Data-Driven Process–Structure–Property Framework for the Design, Understanding, and Prediction of Sustainable Polymers

Data-Driven Process–Structure–Property Framework for the Design, Understanding, and Prediction of Sustainable Polymers | 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 Data-Driven Process–Structure–Property Framework for the Design, Understanding, and Prediction of Sustainable Polymers Yoshifumi Amamoto, Hiroteru Kikutake, Ken Kojio, Atsushi Takahara, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8066698/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Data-driven methodologies are increasingly recognized as pivotal tooks for the efficient development of materials and mechanistic understanding. However, existing approaches are often limited to isolated tasks, hindering their ability to address the complex, multi-process, multitask, and hierarchical nature of sustainable polymers. In this study, we propose an integrated data-driven framework that models the process–structure–property (PSP) relationships of sustainable polymers through three synergisitic components: (1) Design – Bayesian optimization of process conditions to balance multiple material properties using surrogate objective variables derived from structure data; (2) Understanding – extraction of key crystalline features related to single-property and multi-objective axes using dimensionality reduction and XAI on X-ray scattering profiles; and (3) Prediction – hierarchical PSP modeling to regenerate structural X-ray information and predict material properties accurately from processing parameters. This unified framework enables a more systematic and automated approach to sustainable polymer development, reducing dependence on traditional trial-and-error methods and accelerating innovation. Physical sciences/Chemistry Physical sciences/Engineering Physical sciences/Materials science Physical sciences/Mathematics and computing Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 INTRODUCTION The growing environmental impact of conventional plastics and rubbers has fueled demand for high-performance, sustainable polymeric materials. 1-6 For instance, in the field of biodegradable plastics, numerous polymers have been developed with degradation rates tailored to specific environmental conditions. 7-10 In line with circular economy initiatives, composite technologies play a critical role in producing recycled materials with properties comparable to those of virgin polymers. 11-14 Because key properties often exhibit trade-offs, such as toughness versus degradability, achieving the desired balance requires careful control over both primary and higher-order polymer structures. 15,16 However, as material systems become increasingly complex, conventional trial-and-error approaches struggle to achieve optimal results efficiently. This underscores the need for digital research platforms that enable automated analysis, mechanism discovery, and experimental recommendation toward the development of sustainable polymers. Data-driven science has emerged as a powerful strategy in polymer science for both material development and mechanistic understanding. 17-20 Advanced computational techniques can extract key patterns from complex, high-dimensional datasets and automate analysis without human bias, 21-23 leading to increasing applications in polymer science. 24,25 Additionally, machine learning models have been used to design polymeric materials, including biodegradable polymers, by exploring chemical structure/process–property relationships. 26-29 Among them, a Bayesian optimization framework employing surrogate objective variables rather than directly measured properties has been developed, 29 since experimental evaluation of sustainable polymer properties such as degradation tests often requires long periods. Explainable artificial intelligence (XAI) techniques have helped uncover the higher-order structure–property relationships behind target property predictions. 28-31 Despite these advances, most studies have focused on single-variable relationships or isolated stages within the research workflow­–as exemplified by the above two relationships–which limits their ability to address the inherently multi-process, multitask, and hierarchical nature of real-world polymer systems. To overcome these limitations, a more comprehensive framework is required. The process–structure–property (PSP) relationship is a core conceptual framework in materials science, where processing conditions determine structural characteristics in mesoscale, which in turn govern material properties. 32,33 PSP modeling has recently gained attention in data-driven research involving additives and metal alloys. 