9ff-714938a20e96","added_by":"auto","created_at":"2025-04-25 10:54:30","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":364581,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDesign of the current research. \u003c/strong\u003e(a) Polymer dynamics influences low-field NMR curves, which can be useful for process optimization. (b) A CNN denoising model encodes features of low-field NMR curves relating to polymer dynamics, which is useful for process optimization along with outputting denoised curves. (\u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e:\u003cstrong\u003e \u003c/strong\u003eCrystallize temperature, \u003cem\u003et\u003c/em\u003e\u003csub\u003ecryst\u003c/sub\u003e:\u003cstrong\u003e\u0026nbsp; \u003c/strong\u003ecrystallization time, \u003cem\u003eC\u003c/em\u003e\u003csub\u003eNA\u003c/sub\u003e: Concentration of nucleating agents.)\u003c/p\u003e","description":"","filename":"Fig1.png","url":"https://assets-eu.researchsquare.com/files/rs-6364337/v1/89ef6c21ed1d51cdc7385fe4.png"},{"id":81373452,"identity":"b01dfd64-7920-4c2e-9284-ae298ddf43fd","added_by":"auto","created_at":"2025-04-25 11:02:30","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":784692,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eLow-field NMR Relaxation curves of polylactic acid with different process conditions. \u003c/strong\u003e(a-b) Relaxation curve before denoising in (a) real number scale and (b) log scale. Vertical scale “\u003cem\u003e\u003cstrong\u003eR\u003c/strong\u003e\u003c/em\u003e” represent Relaxation Rate. Polylactic acids were crystallized with different crystallization temperatures, crystallization times, and concentrations of nucleating agents. The colors correspond to crystallization temperatures at 75 °C (blue), 90 °C (green), 105 °C (orange), and 120 °C (red).\u003c/p\u003e","description":"","filename":"Fig2.png","url":"https://assets-eu.researchsquare.com/files/rs-6364337/v1/db753f74cca56be977efe83d.png"},{"id":81373037,"identity":"44bd0feb-a278-4f1f-ac1b-102ea65efbc0","added_by":"auto","created_at":"2025-04-25 10:54:31","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":512404,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eLow-field NMR relaxation curves after CNN denoising. \u003c/strong\u003eRelaxation curve of polylactic acid with different crystallization conditions after denoising in real number scale and (b) log scale. The colors correspond to crystallization temperatures at 75 °C (blue), 90 °C (green), 105 °C (orange), and 120 °C (red).\u003c/p\u003e","description":"","filename":"Fig3.png","url":"https://assets-eu.researchsquare.com/files/rs-6364337/v1/32dcec161fa03f1cc60477c4.png"},{"id":81373030,"identity":"4d8ab739-dc22-4ebc-b5b6-2902ba6658b1","added_by":"auto","created_at":"2025-04-25 10:54:31","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":681294,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePrediction of property from low-field NMR curves by random forest regression (RFR). \u003c/strong\u003e(a-b) Root mean squared error (RMSE) of predicted properties using raw (left bar) and denoised (right bar) NMR relaxation curves for (a) train data and (b) test data, (c-d) Parity Plot of Y1 using (c) denoising and raw NMR relaxation curves. Vertical and horizontal axis correspond to predicted values and actual values, respectively. If the predicted and actual values are close, the plots are aligned on the diagonal in the Parity Plot. Color of the bar and plots correspond to train data with denoising curves (blue), test data with denoising curves (orange), train data with raw curves (orange), train data with raw curves (red).\u003c/p\u003e","description":"","filename":"Fig4.png","url":"https://assets-eu.researchsquare.com/files/rs-6364337/v1/d360d2135c9717b4ee37583b.png"},{"id":81373461,"identity":"19834e1d-79d9-47ad-bb4a-e18d9b5451b8","added_by":"auto","created_at":"2025-04-25 11:02:31","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":115364,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFeature importance in NMR relaxation curves estimated by random forest regressors. \u003c/strong\u003e(a-b) Feature importance of the enzyme degradation rate prediction model using (a) the denoising curve, and (b) untreated curve. Vertical axis: Feature Importance, horizontal axis: corresponds to the time axis of the relaxation curve.\u003c/p\u003e","description":"","filename":"Fig5.png","url":"https://assets-eu.researchsquare.com/files/rs-6364337/v1/9e8798fb21f97202c0c0c5e3.png"},{"id":81373457,"identity":"885977f2-7c01-4cb4-826c-2809cddb8970","added_by":"auto","created_at":"2025-04-25 11:02:31","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":267415,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eRelationships between material’s properties and selected GAP values. \u003c/strong\u003e(a) Correspondence between enzymatic degradation rate (Y1) and GAP values. (b) Correspondence between Young's modulus with enzymatic degradation treatments (Y9) and GAP values. The GAP values were selected by the highest correlation coefficients based on absolute values. The colors of the plots correspond to the crystallization temperatures: blue 75 °C, green 90 °C, orange 105 °C, red 120 °C.\u003c/p\u003e","description":"","filename":"Fig7.png","url":"https://assets-eu.researchsquare.com/files/rs-6364337/v1/62a13f69bb4a61d6c2f90327.png"},{"id":81373055,"identity":"64eac1e4-35a3-46d7-9c2c-19c5612bf92d","added_by":"auto","created_at":"2025-04-25 10:54:31","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":279218,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFeature maps in CNN correlating to Y1, and Y9. \u003c/strong\u003e(a-b) Feature maps in CNN for the NMR relaxation curves with (a) the biodegradability (Y1) and (b) Young's modulus with treatments (Y9) for polylactic acid. Vertical axis: sample number, Horizontal axis: time axis of the relaxation curves. The GAP values were selected by the highest correlation coefficients among the relationships between several GAP values and objective properties based on absolute values.\u003c/p\u003e","description":"","filename":"Fig6.png","url":"https://assets-eu.researchsquare.com/files/rs-6364337/v1/3282835bc2ee28aa3d4fa07b.png"},{"id":81373462,"identity":"e8cac1e9-7b08-41de-8b1b-927c58cfcc33","added_by":"auto","created_at":"2025-04-25 11:02:31","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":411716,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eBayesian optimization (BO) of Y9 with GAP as latent space as the objective variable. \u003c/strong\u003eBO was carried out by optimization of process conditions for GAP values with number of trials. The results in vertical axis were plotted as property values (Y9) instead of GAP values. The bootstrap sampling or the resampling with replacement from the original dataset was carried out. Blue: direct Bayesian optimization for properties, Orange: Bayesian optimization for GAP values correlated with properties, Green: random search, Black: maximum properties, Gray: 80% line of maximum properties.\u003c/p\u003e","description":"","filename":"Fig8.png","url":"https://assets-eu.researchsquare.com/files/rs-6364337/v1/db0bff557e936c846ab21435.png"},{"id":85231630,"identity":"87b58797-a9a0-4b2f-a536-799af7139a7c","added_by":"auto","created_at":"2025-06-23 16:09:22","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4320788,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6364337/v1/b0aaf5f5-efb2-49c6-aab8-affba9a2d2fb.pdf"},{"id":81373065,"identity":"158d1fa5-01cb-4ac6-b598-4026aedfc538","added_by":"auto","created_at":"2025-04-25 10:54:32","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":20989740,"visible":true,"origin":"","legend":"","description":"","filename":"Supplimentalinformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-6364337/v1/b18b99c81293dc14dca708d4.