34-37 However, the structural “S” component—typically represented by high-dimensional data such as spectra or images—remains a bottleneck for effective machine learning integration. A major challenge in PSP modeling is the development of an integrated and automated framework that supports design, interpretation, and property prediction in a unified manner. While PSP relationships have long been studied in polymer science 38-42 —such as in vulcanization, conductivity, and composites—applications of data-driven PSP modeling remain limited. Some efforts have been made in areas like polypropylene injection molding and reactor alloy design, 43,44 but a comprehensive, data-driven framework for sustainable polymers has rarely been reported. Here, we propose a data-driven modeling approach to elucidate the PSP relationships in polylactic acid (PLA), a representative sustainable polymer (Fig. 1). Our framework comprises three interconnected components: (1) Design – Single- and Multi-objective Bayesian optimization using surrogate objective variables derived from structural data are employed to identify optimal process and composition parameters; (2) Understanding – Dimensionality reduction and XAI are applied to analyze measurement data and reveal key structural features underlying the structure–property relationships; (3) Prediction – Hierarchical PSP modeling enables the regeneration of high-dimensional structural data (e.g., X-ray scattering profiles) from process conditions and subsequent prediction of material properties. RESULTS Preparation and evaluation of PLA films Polylactic acid (PLA), a widely studied biodegradable and bio-based polymer, was selected as a representative sustainable polymer. 45,46 PLA was isothermally crystallized under various conditions by systematically varying four processing parameters: (i) crystallization temperature ( T c ), (ii) crystallization time ( t c ), (iii) the ratio of poly(L-lactic acid) (PLLA) to poly(D-lactic acid) (PDLA) ( r P(L/D)LA ), and (iv) the presence or absence of a nucleating agent. This design resulted in 80 combinations (5 × 2 × 4 × 2) and 8 quenched films, as illustrated in Fig. 1b. The crystalline structures of the resulting PLA films were characterized using wide-angle X-ray scattering (WAXS) and small-angle X-ray scattering (SAXS) measurements (Fig. 2a–b). For pure PLLA ( r P(L/D)LA = 100/0), α′-form crystals were observed at T c = 90 °C (Fig. 2a, top). 47 As T c increased, peaks corresponding to the α-form became apparent and persisted up to T c = 160 °C. These peaks disappeared at T c = 180 °C, close to the melting temperature ( T m ) of PLLA (~175 °C). In the SAXS profiles, long-period structure derived from lamellar crystals were evident, with the scattering vector q decreasing with increasing T c (Fig. 2b, 120 and 140 °C), indicating an increase in lamellar thickness. For equimolar blends of PLLA and PDLA ( r P(L/D)LA = 50/50), additional peaks corresponding to stereocomplex PLA (scPLA) emerged at q = 8.4 and 14.7 nm⁻¹ (Fig. 2a, bottom). 48,49 At T c = 180 °C, only scPLA peaks remained, owing to its higher T m (~220 °C), attributed to its helical double-stranded structure. SAXS profiles under these conditions showed peaks at lower q values, indicating long-period structures. However, under the current processing conditions, equimolar blends did not form fully developed scPLA structures, but rather mixtures of PLLA, PDLA, and scPLA, as evidenced by dual melting peaks in DSC measurements. These findings demonstrate that variations in T c and PLLA/PDLA ratio lead to distinct crystalline structure. These structural differences influence the material properties. Enzymatic degradation and tensile tests were conducted to characterize biodegradability and mechanical strength, respectively. In the degradation tests, films were immersed in a buffer containing proteinase K for 2 days, and weight loss was measured. Quenched samples (with negligible crystallinity) showed the least degradation at r P(L/D)LA = 50/50 (Fig. 2c, 0 °C), consistent with reports that PDLA degrades more slowly than PLLA. 50,51 At T c = 140 °C, degradation decreased, likely due to increased crystallinity. Interestingly, samples crystallized at T c = 180 °C showed higher degradation, particularly at r P(L/D)LA = 50/50, possibly due to the presence of residual amorphous regions (Fig. 2a,c). Tensile tests conducted at 55 °C (below the T g of PLLA and PDLA) revealed that yield stress increased with crystallinity, following a trend opposite to degradation (Fig. 2d). These results confirm that the mechanical and degradative properties of PLA films are closely linked to both the processing conditions and the resulting crystalline structure. Direct process/X-ray profile–property relationships In conventional data-driven approaches, material properties are predicted directly from either processing parameters or structural data such as X-ray profiles using machine learning models. To explore this, we applied two representative regression techniques: Least absolute shrinkage and selection operator (LASSO, linear) and random forest regression (RFR, non-linear), to model (A) process–property and (B) X-ray profile–property relationships (Fig. 1b). For process–property modeling, RF regression exhibited higher predictive performance than LASSO, as indicated by the coefficient of determination (Fig. 3a). This suggests that the property responses to process variations are non-linear and better captured by RFR. In contrast, both methods performed well in modeling the X-ray profile–property relationship (Fig. 3b), indicating a relatively straightforward, possibly linear relationship between structure and properties. It is worth noting that conventional approaches treat processing and structural data separately, without capturing the full process–structure–property (PSP) hierarchy that materials scientists intuitively rely on. Both LASSO and RF can also provide feature importance metrics, such as regression coefficients and feature importance scores, respectively—tools that fall under the umbrella of XAI for global interpretability. In the process–property model, T c emerged as the most influential parameter in RFR (Fig. 3c). For the X-ray profile–property model, LASSO highlighted diffraction peaks at q ≈ 11.7–11.9 nm⁻¹ (α-form), with negative coefficients suggesting that decreased crystallinity enhances degradability (Fig. 3d, top). RFR, on the other hand, emphasized non-diffraction regions—suggesting that amorphous halo contributions were more important for predicting degradation (Fig. 3d, bottom). These differences highlight the strengths and limitations of different regression algorithms in handling high-dimensional data. However, it also emphasizes the challenge: humans often interpret X-ray data using simplified abstractions, making direct analysis of structural data difficult when integrating “S” into hierarchical PSP models. Dimensionality reduction of X-ray profiles X-ray diffraction and scattering profiles typically contain intensity information over hundreds or thousands of q -values, making them high-dimensional and computationally intensive to analyze. To address this, we applied principal component analysis (PCA) and non-negative matrix factorization (NMF) to reduce the dimensionality of the WAXS (1465 q -values) and SAXS (528 q -values) datasets down to 10 components. The cumulative contribution of the first 10 PCA components exceeded 99%. In total, 122 samples were considered, including the initial 88, additional samples suggested via Gaussian process regression (GPR) in section 3.9, and randomly selected samples from an expanded processing space. In PCA, each low-dimensional component can be inversely transformed into the original high-dimensional space, allowing direct interpretation. For WAXS_PCA1 and WAXS_PCA2 corresponded to α-form and α′-form crystalline peaks, respectively, based on slight differences in peak positions (Fig. 4a). WAXS_PCA3 aligned with features of scPLA, while PCA5 emphasized peak shoulders, potentially capturing crystallite disorder or peak width. In NMF, the basis vectors are inherently non-negative, enabling clearer interpretation of peak shapes. In WAXS data, WAXS_NMF1, NMF3, and NMF4 captured α-form, α′-form, and scPLA peaks, respectively (Fig. 4a). Notably, WAXS_NMF2 corresponded to the amorphous phase. For SAXS data, both PCA and NMF identified dominant signals at low q values near the beam center, likely due to high-intensity scattering unrelated to crystalline order (Fig. 4b). However, SAXS components SAXS_PCA5 and SAXS_NMF5 revealed long-range periodic peaks, indicating successful feature separation. These results demonstrate that both PCA and NMF can effectively extract and separate meaningful structural features from high-dimensional X-ray profiles. Understanding of structural importance by XAI Dimensionality-reduced X-ray data were used to predict the enzymatic degradation weight and yield stress of the 122 PLA samples. Each sample was represented by 40 structural features: 10 components from both PCA and NMF for WAXS and SAXS data. These features served as input for predictive models built using nested cross-validation (10-fold outer loop for testing, 5-fold inner loop for hyperparameter tuning) (Fig. 1b, (C)). Both LASSO and RFR achieved high coefficients of determination ( R ²) for degradation weight and yield stress predictions (Fig. 5a–b). Additionally, we evaluated prediction performance in terms of Pareto optimization using the hypervolume metric defined over the two objectives (degradation weight and yield stress). In this case, predictive accuracy declined; LASSO showed minimal performance, while RFR still yielded moderate R ² values (Fig. 5c). These results suggest that PCA- and NMF-derived structural