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Bayesian Optimization of Biodegradable Polymers via Machine Learning Driven Features from Low-Field NMR Data","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eIn recent years, several approaches (e.g., establishing resource recycling systems and using biomass as an alternative to petroleum) have been attracting attention in efforts to develop a sustainable society \u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. Among these, research and development of biodegradable polymers is regarded as a key strategy for societal implementation \u003csup\u003e\u003cspan additionalcitationids=\"CR3\" citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. To expand the use of biodegradable polymers in recycling processes, it is necessary to examine material properties such as degradability and mechanical strength after degradation for specific applications. However, since degradation tests of biodegradable polymers require many days, there is concern that conventional trial-and-error processes based on empirical rules may prolong material development t\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eIn materials development, efficient property optimization approaches utilizing machine learning to handle complex polymer systems have drawn attention in recent years \u003csup\u003e\u003cspan additionalcitationids=\"CR7 CR8\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e. Such reverse-design approaches may be effective for biodegradable materials as well. Because polymer properties are influenced by a wide variety of factors, it is difficult to formulate explicit relationships between chemical structure or molding conditions and the resulting properties\u003csup\u003e\u003cspan additionalcitationids=\"CR11\" citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e. Traditionally, optimizing material properties has required exhaustive prototyping, measurement of properties, and identification of important factors based on empirical rules. On the other hand, Bayesian optimization (BO) is one of the important methods in materials informatics used to search for processing conditions that optimize material properties with a small number of trials\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e,\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e,\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e,\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e. However, as noted above, in the case of biodegradable polymers, degradation tests are time-consuming, making it difficult to apply an iterative BO process.\u003c/p\u003e \u003cp\u003eLow-field NMR is a convenient tool that has been used in various fields, such as oil logging \u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e,\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e, food analysis \u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e, rubber quality control \u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e and studies of polymer molecular mobility. The relaxation curves obtained by low-field NMR provide comprehensive information on material properties derived from molecular motion and higher-order structure \u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e, and this technique is widely used in materials research \u003csup\u003e\u003cspan additionalcitationids=\"CR21 CR22\" citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. Among several pulse sequencing, Magic Sandwich Echo (MSE) pulse sequencing can acquire a wide range of higher-order structural information along with dynamics from the rigid to mobile regions. In the case of biodegradable polymers, crystalline regions of polymers with densely folded molecular chains have low molecular mobility and exhibits fast NMR relaxation (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea colored with blue), strongly corresponding with stiffness. Interface regions exhibit medium molecular mobility and NMR relaxation (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea colored with purple). Non-crystalline regions where molecular chains are relatively weakly folded have high molecular mobility and exhibits slow NMR relaxation (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea colored with red), strongly corresponding with toughness and degradability (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea, left). Various physical properties, such as mechanical strength and biodegradability, are known to correspond to the molecular structure of polymers \u003csup\u003e\u003cspan additionalcitationids=\"CR25\" citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e. Therefore, comprehensive molecular-structure data(molecular-structural dataの方がいい༟) may contain descriptors for a wide variety of properties. Descriptors constructed from the dynamics of these molecular structures may provide an efficient trial-and-error approach to targeting(discovering?) promising materials. One of remaining tasks is how to obtain the superior dynamics descriptors when the relaxation curves include the noises, especially when the measurement time is limited or the difference between the relaxation curves are small.\u003c/p\u003e \u003cp\u003eConvolutional neural network (CNN) is one of suitable ways to denoise the measurement data along with obtaining the features from input data. The convolutional layers in CNN catch the feature in local regions and subsequent hierarchically spatial structure. Therefore, CNN have been applied for denoising of various measurement data such as NMR, X-ray scattering data, and so on\u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e, using autoencoder types models consisting of encoder and decoder. The encoder layer extracts information by convolution and projects it into a low-dimensional space called the latent space, while the decoder layer forms a denoising curve based on the information from latent space. The representation in the latent space is derived from the abstraction of the input data, which is information on molecular structure and material properties and can be extracted to apply the material design. \u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e. Although CNNs are an effective method for one-dimensional time series data such as relaxation curves and are expected to provide effective noise reduction, to the best of our knowledge, there have been no reports of applying BO in the latent space of relaxation curves obtained from low-field NMR measurements.\u003c/p\u003e \u003cp\u003eIn this study, we demonstrate that, instead of using material properties as the objective variable, the latent space in the denoising CNN model of relaxation curves from low-field NMR can be used for Bayesian optimization (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea). The CNN denoising model achieves to distinguish even small difference in the relaxation curves of polylactic acid obtained by different molding conditions. The latent space features that most strongly correlated with the properties were used to visualize the important time regions in the relaxation curves and to optimize the process conditions (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb). Since the relaxation curves used in this denoising task can be obtained in 30 minutes to 1 hour of low-field NMR measurements, this method may provide a framework to speed up polymer understanding and design by optimizing process conditions and acquiring important dynamics information (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb).\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"RESULTS AND DISCUSSION","content":"\u003cp\u003eIn this study, polylactic acid (PLA) was utilized as a representative biodegradable polymer. Sixty-four different films were prepared by changing molding or crystallization conditions of crystallization temperature (75 \u0026deg;C\u0026ndash;120 \u0026deg;C), crystallization time (5 min\u0026ndash;40 min), and nucleating agent concentration (0wt%\u0026ndash;1.5wt%) of PLA (Table S1). These factors affect the molecular structure and properties of polymers. For example, Ma et al. demonstrated that crystallization temperature (100 \u0026deg;C\u0026ndash;130 \u0026deg;C) influences the crystallinity, tensile strength, and molecular structure of PLA \u003csup\u003e29\u003c/sup\u003e. Therefore, it can be assumed that differences in the molding conditions of the samples prepared in this study will cause variations in the propriety and molecular structure of the polylactic acid film. The wide ranges of crystal structures, from almost amorphous to high degree of crystallinity, were confirmed in X-ray scattering/diffraction measurement and polarized optical microscopic observations (Fig. S1). Low-field NMR measurements were carried out to evaluate the chain dynamics of PLA, and enzymatic degradation tests and tensile tests were conducted to obtain mechanical properties. Low-field NMR captures changes in molecular mobility associated with differences in the polymer\u0026rsquo;s higher-order structure and state. In particular, using the MSE pulse sequence, the shape of the relaxation curve in the sub-millisecond time domain can be interpreted in terms of contributions from crystalline, intermediate, and non-crystalline regions. The low-field NMR relaxation curves for all samples are shown in Fig. 2a-b. With increasing the crystallization temperature, the difference in slower relaxation regions in the time after 0.05 ms was seemed to appear, suggesting that the difference in relaxation behavior is derived from the difference in crystalline structure of PLA. These differences were less pronounced when the dependence of nucleating agent concentration and crystallization time was plotted (Figs. S2 and S3). This may be due to the increase in crystal regions of PLA promotes faster \u003cem\u003eT\u003c/em\u003e\u003csub\u003e2\u0026nbsp;\u003c/sub\u003erelaxation, thereby reducing signals from the non-crystalline regions, which exhibit slower T2 relaxation. It should be noted the differencces were hardly observable in real scale, suggesiting the difference of dynamics in amorphos regions of PLA between the samples were lessly observed, because the chain mobility of PLA is frozen at room temperature due to high glass transition temperature (\u003cem\u003eT\u003c/em\u003e\u003csub\u003eg\u003c/sub\u003e ~ 60 \u0026deg;C). Furthermore, the samples crystallized at 90 \u0026deg;C\u0026ndash;120 \u0026deg;C have a high noise level even in log scale, making it difficult to discern the relative magnitudes of the signals.