features effectively capture linear property relationships. However, the Pareto front, involving trade-offs between objectives, reflects more complex, nonlinear dependencies—better handled by non-linear models such as RF. The most important structural features were identified via LASSO coefficients and RFR feature importances. For both degradation weight and yield stress, WAXS_NMF2 and WAXS_PCA1 were consistently highlighted as key contributors (Fig. 5d–e). WAXS_NMF2 corresponds to the amorphous phase, while WAXS_PCA1 represents the α- form of PLA. Notably, the LASSO coefficient for WAXS_NMF2 was positive for degradation weight (0.630) and negative for yield stress (-0.785), illustrating the trade-off between degradability and mechanical strength. Conversely, WAXS_PCA1 exhibited the opposite trend (-0.153 for degradation, 0.064 for yield stress). These trends reaffirm that increasing crystallinity reduces enzymatic degradability while enhancing toughness—an established phenomenon in PLA materials. This validates that the data-driven structure–property models provide physically interpretable insights from high-dimensional structural data. The same analysis was extended to the Pareto solutions. Feature contributions for hypervolume prediction were generally lower than for individual property predictions (Fig. 5f), suggesting increased complexity. Nonetheless, SAXS_NMF5 (related to lamellar thickness), WAXS_NMF4, and WAXS_PCA4 (associated with scPLA crystal lattice) were prominent, implying that stereocomplex formation contributes positively to overcoming property trade-offs. It should be noted that the use of dimensionality reduction enables capturing the overall shapes of X-ray profiles, making them more interpretable to humans. To provide local explanations for individual samples, SHAP (SHapley Additive exPlanations) analysis was performed using the RF regression models. 52,53 SHAP values confirmed that WAXS_NMF2 and WAXS_PCA1 were the most significant features across most samples for both degradation weight and yield stress—consistent with global model results (Supplementary Video 1). However, for Pareto solutions, which involve nonlinear dependencies, the most influential features varied between samples. For instance, WAXS_NMF3 and WAXS_NMF7 (corresponding to α′- and α-forms of PLA) emerged as key contributors depending on the sample location in feature space. These findings highlight the effectiveness of XAI methods in elucidating complex and localized structure–property relationships in nonlinear systems, where the contribution of each feature varies across individual samples. Materials design by Bayesian optimization In biodegradable polymers, degradability and mechanical strength often exhibit a trade-off relationship. 15,16,28 Consistent with this, enzymatic degradation and yield stress in PLA samples showed strong negative correlation (Spearman’s ρ = −0.89, p < 0.01, Fig. 6a). To address this conflict, Bayesian Optimization (BO) was employed using Gaussian process regression (GPR). 54-56 The BO model was trained on the original 88 samples. The design space was then expanded to include 660 process parameter combinations (11 × 5 × 6 × 2; see Fig. 1b). New candidate points were suggested based on multi-objective optimization by maximizing Expected Hypervolume Improvement (EHVI) or Hypervolume-based Probability of Improvement (HVPI) (Fig. 1b, (D)). 28,57,58 Several new samples were identified on or near the Pareto front, showing moderate yield stress (>14 MPa) and high degradation (>0.7 mg) (Fig. 6a). While dramatic breakthroughs were limited—likely due to a constrained design space—this approach demonstrates potential for optimizing difficult trade-offs. 28 More recently, surrogate optimization strategies have emerged, wherein easily measurable intermediate variables are used in place of expensive or difficult-to-measure objective properties. 29 In the context of PSP modeling, this suggests the possibility of optimizing structure, rather than final properties (Fig. 1b, (E)). Thus, we performed BO simulations using selected PCA and NMF features (e.g., WAXS_NMF3, NMF8) as surrogate objectives—identified as important contributors via XAI analysis (Fig. 5d, 5f). Remarkably, BO targeting WAXS_NMF8 achieved similar or even superior early performance in degradation prediction compared to property-based BO (Fig. 6b). This advantage was even more pronounced for multi-objective optimization (hypervolume) where BO using WAXS_NMF3 matched or exceeded direct optimization (Fig. 6c–d). These results support the feasibility of structure-based BO, effectively bypassing costly experimental tests such as degradation assays or mechanical evaluations. This surrogate-variable approach holds significant promise for sustainable materials research, where resource-intensive evaluations (e.g., degradation, recyclability, mechanical strength) often limit experimental throughput. Hierarchical modeling for prediction of X-ray profiles and property In previous sections, we separately modeled process–property and structure–property relationships. However, the hierarchical nature of the PSP framework suggests that integrated models—where process data predict structure, which in turn predicts properties—may offer more robust, interpretable, and generalizable insights. As a first step toward such hierarchical modeling, we constructed regression models from process parameters to individual structural features (from PCA/NMF), and then from these structural features to target properties using LASSO (Fig. 1b, (F)). For the process–structure step, LASSO regression yielded low R ² values, indicating poor performance (Fig. 7a). In contrast, RF regression significantly improved R ² values, suggesting that the process–structure mapping is inherently nonlinear. Using the predicted structural features, we then attempted to reconstruct the full X-ray profiles via inverse transformation of the PCA or NMF components. The regenerated WAXS and SAXS profiles showed good agreement with the original data across a wide range of crystalline morphologies, including amorphous, α-form PLLA, and scPLA samples (Fig. 7b–d). Simultaneously, material properties were also predicted from the reconstructed structural features. These results demonstrate the viability of hierarchical PSP modeling, where processing conditions can be used to predict not only properties but also high-dimensional structural data—supporting both design and mechanistic understanding in a unified framework. DISCUSSION In this study, we have established a comprehensive data-driven framework for modeling process–structure–property (PSP) relationships in sustainable polymers, exemplified by polylactic acids (PLA). By systematically varying crystallization processing conditions, we characterized the resulting crystalline structures and their corresponding material properties via X-ray diffraction/scattering, enzymatic degradation assays, and tensile testing. Leveraging single- and multi-objective Bayesian optimization, we successfully identified new Pareto-optimal processing parameters that effectively balance the trade-off between degradability and mechanical toughness using structure parameters as surrogate objective variables. To gain structural insights, dimensionality reduction techniques combined with explainable AI (XAI) were employed, revealing key diffraction features closely linked to material performance. Furthermore, we developed hierarchical PSP models that enable the sequential prediction of both structural profiles and functional properties directly from processing inputs. The development of sustainable polymers typically involves navigating complex, multivariate process-structure-property spaces, where conventional trial-and-error experimentation is inefficient and costly. Existing materials informatics approaches often address isolated problems—such as single-property prediction or feature extraction—and thus fall short in handling the inherently multimodal, multiscale, multitask, and multi-process nature of polymer design. Our integrated PSP modeling framework demonstrates the power of data-driven science to unify these disparate tasks into a coherent platform for automated and holistic analysis, similar to human performance. We envision this approach as a foundational step toward the creation of generalized materials models that can accelerate discovery and optimization across diverse polymer systems, ultimately advancing sustainable materials technologies. METHODS Molding of PLA PLA films were prepared via hot pressing. PLA and the nucleator (Ecopromote® TF) were supplied by Teijin Limited and Nissan Chemical Corporation, respectively. The mixture of poly L-lactic acid (PLLA) and/or poly D-lactic acid (PDLA) (5 wt.%) in the present/absence of the nucleator (0.1 wt.% for PLA) were dissolved in dioxane and stirred for 18 h at 60 °C. The solution was then freeze-dried using FDU-506 (EYELA) and heated at 100 °C for 15 h under vacuum. The obtained white solids were placed between a silicon wafer treated with n -octadecyl trimethoxy silane and melted at 240 °C for 10 min at 10 MPa using a hot-press machine (Imoto Machinery Co., Ltd.). Crystallization was conducted at a specific temperature (90-180 °C) for 5 or 20 min at 5 MPa in different pre-heated hot press machines (Imoto Machinery Co., Ltd.). The crystallization of PLA was quenched in ice water to obtain a film of approximately 150 mm in thickness. For original samples, eighty crystallized samples (five crystalline temperatures (90, 120, 140, 160, and 180 °C), two crystallization times (5 and 20 min), four ratios of PLLA/PDLA ( r P(L/D)LA = 100/0, 90/10, 70/30, and 50/50), and two concentrations of nucleator (0 and 0.1 wt.%)) and eight quenched samples (four ratios of PLLA/PDLA and two concentrations of nucleator) were prepared, obtaining a total of 88 samples. X-ray scattering/diffraction measurements Wide-angle X-ray scattering (WAXS) and small-angle X-ray scattering (SAXS) measurements were performed using BL40XU or BL05XU at SPring-8. The PLA films were exposed to X-rays (0.1 nm) for 0.5 s and 5 s, which were detected by SOPHIAS and PILATUS (1 M) with a sample-to-detector distance of 100.3 mm and 3870 mm for WAXS and SAXS, respectively. The beam centers and sample-to-detector distances were estimated using CeO 2 and AgBe as the standard samples for WAXS and SAXS, respectively. The two-dimensional image data were converted to one-dimensional profiles using the FIT2D software, and the profiles were subtracted from the background profiles without samples using any coefficient. The scattering vector was defined as q = 4π sin( q / λ ), where λ is the wavelength of the X-ray, and 2 q is the scattering angle. Enzymatic degradation test Enzymatic degradation tests were performed using proteinase K. The PLA films were cut using an elliptical mold with a length of 14 mm and short axis of 3 mm to obtain nearly identical surface areas. The films were treated with proteinase K (1 mg, Nacalai Tesque) in Tris buffer solution (1 mL, pH 7.4) at 37 °C for 2 d. The solutions were replaced with new solutions after 1 d. After 2 d, the films were washed with pure water and dried under vacuum. The degradation weights were estimated based on the decreased weight of the films before and after the degradation tests, considering the averages of the three tests. Tensile test Tensile tests were performed via the uniaxial elongation of the sample under heating. The samples were cut using a dumbbell-shaped mold with a length of 12 mm and a width of 2 mm. Uniaxial elongations were conducted using a tensile machine (Imoto Machinery Co., Ltd.) at 55 °C at a rate of 10 mm/min. Before the test, samples were maintained under the heating condition for 10 min. The yield stress was evaluated as the highest stress below a strain of 0.3. In some cases, the samples ruptured before reaching the yield points, in which case the stress at break was treated as the yield stress. The elongation at break was estimated as the elongation ratio at which the sample ruptured. Both values were obtained using the average values of three tests. Regression model by LASSO Least absolute shrinkage and selection operator (LASSO) was performed using the module in Scikit-learn library. 59,60 Regressions were performed using the Lasso function in the linear_model module, and predicted values were obtained via nested cross-validation (CV) with 10-fold outer CV for test estimation and 5-fold inner CV for hyperparameter tunning. Random forest regression Random forest regression (RFR) was conducted using RandomForestRegressor module in scikit-learn. 60 The nested CV was performed, where the hyperparameters max_depth (1, 3, 5, 10, 30 and 50), n_estimators (10, 30, 50, 100, 300), and max_features (sqrt, log2, and None) were determined using 5-fold inner CV, and the predicted values were obtained by the 10-fold outer CV. Dimensional reduction of X-ray data by PCA and NMF Dimensional reductions were conducted using principal component analysis (PCA) and non-negative matrix factorization (NMF) functions in Scikit-learn. 60 The n_components were set to 20 in both cases, and only the most significant 10 dimensions were used for the next procedure. In PCA, the profiles corresponding to the PCA space were obtained using the inverse_transform function treated with a zero array containing only 1 in a specific component. The profiles separated by NMF were obtained by an attribute of component_ in the function. Evaluation of SHAP values SHAP values were evaluated using the SHAP library. 52 Regression models were constructed using a random forest regressor, as explained above. The SHAP values were obtained by the explainer functions in SHAP for test data in the 10-fold outer cross-validation. Bayesian optimization using Gaussian process regression Multi-objective optimization was performed using COMBO or PHYSBO 61 , a Bayesian optimization library based on a Gaussian process regression (GPR). The molding process of the original 88 combinations was input for multi-objective properties: degradation weight vs. yield stress. Subsequently, the next process conditions were recommended among the expanded combinations of the molding process ( combinations, Fig. 1b), with max_num_probes = 1 and num_search_each_prob = 3. The scores of the Pareto solutions were estimated based on the EHVI or HVPI, where a total of four process conditions were adapted for the next step. In addition, three randomly chosen process conditions were