\u003c/p\u003e\n\u003cp\u003eThe relaxation curves were denoised by CNN model. We constructed a custom architecture based on SE-ResNet as shown in Fig. S4\u003csup\u003e\u0026nbsp;30,31\u003c/sup\u003e. Noiseless and noisy artificial data were created to mimic relaxation curves. The CNN model was trained with the artificial relaxation curves with noisy data (input) and denoised data (output). \u0026nbsp;An example of denoising for a simulation curve is shown in Fig. S5. The noises in relaxation curves were reduced through the CNN, indicating the CNN model worked effectively for the denoising task.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAfter training, real data of polylactic acid relaxation curves was inputted for denoising. The denoising for the real data of low-field NMR measurements of PLA by the CNN model was attempted as show in Fig. 3a-b. The denoised curves showed a linear decay on the logarithmic axis in the slow time region, suggesting high noise rejection performance in the measured data. In addition, the separation of the relaxation curves by molding conditions such as crystallization temperature was clearly visualized, suggesting improved interpretability of differences in molecular dynamics between samples. Similarly, the moderate differences in nucleating agent concentration and crystallization time were also distinguishable (Figs. S6 and S7). These results indicate that denoising the relaxation curves even when differences are subtle can assist in correlating relaxation behavior with the crystal structure of PLA. Furthermore, this suggests that the latent representation of the relaxation curves learned by the denoising model may correspond to material property information.\u003c/p\u003e\n\u003cp\u003eThe material properties of PLA were predicted by random forest regression (RFR). As the material properties, enzymatic degradation rates (\u003cem\u003er\u003c/em\u003e\u003csub\u003eenzyme\u003c/sub\u003e), strain at break, and Young\u0026apos;s modulus were evaluated for all films. For strain at break and Young\u0026rsquo;s modulus, the films were pre-treated by enzymatic degradation and/or light irradiation before the tensile tests (Y2-Y9, Table 1). All data points from the relaxation curves (either denoised or raw) were used as explanatory variables, and the property values were used as objective variables. Fig. 4 shows the root mean square error (RMSE) of each property predicted by RFR. The RFR showed a similar RMSE trend for train data with and without noise removal (Fig. 4a). However, the prediction using the test data of the non-denoised curves showed an increase in RMSE, suggesting that the regression performance of the RFR was reduced by noise especially in unseen or test data (Figs. 4c-d and S8). A similar trend was observed in the coefficient of determination \u0026nbsp;(\u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e) for most propertoes (Table 1), indicating that the predictions from the denoised relaxation curves show stable accuracy for both train and test. The improvement of prediction performance of material properties by denoising may be due to the clarification of the difference in relaxation curves by property, as shown in Fig. 3. In other words, noise in the relaxation curves likely caused overfitting on the training data, reducing predictive performance on unseen test data. Although there have been many attempts to predict properties and extract descriptors of polymers \u003csup\u003e23,32,33\u003c/sup\u003e, this study successfully predicted a wide variety of properties while using only low-field NMR relaxation curves as explanatory variables, which are a relatively easy method to obtain the information of chain dynamics as well as higher order sturcutre. Our approach demonstrates the feasibility of a prediction approach of material properties based on simple low-field NMR measurements.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 1\u003c/strong\u003e\u003cstrong\u003e. Kind of material\u0026rsquo;s properties and results on machine learning.\u0026nbsp;\u003c/strong\u003eNine materials properties labelled as Y1-Y9 were evaluated in this study. The enzymatic degradation rate (\u003cem\u003er\u003c/em\u003e\u003csub\u003eenzyme\u003c/sub\u003e), strain at break, and Young\u0026rsquo; modulus were indicated as materials properties. In the last two case, after the films were treated by enzymatic degradation (deg) and/or light irradiation (light), tensile tests were carried out. The \u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e and \u003cem\u003er\u003c/em\u003e correspond to coefficient of determination and correlation coefficient, respectively. The train and test mean the predicted values for train and test data, respectively. The \u0026lsquo;denoised\u0026rsquo; and \u0026lsquo;no denoise \u0026rsquo;indicate the relaxation curves with and without denoising, respectively. \u0026lsquo;latent\u0026rsquo; in \u003cem\u003er\u003c/em\u003e\u003csub\u003elatent-property\u003c/sub\u003e is the GAP values with highest correlation coefficient to the properties.\u0026nbsp;\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" align=\"\" width=\"593\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 68px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"11\" style=\"width: 525px;\"\u003e\n \u003cp\u003eProperties\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" style=\"width: 68px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e\u003cem\u003er\u003c/em\u003e\u003csub\u003eenzyme\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"4\" style=\"width: 219px;\"\u003e\n \u003cp\u003eStrain at break\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"4\" style=\"width: 219px;\"\u003e\n \u003cp\u003eYoung\u0026apos;s modulus\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003edeg\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003elight\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003edeg+\u003c/p\u003e\n \u003cp\u003elight\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003edeg\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003elight\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003edeg+\u003c/p\u003e\n \u003cp\u003elight\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 68px;\"\u003e\n \u003cp\u003elabel\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003eY1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003eY2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003eY3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003eY4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003eY5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003eY6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003eY7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003eY8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003eY9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 68px;\"\u003e\n \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u003csub\u003etrain,\u003c/sub\u003e\u003c/p\u003e\n \u003cp\u003e\u003csub\u003edenoised\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.964\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.935\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.898\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.928\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.937\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.923\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.897\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.829\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.922\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 68px;\"\u003e\n \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u003csub\u003etest,\u003c/sub\u003e\u003c/p\u003e\n \u003cp\u003e\u003csub\u003edenoised\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.927\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.618\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.649\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.872\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.601\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.616\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.472\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e-1.171\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.518\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 