used. In the actual procedure, the two multi-objective optimizations proceeded at the same time, where the result of one optimization was reflected in the next input data in the other optimization. Therefore, 11 samples were added to the input data. This cycle was repeated three times with increasing sample numbers. Bayesian optimization using surrogate objective variables was carried out on a total of 122 samples obtained by the above procedure. The surrogate variables were determined from the top five most important PCA or NMF structural components based on the feature importances of the RFR model. GPR was performed using the process conditions and the surrogate variables as inputs and objectives, respectively. The initial three samples were selected by random sampling, and subsequently one sample was obtained by GPR for 50 iterations. The results were plotted based on the averages of 100 trials. Declarations DATA AVAILABILITY The datasets used and/or analysed during the current study available from the corresponding author on reasonable request. CODE AVAILABILITY The underlying code for this study is not publicly available but may be made available to qualified researchers on reasonable request from the corresponding author. ACKNOWLEDGEMENTS The synchrotron radiation experiments were performed at the BL40XU and BL05XU beamlines of SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal No. 2020A1525 and 2021B1476). FUNDING This work was supported by the Cabinet Office, Government of Japan, Cross-ministerial Strategic Innovation Promotion Program (SIP), “Technologies for Smart Bio-industry and Agriculture” (funding agency: Bio-oriented Technology Research Advancement Institution, NARO). This paper is based on results obtained from a project, JPNP18016, commissioned by the New Energy and Industrial Technology Development Organization (NEDO). This work was also supported by the JSPS Grant-in-Aid for Scientific Research on Innovative Areas, Discrete Geometric Analysis for Materials Design: 20H04644, by the Grant-in-Aid for Scientific Research (B): 20H02800, by Data Creation and Utilization Type Material Research and Development Project Grant Number JPMXP1122683430, JST-Mirai Program Grant Number JPMJMI21EH, JST FOREST program (Grant Number: JPMJFR232U), and by Institute of Mathematics for Industry, Joint Usage/Research Center in Kyushu University (Workshop (II), Reference No. 2023a011, 2024a011, and 2025a041). Y.A. and K.T. acknowledges the financial support of the Grant-in-Aid for RIKEN-Kyushu Univ Science and Technology Hub Collaborative Research Program. AUTHOR CONTRIBUTIONS Y.A. and K.T. conceived the study. Y.A. and H.K. performed the experiments. Y.A. and H.K. analyzed the data. K.K. and A.T. were responsible for the measurements. M.H. and K.H. proposed the use of XAI and sparse modeling, respectively. 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Swarm Evol Comput 44 , 945-956, (2019). doi:10.1016/j.swevo.2018.10.007 Tibshirani, R. Regression shrinkage and selection via the Lasso. J Roy Stat Soc B Met 58 , 267-288, (1996). doi:DOI 10.1111/j.2517-6161.1996.tb02080.x Pedregosa, F. et al. Scikit-learn: Machine Learning in Python. J Mach Learn Res 12 , 2825-2830, (2011) Motoyama, Y. et al. Bayesian optimization package: PHYSBO. Comput Phys Commun 278 , 108405, (2022). doi:10.1016/j.cpc.2022.108405 Additional Declarations No competing interests reported. Supplementary Files SupplementaryVideo1.mov Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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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-8066698","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":550588994,"identity":"baf94da7-4aeb-40b6-a643-3748cf3c32f8","order_by":0,"name":"Yoshifumi Amamoto","email":"data:image/png;base64,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","orcid":"","institution":"The University of Tokyo","correspondingAuthor":true,"prefix":"","firstName":"Yoshifumi","middleName":"","lastName":"Amamoto","suffix":""},{"id":550588995,"identity":"33b15ba4-765b-472a-b347-fc1dfab15302","order_by":1,"name":"Hiroteru Kikutake","email":"","orcid":"","institution":"Kyushu University","correspondingAuthor":false,"prefix":"","firstName":"Hiroteru","middleName":"","lastName":"Kikutake","suffix":""},{"id":550588996,"identity":"eae8b168-a37a-4df9-ac37-3d0f3b8d615e","order_by":2,"name":"Ken Kojio","email":"","orcid":"","institution":"Kyushu University","correspondingAuthor":false,"prefix":"","firstName":"Ken","middleName":"","lastName":"Kojio","suffix":""},{"id":550588997,"identity":"a2a83a42-6e8d-41e8-8ba7-b6cd6e117efd","order_by":3,"name":"Atsushi Takahara","email":"","orcid":"","institution":"Kyushu University","correspondingAuthor":false,"prefix":"","firstName":"Atsushi","middleName":"","lastName":"Takahara","suffix":""},{"id":550588998,"identity":"6ed78716-7ce5-4193-8772-d64fdff9416a","order_by":4,"name":"Kei