68px;\"\u003e\n \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u003csub\u003etrain,\u003c/sub\u003e\u003c/p\u003e\n \u003cp\u003e\u003csub\u003eno denoise\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.941\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.923\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.915\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.926\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.931\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.923\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.903\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.842\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.925\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 68px;\"\u003e\n \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u003csub\u003etest,\u003c/sub\u003e\u003c/p\u003e\n \u003cp\u003e\u003csub\u003eno denoise\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.561\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.123\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.408\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.410\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.413\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.553\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.541\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e-0.515\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.489\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 68px;\"\u003e\n \u003cp\u003e\u003cem\u003er\u003c/em\u003e\u003csub\u003el\u003c/sub\u003e\u003csub\u003eatent\u003c/sub\u003e\u003c/p\u003e\n \u003cp\u003e\u003csub\u003e-properties\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.510\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.428\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.569\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.515\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.514\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.617\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.572\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.341\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 55px;\"\u003e\n \u003cp\u003e0.662\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u0026nbsp;The important time regions in relaxation curves, before and after denoising, were evaluated using feature Importance of RFR. In the case of prediction of Y1, the feature importance from the denoising curve is high around the 0.1 ~ 0.15 msec region, while that without denoising shows localized distributions (Fig. 5). The feature Importance distributions for other properties showed a similar trend (Figs. S9 and S10). While the averaging of multiple weak decision trees in RFR provides robustness to noise, the result of RFR were affected by the noise. These results consistently show the improvements in RFR performance due to noise removal by CNN. Since RFR is one of the effective approaches to NMR analysis \u003csup\u003e21,34\u0026ndash;36\u003c/sup\u003e,\u0026nbsp;the improved performance and interpretability achieved through denoising could assist in extracting effective descriptors from relaxation curves for property prediction.\u003c/p\u003e\n\u003cp\u003eThe features of the relaxation curves were also extracted from latent space in CNN. In the current study, the global average pooling (GAP) layer was treated as the latent space in denoising CNN model (Fig. S3). The correlation coefficients between each node values of GAP layers (GAP values) and each physical properties were calculated, and the one latent space with the strongest correlation with each material property was identified (Table 1, \u003cem\u003er\u003c/em\u003e\u003csub\u003elatent-properties\u003c/sub\u003e). A notable correlation was observed for all properties except Y8, consistent with the poor RFR prediction accuracy for that property (Fig. 4a). Linear relationships between the GAP values and material properties were identified, as shown in Fig. 6a-b. These correlations suggest that the latent space of the CNN denoising model extract the information of dynamics, which related to the property. In addition, clusters corresponding to the crysallization temperature were observed in the scatter plot (Figs 6 and S10), suggesting the extraction of crystal structure information from the relaxation curves in the latent space. These results indicate the effectiveness of the noise reduction model in extracting features from the relaxation curves.\u003c/p\u003e\n\u003cp\u003eIt has been pointed out that material properties of polymers can correspond to the latent space of neural networks \u003csup\u003e28,37\u003c/sup\u003e. Attempts have been made to analyze \u0026nbsp;correspondence between latent space and glass transition temperature, to visualize the latent space by PCA analysis, and to map the polymer properties to the properties using RFR \u003csup\u003e37\u0026ndash;40\u003c/sup\u003e. In these attempts, training data are generally expressed as strings in SMILES format, etc., to construct large-scale chemical language models. In contrast, our study used lightweight training dataset with 310 data points and artificial 50,000 numbers of mimic relaxation curves, to form polymer fingerprints corresponding to various physical properties of mechanical strength and biodegradability before and after degradation. Since the relaxation curve shape reflects the physical and chemical state of the nucleus, the approach using pattern recognition architecture may lead to essential and efficient information extraction. Visualization of important regions from relaxation curves using machine learning has been attempted by Okada et al. \u003csup\u003e21\u003c/sup\u003e, but this study extends this approach by synthesizing variables that correspond linearly to physical properties from the relaxation curves to construct effective indicators as objective variables in the material properties.\u003c/p\u003e\n\u003cp\u003eEach latent space in the encoder-decoder structure include any information in input and/or output data, which can be dealt with important feature in the original dimentsion. We therefore visualized the feature maps in the last convolutional layers corresponding to the selected GAP latent variables. Fig. 7 the feature maps corresponding to the GAP variables highly correlated with Y1 and Y9. Since the GAP value is calculated as the average of the feature maps, regions with large absolute values in the feature maps are considered to be regions with a strong contribution to the latent space-material property correspondence representing important patterns of the input data \u003csup\u003e41\u003c/sup\u003e. The regions in the relatively early relaxation time were recognized as the important regins in the relaxation curve (Figs. 7 and S11). This behavior showed a different tendency for the feature importance of RFR (Fig. 5b). Because the kernel in CNN is suitable to extract the information in attenuation of the relaxation curve, more fluctuated regions were recognized as the important descriptors of low-field NMR for the properties. Generally, the entire latent space is often targeted as a black box in model validation ,as seen in teqniques such as in Grad-CAM or non-linear \u0026nbsp;analysis \u0026nbsp; \u003csup\u003e39,42,43\u003c/sup\u003e. On the other hand, in this study, by calculating the correlation of properties for each latent space and specifying the latent space corresponding to the properties, the feature map was visualized as a heat map highlighting the regions with strong influence on that property.\u003c/p\u003e\n\u003cp\u003eWe then performed BO using the latent space to identify effective process conditions. The BO is an algorithm that finds the x that y maximizes for an unknown function y=f(x) with a small number of trials, and it is widely applied in the process of searching for conditions to optimize material properties. To evaluate the contribution of the latent space to the optimization of the molding process, optimizations of the crystallization conditions with GAP values as the objective variable was performed, along with Bayesian optimization for conventional material properties and random search for comparisons. In order to reduce the influence of randomness on the interpretation of the results, a series of optimization processes were performed 200 times for each property. In the most cases, the BO for GAP values and material properties showed higher performances compared with the random searches (Figs. 8 and S12). The number of trials required to achieve 80% of the maximum value of a property was tested for significant differences between the optimization processes, and the magnitude of the difference in the number of trials was determined numerically using Cohen\u0026apos;s d (Table 2). BO using GAP values significantly outperformed random search for Y6~Y9, and Cohen\u0026apos;s d also indicated a high-performance difference. The only other case of Y1 showed slightly worse performance than the random search, resulting in Cohen\u0026apos;s d of -0.2389, suggesting that the effect was small. The comparison of optimization from physical properties and optimization from GAP also showed no significant difference for Y1~Y5 and Y8, while optimization from GAP had a weaker effect than optimization from physical properties for Y6 and Y9, and a moderate effect for Y7. Overall, BO using latent-space objectives achieved improvements comparable to those achieved by conventional BO using actual property values, and both approaches performed better than random search.\u003c/p\u003e\n\u003cp\u003ePrevious studies include Bayesian optimization of the degradability of polylactic acid using NMR spectral data as the objective variable \u003csup\u003e44\u003c/sup\u003e, materials property optimization combining evaluation of physical properties by a neural network that has been pre-trained with a large amount of real data and candidate submission by a genetic algorithm \u003csup\u003e45\u003c/sup\u003e, and data derived from biological samples. The correspondence between latent space and qualitative scores of image classification models of biological samples has been studied \u003csup\u003e46\u003c/sup\u003e. Our study combines elements of these approaches, emphasizing both the use of readily obtainable experimental data and the ease of constructing an analytical model. The denoising model can be easily trained with artificial data, and once trained, its latent space encodes material property information extracted from measured low-field NMR data. It was shown that Bayesian optimization using the latent space can optimize various properties of polymers as well as real data, suggesting the feasibility of a property optimization process based on data that can be obtained more quickly and inexpensively than before.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 2\u003c/strong\u003e\u003cstrong\u003e. Statical test to confirm difference in Bayesian optimization and random search.\u0026nbsp;\u003c/strong\u003eThe random search (Random), property optimization (Pro. opt.) and GAP optimization (GAP opt.) were compared by t-test (p-value) and Cohen\u0026rsquo;s d.\u0026nbsp;\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" align=\"\" width=\"605\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 72px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 57px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003eY1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003eY2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003eY3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003eY4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003eY5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003eY6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003eY7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003eY8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003eY9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" style=\"width: 72px;\"\u003e\n \u003cp\u003eRandom vs\u003c/p\u003e\n \u003cp\u003ePro. opt.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 57px;\"\u003e\n \u003cp\u003ep- value\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.023\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.041\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.183\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.085\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e\u0026lt;\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e\u0026lt;\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.052\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e\u0026lt;\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 57px;\"\u003e\n \u003cp\u003eCohen\u0026apos;s d\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e-0.228\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.205\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.133\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.328\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.173\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e1.332\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.751\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.195\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.730\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" style=\"width: 72px;\"\u003e\n \u003cp\u003eRandom vs\u0026nbsp;\u003c/p\u003e\n \u003cp\u003eGAP opt.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 57px;\"\u003e\n \u003cp\u003ep-value\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.017\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.135\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.245\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.082\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.051\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e\u0026lt;\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e\u0026lt;\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e\u0026lt;\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e\u0026lt;\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 57px;\"\u003e\n \u003cp\u003eCohen\u0026apos;s d\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e-0.239\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.150\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.116\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.175\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.196\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e1.066\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e1.345\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.339\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.585\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" style=\"width: 72px;\"\u003e\n \u003cp\u003ePro. opt.\u003c/p\u003e\n \u003cp\u003evs\u003c/p\u003e\n \u003cp\u003eGAP opt.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 57px;\"\u003e\n \u003cp\u003ep- value\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.991\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.561\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.183\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.068\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.716\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e\u0026lt;\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.163\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.123\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 57px;\"\u003e\n \u003cp\u003eCohen\u0026apos;s d\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e-0.058\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e-0.015\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e-0.183\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.036\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e-0.323\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.510\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e0.140\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 53px;\"\u003e\n \u003cp\u003e-0.154\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eThis study demonstrates the feasibility of using a CNN latent space obtained from a denoising task, instead of direct material property values, for optimizing biodegradable polymer processing. The denoising model developed in this study removed noise components from the signal and visualized small differences in the relaxation curves reflecting molecular dynamics. Noise removal also improved the accuracy of property regression and contributed to the visualization of important components. Furthermore, the specific latent space that correlate with material properties were identified among many latent spaces of the denoised model, suggesting the possibility of extracting information relating to material properties of biodegradable polymers. BO using these latent features as the objective variable for optimizing molding conditions showed performance comparable to using actual measured properties as the objective. Hence, this method is applicable to optimize the material design of biodegradable polymers without high experimental costs of degradations.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe application of the noise reduction model to the optimization of material properties in this study suggests the feasibility of a material property optimization process that omits the process of obtaining material properties. Since relaxation curves reflect molecular dynamics of polymers, some latent spaces in the denoising model linearly correlated with the material property. This may enable the integrated replacement of multiple measurements for material properties with simple and high-throughput low-field NMR measurements, which is expected to contribute to the efficiency of material property optimization. In general, noise reduction models can be created relatively easily by constructing data sets by creating artificial data using random numbers or by adding white noise to measured data. Thus, this method is useful for the materials with high experimental costs to evaluate the properties. Furthermore, noise reduction models have the potential to extract effective features form wide range of NMR measurement such as solution NMR, which extracts exhaustive information at frequencies that reflect the exhaustive information of the chemicals and materials as well as low-field NMR \u003csup\u003e47,48\u003c/sup\u003e. Thus, the latent space utilization of the noise reduction model treated in this study is expected to be applied to diverse fields not limited to polymers and low-field NMR.\u0026nbsp;\u003c/p\u003e"},{"header":"METHODS","content":"\u003cp\u003e\u003cstrong\u003eMolding of polylactic acid and evaluation of material properties\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003ePoly lactic acid pellets were obtained by TEIJIN LIMITTED. After melting pellets of polylactic acid at 200 \u0026deg;C, isothermal crystallizations were carried out using hot press machine (Imoto Machinery CO., Ltd.) in sixty-four different molding conditions corresponding to all combinations by changing each condition one by one, with crystallization temperatures of 75, 90, 105, 120 \u0026deg;C, crystallization times of 5, 10, 20, and 40 minutes, and nucleating agent concentrations of 0, 0.167, 0.5, and 1.5%. The molding conditions of the polylactic acid are summarized in Table S1. The obtained films were subjected to three types of treatments: enzymatic degradation, light irradiation, and enzymatic degradation plus light irradiation. The strain at break and Young\u0026apos;s modulus were obtained by uniaxial elongation a tensile-testing machine (Imoto Machinery CO., Ltd.) at 10 mm/min and room temperature with the dumbbell-shape of a 2 \u0026nbsp;\u0026acute; 12 mm\u003csup\u003e2\u003c/sup\u003e. Enzymatic degradation rates were carried out by immersing the films in Proteinase K solution (1 mg/mL, 1 mL, pH 7.4) for 2 d at 37 \u0026deg;C. The degradation rate (\u003cem\u003er\u003c/em\u003e\u003csub\u003eenzyme\u003c/sub\u003e) was calculated from the weights of the film before and after degradation (\u003cem\u003ew\u003c/em\u003e\u003csub\u003ebefore\u003c/sub\u003e and \u003cem\u003ew\u003c/em\u003e\u003csub\u003eafter\u003c/sub\u003e, respectively) as: \u003cem\u003er\u003c/em\u003e\u003csub\u003eenzyme\u003c/sub\u003e = \u003cem\u003ew\u003c/em\u003e\u003csub\u003eafter\u003c/sub\u003e/\u003cem\u003ew\u003c/em\u003e\u003csub\u003ebefore\u003c/sub\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eLow-field NMR measurement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSheets of polylactic acid films were cut to 1 cm height and placed in a 10 mm tube for low-field NMR measurements (Bruker mq20 Minispec, Milton, ON, Canada). A Magic Sandwich Echo (MSE) was used for pulse sequencing. Relaxation curves of low-field NMR measurements were obtained at 25 \u0026deg;C for each sample before degradation treatment. The relaxation curves were normalized by dividing them by the maximum intensity.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConvolutional neural network (CNN)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe CNN model was constructed by artificial data of relaxation curves, and used to denoise the experimental data, where the GAP values were obtained as values in latent spaces. As the artificial data, relaxation curves were randomly obtained by sampling from three exponential curves with \u003cem\u003eT\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e parameters in the range of (0.0200,0.035), (0.031,0.07), (0.07,0.145), (0.145,0.195), respectively with Weibull coefficients in the range of 1~2 for the component with the shortest \u003cem\u003eT\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e among the four components. The structure of CNN was indicated in Fig. S4. The noise-added relaxation curves were inputted in CNN to train for minimizing the squared error between the output and the curve before adding the noise. The mean squared error between the artificial curve before adding the noise and the curve generated by the CNN model during training was estimated to be 3.96 \u0026times; 10\u003csup\u003e-6\u003c/sup\u003e and 3.33 \u0026times; 10\u003csup\u003e-6\u003c/sup\u003e for train data and test data, respectively, indicating high noise-rejection performance of the model for the dataset. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eRandom forest regressor (RFR)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eRFR was constructed using scikit-learn library (1.5.2)\u003csup\u003e49\u003c/sup\u003e in Python language with the number of trees as 300, fixed seed and dividing the data set into 70% train data and 30% test data. The explanatory variables were 310 data points of the relaxation curve of low-field NMR, and the objective variable was one of the material properties Y1-Y9. Default values were used for the hyperparameters except for the number of trees. \u0026nbsp;The feature importance of RFR in NMR relaxation curves were obtained by feature_importances_ functions.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eBayesian optimization\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003ePython library Bayesian-optimization (2.0.3) was used to implement Bayesian optimization, and hyperparameters were set to default values. BO was carried out for two types of objectives: (1) each material property Y1\u0026ndash;Y9, and (2) the single GAP latent variable most strongly correlated with each property (selected from 256 candidates).The explanatory variable in both cases was the molding condition. A random search was also performed as a control by randomly choosing molding conditions to check whether the optimization algorithm works effectively. All optimization processes, including random search, were run 200 times in each property to make sure optimization performance without randomness by bootstrap sampling or sampling with replacement from the original dataset. BO and random search are performed in real number space. However, since the molding conditions of real data are discrete, when the model actually specifies the molding conditions in the search process, the explanatory variable of the sample molded with the closest conditions was selected. \u0026nbsp;\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eDATA AVAILABILITY\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll data and code used in this study is publicly available. The datasets and source code be accessed on GitHub (URL: https://github.com/neko166/Python-Code-for-NMR-denoising-and-analysis/tree/main) .\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eACKNOWLEDGEMENTS\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe would like to express our gratitude to Yuuri Tsuboi (RIKEN), for her contribution to the acquisition of NMR Relaxation data.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCREATIVE COMMONS\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eOpen Access\u0026nbsp;\u003c/strong\u003eThis airticle is licenced under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptaion, distribution, reproduction in any medium or format, as long as you give appropriate credit to the oridinal authors and \u0026nbsp; the source provide a link to the Creative Commons license, and indicated \u0026nbsp;if change were made. The image or other third party material in this article are included in the airticle\u0026rsquo;s Creative Commons license, unless indicated otherwisein a credit line to the material. If material is not included in the article\u0026rsquo;s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit URL\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAUTHOR CONTRIBUTIONS\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eY.A. performed the experiments. R.F. analyzed the data. J.K. supervised the research. R.F. drafted the manuscript, and the others reviewed it.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCOMPETING INTERESTS\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eMohanty, A. K. \u003cem\u003eet al.\u003c/em\u003e Sustainable polymers. \u003cem\u003eNature Reviews Methods Primers\u003c/em\u003e \u003cstrong\u003e2\u003c/strong\u003e, 46 (2022).\u003c/li\u003e\n\u003cli\u003eGbadeyan, O. J., Linganiso, L. Z. \u0026amp; Deenadayalu, N. Thermomechanical characterization of bioplastic films produced using a combination of polylactic acid and bionano calcium carbonate. \u003cem\u003eSci Rep\u003c/em\u003e \u003cstrong\u003e12\u003c/strong\u003e, 15538 (2022).\u003c/li\u003e\n\u003cli\u003eGuicherd, M. \u003cem\u003eet al.\u003c/em\u003e An engineered enzyme embedded into PLA to make self-biodegradable plastic. \u003cem\u003eNature\u003c/em\u003e \u003cstrong\u003e631\u003c/strong\u003e, 884\u0026ndash;890 (2024).\u003c/li\u003e\n\u003cli\u003eSamir, A., Ashour, F. H., Hakim, A. A. A. \u0026amp; Bassyouni, M. Recent advances in biodegradable polymers for sustainable applications. \u003cem\u003enpj Materials Degradation\u003c/em\u003e vol. 6 68 Preprint at https://doi.org/10.1038/s41529-022-00277-7 (2022).\u003c/li\u003e\n\u003cli\u003eDiwale, S. \u003cem\u003eet al.\u003c/em\u003e Bayesian optimization for material discovery processes with noise. \u003cem\u003eMol Syst Des Eng\u003c/em\u003e \u003cstrong\u003e7\u003c/strong\u003e, 622\u0026ndash;636 (2022).\u003c/li\u003e\n\u003cli\u003eNoguchi, S. \u0026amp; Inoue, J. Bayesian inverse inference of material properties from microstructure images. \u003cem\u003eComput Mater Sci\u003c/em\u003e \u003cstrong\u003e245\u003c/strong\u003e, 113306 (2024).\u003c/li\u003e\n\u003cli\u003eRamprasad, R., Batra, R., Pilania, G., Mannodi-Kanakkithodi, A. \u0026amp; Kim, C. Machine learning in materials informatics: Recent applications and prospects. \u003cem\u003enpj Computational Materials\u003c/em\u003e vol. 3 54 Preprint at https://doi.org/10.1038/s41524-017-0056-5 (2017).\u003c/li\u003e\n\u003cli\u003eChitturi, S. R. \u003cem\u003eet al.\u003c/em\u003e Targeted materials discovery using Bayesian algorithm execution. \u003cem\u003eNPJ Comput Mater\u003c/em\u003e \u003cstrong\u003e10\u003c/strong\u003e, 156 (2024).\u003c/li\u003e\n\u003cli\u003eHerbol, H. C., Poloczek, M. \u0026amp; Clancy, P. Cost-effective materials discovery: Bayesian optimization across multiple information sources. \u003cem\u003eMater Horiz\u003c/em\u003e \u003cstrong\u003e7\u003c/strong\u003e, 2113\u0026ndash;2123 (2020).\u003c/li\u003e\n\u003cli\u003ePai, S. M. \u003cem\u003eet al.\u003c/em\u003e Machine learning applied to the design and optimization of polymeric materials: A review. \u003cem\u003eNext Materials\u003c/em\u003e \u003cstrong\u003e7\u003c/strong\u003e, 100449 (2025).\u003c/li\u003e\n\u003cli\u003ePatra, T. K. Data-Driven Methods for Accelerating Polymer Design. \u003cem\u003eACS Polymers Au\u003c/em\u003e \u003cstrong\u003e2\u003c/strong\u003e, 8\u0026ndash;26 (2022).\u003c/li\u003e\n\u003cli\u003eAmamoto, Y. Data-driven approaches for structure-property relationships in polymer science for prediction and understanding. \u003cem\u003ePolymer Journal\u003c/em\u003e vol. 54 957\u0026ndash;967 Preprint at https://doi.org/10.1038/s41428-022-00648-6 (2022).\u003c/li\u003e\n\u003cli\u003eFukazawa, T., Ikegami, T., Kawata, M. \u0026amp; Miyake, T. Materials Secure Computation with Secret Sharing: A Bayesian Optimization Scheme and Its Performance. \u003cem\u003eJ Physical Soc Japan\u003c/em\u003e \u003cstrong\u003e94\u003c/strong\u003e, 013801 (2025).\u003c/li\u003e\n\u003cli\u003eLuo, S. H. \u003cem\u003eet al.\u003c/em\u003e A machine learning framework for low-field NMR data processing. \u003cem\u003ePet Sci\u003c/em\u003e \u003cstrong\u003e19\u003c/strong\u003e, 581\u0026ndash;593 (2022).\u003c/li\u003e\n\u003cli\u003eLuo, G., Xiao, L., Luo, S., Liao, G. \u0026amp; Shao, R. A study on multi-exponential inversion of nuclear magnetic resonance relaxation data using deep learning. \u003cem\u003eJournal of Magnetic Resonance\u003c/em\u003e \u003cstrong\u003e346\u003c/strong\u003e, 107358 (2023).\u003c/li\u003e\n\u003cli\u003eNakashima, Y. \u0026amp; Shiba, N. Nondestructive measurement of intramuscular fat content of fresh beef meat by a hand-held magnetic resonance sensor. \u003cem\u003eInt J Food Prop\u003c/em\u003e \u003cstrong\u003e24\u003c/strong\u003e, 1722\u0026ndash;1736 (2021).\u003c/li\u003e\n\u003cli\u003eda Silva Ruiz, N. M. \u003cem\u003eet al.\u003c/em\u003e Time domain NMR evaluation of thermal and thermochemical aging of nitrile rubber on crosslinking and mechanical properties. \u003cem\u003ePolym Degrad Stab\u003c/em\u003e \u003cstrong\u003e224\u003c/strong\u003e, 110727 (2024).\u003c/li\u003e\n\u003cli\u003eB. Blu\u0026uml; mich, S. A. K. K. S. S. V. H. and A. S. Unilateral Nuclear Magnetic Resonance for Quality Control: The NMR-MOUSE. \u003cem\u003eSpectroscopy\u003c/em\u003e \u003cstrong\u003e18\u003c/strong\u003e, 24\u0026ndash;54 (2003).\u003c/li\u003e\n\u003cli\u003eYamada, S., Kurotani, A., Chikayama, E. \u0026amp; Kikuchi, J. Signal deconvolution and noise factor analysis based on a combination of time\u0026ndash;frequency analysis and probabilistic sparse matrix factorization. \u003cem\u003eInt J Mol Sci\u003c/em\u003e \u003cstrong\u003e21\u003c/strong\u003e, 2978 (2020).\u003c/li\u003e\n\u003cli\u003eBesghini, D., Mauri, M. \u0026amp; Simonutti, R. Time domain NMR in polymer science: From the laboratory to the industry. \u003cem\u003eApplied Sciences (Switzerland)\u003c/em\u003e vol. 9 1801 Preprint at https://doi.org/10.3390/app9091801 (2019).\u003c/li\u003e\n\u003cli\u003eOkada, M., Amamoto, Y. \u0026amp; Kikuchi, J. Designing Sustainable Hydrophilic Interfaces via Feature Selection from Molecular Descriptors and Time-Domain Nuclear Magnetic Resonance Relaxation Curves. \u003cem\u003ePolymers (Basel)\u003c/em\u003e \u003cstrong\u003e16\u003c/strong\u003e, 824 (2024).\u003c/li\u003e\n\u003cli\u003eMatlahov, I. \u0026amp; van der Wel, P. C. A. Hidden motions and motion-induced invisibility: Dynamics-based spectral editing in solid-state NMR. \u003cem\u003eMethods\u003c/em\u003e vol. 148 123\u0026ndash;135 Preprint at https://doi.org/10.1016/j.ymeth.2018.04.015 (2018).\u003c/li\u003e\n\u003cli\u003eHara, K., Yamada, S., Kurotani, A., Chikayama, E. \u0026amp; Kikuchi, J. Materials informatics approach using domain modelling for exploring structure\u0026ndash;property relationships of polymers. \u003cem\u003eSci Rep\u003c/em\u003e \u003cstrong\u003e12\u003c/strong\u003e, 10558 (2022).\u003c/li\u003e\n\u003cli\u003eSrikanth, M., Sandeep, T. S. R. S., Sucharitha, K. \u0026amp; Godi, S. Biodegradation of plastic polymers by fungi: a brief review. \u003cem\u003eBioresources and Bioprocessing\u003c/em\u003e vol. 9 42 Preprint at https://doi.org/10.1186/s40643-022-00532-4 (2022).\u003c/li\u003e\n\u003cli\u003eMierzwa-Hersztek, M., Gondek, K. \u0026amp; Kopeć, M. Degradation of Polyethylene and Biocomponent-Derived Polymer Materials: An Overview. \u003cem\u003eJ Polym Environ\u003c/em\u003e \u003cstrong\u003e27\u003c/strong\u003e, 600\u0026ndash;611 (2019).\u003c/li\u003e\n\u003cli\u003ePlota, A. \u0026amp; Masek, A. Lifetime prediction methods for degradable polymeric materials\u0026mdash;a short review. \u003cem\u003eMaterials\u003c/em\u003e vol. 13 1\u0026ndash;25 Preprint at https://doi.org/10.3390/ma13204507 (2020).\u003c/li\u003e\n\u003cli\u003eZhou, Z. \u003cem\u003eet al.\u003c/em\u003e A machine learning model for textured X-ray scattering and diffraction image denoising. \u003cem\u003eNPJ Comput Mater\u003c/em\u003e \u003cstrong\u003e9\u003c/strong\u003e, 58 (2023).\u003c/li\u003e\n\u003cli\u003eG\u0026oacute;mez-Bombarelli, R. \u003cem\u003eet al.\u003c/em\u003e Automatic Chemical Design Using a Data-Driven Continuous Representation of Molecules. \u003cem\u003eACS Cent Sci\u003c/em\u003e \u003cstrong\u003e4\u003c/strong\u003e, 268\u0026ndash;276 (2018).\u003c/li\u003e\n\u003cli\u003eMa, B. \u003cem\u003eet al.\u003c/em\u003e Effect of poly(lactic acid) crystallization on its mechanical and heat resistance performances. \u003cem\u003ePolymer (Guildf)\u003c/em\u003e \u003cstrong\u003e212\u003c/strong\u003e, 123280 (2021).\u003c/li\u003e\n\u003cli\u003eHu, J., Shen, L., Albanie, S., Sun, G. \u0026amp; Wu, E. Squeeze-and-Excitation Networks. (2017).\u003c/li\u003e\n\u003cli\u003eHe, K., Zhang, X., Ren, S. \u0026amp; Sun, J. Deep Residual Learning for Image Recognition. (2015).\u003c/li\u003e\n\u003cli\u003eWang, J. \u003cem\u003eet al.\u003c/em\u003e Estimating the Relative Crystallinity of Biodegradable Polylactic Acid and Polyglycolide Polymer Composites by Machine Learning Methodologies. \u003cem\u003ePolymers (Basel)\u003c/em\u003e \u003cstrong\u003e14\u003c/strong\u003e, 527 (2022).\u003c/li\u003e\n\u003cli\u003eOmigbodun, F. T., Osa-Uwagboe, N., Udu, A. G. \u0026amp; Oladapo, B. I. Leveraging Machine Learning for Optimized Mechanical Properties and 3D Printing of PLA/cHAP for Bone Implant. \u003cem\u003eBiomimetics\u003c/em\u003e \u003cstrong\u003e9\u003c/strong\u003e, 587 (2024).\u003c/li\u003e\n\u003cli\u003eYamada, S., Tsuboi, Y., Yokoyama, D. \u0026amp; Kikuchi, J. Polymer composition optimization approach based on feature extraction of bound and free water using time-domain nuclear magnetic resonance. \u003cem\u003eJournal of Magnetic Resonance\u003c/em\u003e \u003cstrong\u003e351\u003c/strong\u003e, 107438 (2023).\u003c/li\u003e\n\u003cli\u003eTakamura, A., Tsukamoto, K., Sakata, K. \u0026amp; Kikuchi, J. Integrative measurement analysis via machine learning descriptor selection for investigating physical properties of biopolymers in hairs. \u003cem\u003eSci Rep\u003c/em\u003e \u003cstrong\u003e11\u003c/strong\u003e, 24359 (2021).\u003c/li\u003e\n\u003cli\u003eLeniak, A., Pietruś, W., Świderska, A. \u0026amp; Kurczab, R. From NMR to AI: Do We Need 1H NMR Experimental Spectra to Obtain High-Quality logD Prediction Models? \u003cem\u003eJ Chem Inf Model\u003c/em\u003e \u003cstrong\u003e65\u003c/strong\u003e, 2924\u0026ndash;2939 (2025).\u003c/li\u003e\n\u003cli\u003eCasado, U. M., Altuna, F. I. \u0026amp; Miccio, L. A. Towards Sustainable Material Design: A Comparative Analysis of Latent Space Representations in AI Models. \u003cem\u003eSustainability (Switzerland)\u003c/em\u003e \u003cstrong\u003e16\u003c/strong\u003e, 10681 (2024).\u003c/li\u003e\n\u003cli\u003eKuenneth, C. \u0026amp; Ramprasad, R. polyBERT: a chemical language model to enable fully machine-driven ultrafast polymer informatics. \u003cem\u003eNat Commun\u003c/em\u003e \u003cstrong\u003e14\u003c/strong\u003e, 4099 (2023).\u003c/li\u003e\n\u003cli\u003eGurnani, R. \u003cem\u003eet al.\u003c/em\u003e PolyG2G: A Novel Machine Learning Algorithm Applied to the Generative Design of Polymer Dielectrics. \u003cem\u003eChemistry of Materials\u003c/em\u003e \u003cstrong\u003e33\u003c/strong\u003e, 7008\u0026ndash;7016 (2021).\u003c/li\u003e\n\u003cli\u003eHu, J., Li, Z., Lin, J. \u0026amp; Zhang, L. Prediction and Interpretability of Glass Transition Temperature of Homopolymers by Data-Augmented Graph Convolutional Neural Networks. \u003cem\u003eACS Appl Mater Interfaces\u003c/em\u003e \u003cstrong\u003e15\u003c/strong\u003e, 54006\u0026ndash;54017 (2023).\u003c/li\u003e\n\u003cli\u003eAzam, S. \u003cem\u003eet al.\u003c/em\u003e Using feature maps to unpack the CNN \u0026lsquo;Black box\u0026rsquo; theory with two medical datasets of different modality. \u003cem\u003eIntelligent Systems with Applications\u003c/em\u003e \u003cstrong\u003e18\u003c/strong\u003e, 200233 (2023).\u003c/li\u003e\n\u003cli\u003eBatra, R. \u003cem\u003eet al.\u003c/em\u003e Polymers for Extreme Conditions Designed Using Syntax-Directed Variational Autoencoders. \u003cem\u003eChemistry of Materials\u003c/em\u003e \u003cstrong\u003e32\u003c/strong\u003e, 10489\u0026ndash;10500 (2020).\u003c/li\u003e\n\u003cli\u003eSzandała, T. Unlocking the black box of CNNs: Visualising the decision-making process with PRISM. \u003cem\u003eInf Sci (N Y)\u003c/em\u003e \u003cstrong\u003e642\u003c/strong\u003e, 119162 (2023).\u003c/li\u003e\n\u003cli\u003eYamawaki, R., Tei, A., Ito, K. \u0026amp; Kikuchi, J. Decomposition factor analysis based on virtual experiments throughout bayesian optimization for compost-degradable polymers. \u003cem\u003eApplied Sciences (Switzerland)\u003c/em\u003e \u003cstrong\u003e11\u003c/strong\u003e, 2820 (2021).\u003c/li\u003e\n\u003cli\u003eAtasi, C., Kern, J. \u0026amp; Ramprasad, R. Design of Recyclable Plastics with Machine Learning and Genetic Algorithm. \u003cem\u003eJ Chem Inf Model\u003c/em\u003e \u003cstrong\u003e64\u003c/strong\u003e, 9249\u0026ndash;9259 (2024).\u003c/li\u003e\n\u003cli\u003eRotem, O. \u003cem\u003eet al.\u003c/em\u003e Visual interpretability of image-based classification models by generative latent space disentanglement applied to in vitro fertilization. \u003cem\u003eNat Commun\u003c/em\u003e \u003cstrong\u003e15\u003c/strong\u003e, 7390 (2024).\u003c/li\u003e\n\u003cli\u003eAsakura, T., Date, Y. \u0026amp; Kikuchi, J. Application of ensemble deep neural network to metabolomics studies. \u003cem\u003eAnal Chim Acta\u003c/em\u003e \u003cstrong\u003e1037\u003c/strong\u003e, 230\u0026ndash;236 (2018).\u003c/li\u003e\n\u003cli\u003eDate, Y. \u0026amp; Kikuchi, J. Application of a Deep Neural Network to Metabolomics Studies and Its Performance in Determining Important Variables. \u003cem\u003eAnal Chem\u003c/em\u003e \u003cstrong\u003e90\u003c/strong\u003e, 1805\u0026ndash;1810 (2018).\u003c/li\u003e\n\u003cli\u003ePedregosa FABIANPEDREGOSA, F. \u003cem\u003eet al.\u003c/em\u003e \u003cem\u003eScikit-Learn: Machine Learning in Python Ga\u0026euml;l Varoquaux Bertrand Thirion Vincent Dubourg Alexandre Passos PEDREGOSA, VAROQUAUX, GRAMFORT ET AL. Matthieu Perrot\u003c/em\u003e. \u003cem\u003eJournal of Machine Learning Research\u003c/em\u003e vol. 12 http://scikit-learn.sourceforge.net. (2011).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"npj-materials-degradation","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"npjmatdeg","sideBox":"Learn more about [npj Materials Degradation](http://www.nature.com/npjmatdeg/)","snPcode":"41529","submissionUrl":"https://submission.springernature.com/new-submission/41529/3","title":"npj Materials Degradation","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-6364337/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6364337/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Effective designs of biodegradable polymers are highly desirable for achieving a sustainable society by decreasing environmental burden and replacing petroleum-based resources with biomass. Low-field NMR is one of the candidate techniques because it provides information on the higher-order structure and dynamics of polymers quickly and conveniently. Although machine learning approaches such as Bayesian optimization (BO) and convolutional neural networks (CNNs) are significant, there have been almost no reports on effective material design based on low-field NMR data. This study proposes a method for optimizing polymer process conditions using CNN-based features extracted from relaxation curves. This approach identified important features related to material properties while reconstructing denoised relaxation curves of polylactic acid. BO of process conditions using these features achieved an optimization rate comparable to using material property values, suggesting that effective material design is possible without directly evaluating a large number of properties. This provides a framework to accelerate polymer development through low-field NMR with minimal property data.","manuscriptTitle":"Bayesian Optimization of Biodegradable Polymers via Machine Learning Driven Features from Low-Field NMR Data","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-25 10:54:25","doi":"10.21203/rs.3.rs-6364337/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-04-24T06:57:52+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-23T11:14:21+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-16T07:55:56+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"221621478647987944892941394241835940732","date":"2025-04-05T08:40:38+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"26101266146115000309659886569575938107","date":"2025-04-04T07:44:21+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-04-04T04:56:27+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-04-03T10:20:32+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-04-03T07:51:29+00:00","index":"","fulltext":""},{"type":"submitted","content":"npj Materials Degradation","date":"2025-04-02T22:05:04+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"npj-materials-degradation","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"npjmatdeg","sideBox":"Learn more about [npj Materials Degradation](http://www.nature.com/npjmatdeg/)","snPcode":"41529","submissionUrl":"https://submission.springernature.com/new-submission/41529/3","title":"npj Materials Degradation","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"60463a78-eb09-4244-adba-ff31387320e3","owner":[],"postedDate":"April 25th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":47609104,"name":"Physical sciences/Materials science"},{"id":47609105,"name":"Physical sciences/Materials science/Techniques and instrumentation"}],"tags":[],"updatedAt":"2025-06-23T16:07:41+00:00","versionOfRecord":{"articleIdentity":"rs-6364337","link":"https://doi.org/10.1038/s41529-025-00613-7","journal":{"identity":"npj-materials-degradation","isVorOnly":false,"title":"npj Materials Degradation"},"publishedOn":"2025-06-18 15:57:10","publishedOnDateReadable":"June 18th, 2025"},"versionCreatedAt":"2025-04-25 10:54:25","video":"","vorDoi":"10.1038/s41529-025-00613-7","vorDoiUrl":"https://doi.org/10.1038/s41529-025-00613-7","workflowStages":[]},"version":"v1","identity":"rs-6364337","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6364337","identity":"rs-6364337","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}