Hirose","email":"","orcid":"","institution":"Kyushu University","correspondingAuthor":false,"prefix":"","firstName":"Kei","middleName":"","lastName":"Hirose","suffix":""},{"id":550588999,"identity":"528a170d-5fcb-42ea-826a-2ee9700d187b","order_by":5,"name":"Maiya Hori","email":"","orcid":"","institution":"Kyushu University","correspondingAuthor":false,"prefix":"","firstName":"Maiya","middleName":"","lastName":"Hori","suffix":""},{"id":550589000,"identity":"893aaecd-68f6-473e-a266-be90ae73ef1b","order_by":6,"name":"Kei Terayama","email":"","orcid":"","institution":"Yokohama City University","correspondingAuthor":false,"prefix":"","firstName":"Kei","middleName":"","lastName":"Terayama","suffix":""}],"badges":[],"createdAt":"2025-11-09 03:08:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8066698/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8066698/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":96904192,"identity":"d8c9bac7-6c54-4d6e-8650-ca14266b4003","added_by":"auto","created_at":"2025-11-27 12:01:42","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":103317,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eData-driven modeling of PSP relationship of sustainable polymers. \u003c/strong\u003e(\u003cstrong\u003ea\u003c/strong\u003e) An integrated PSP framwork for the design, understanding, and prediction of sustainable polymers was constructed via data-driven approaches. (\u003cstrong\u003eb\u003c/strong\u003e) PSP relationships of PLA with four kinds of process conditions were modeled. Desired properties for the degradation weight and yield stress were obtained using Bayesian optimization by surrogate objective variables derived from structural data. X-ray data were dimensionally reduced, and the important features in the profiles were extracted by the explainable AI techniques. RFR, random forest regression; GPR, Gaussian process regression.\u003c/p\u003e","description":"","filename":"Picture1.png","url":"https://assets-eu.researchsquare.com/files/rs-8066698/v1/8ba23113dc7d15c6c6d79a43.png"},{"id":96904193,"identity":"431734e8-fe5f-4f99-8e6e-92c1d37de533","added_by":"auto","created_at":"2025-11-27 12:01:42","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":54108,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTypical X-ray profiles and properties of PLA with different molding process.\u003c/strong\u003e (\u003cstrong\u003ea\u003c/strong\u003e) WAXS and (\u003cstrong\u003eb\u003c/strong\u003e) SAXS profiles of PLA with \u003cem\u003er\u003c/em\u003e\u003csub\u003eP(L/D)LA\u003c/sub\u003e = 100/0 or 50/50 crystallized at several crystallization temperature for 20 min in the presence of nucleator. These profiles reflect the crystal structure with high-dimensional data. (\u003cstrong\u003ec\u003c/strong\u003e-\u003cstrong\u003ed\u003c/strong\u003e) Enzymatic degradation weight and yield stress of PLA prepared using several compositions of PLLA and PDLA crystallized at different temperatures. Sizes of circles correspond to the values of the properties.\u003c/p\u003e","description":"","filename":"Picture2.png","url":"https://assets-eu.researchsquare.com/files/rs-8066698/v1/7f6cf3e2ea9b657a64289b35.png"},{"id":96904196,"identity":"444d983f-02cd-4008-b565-4d0cfe02cfe3","added_by":"auto","created_at":"2025-11-27 12:01:42","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":56511,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDirect process/X-ray profile–property relationships using LASSO and RF regression models.\u003c/strong\u003e Parity plots of degradation (deg.) weights for (\u003cstrong\u003ea\u003c/strong\u003e) process–property and (\u003cstrong\u003eb\u003c/strong\u003e) WAXS profile–property relationships obtained via nested cross-validation using LASSO and RFR. The coefficient of determination (\u003cem\u003eR\u003c/em\u003e²) indicates predictive performance. (\u003cstrong\u003ec\u003c/strong\u003e) Important explanatory variables in the process–property models, showing the average feature importance values from the outer 10-fold nested CV in RF regression. Error bars represent the standard deviations. (\u003cstrong\u003ed\u003c/strong\u003e) Key features in WAXS profile–property models, where cumulatively stacked bars represent the absolute LASSO coefficients and RF feature importances across nested CV folds.\u003c/p\u003e","description":"","filename":"Picture3.png","url":"https://assets-eu.researchsquare.com/files/rs-8066698/v1/cc6bf241bd71e1f13d9a582a.png"},{"id":96920859,"identity":"e6683fe1-b2c6-45ca-bc35-719013a06ee6","added_by":"auto","created_at":"2025-11-27 14:15:28","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":53459,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eWAXS and SAXS profiles subjected to PCA and NMF. \u003c/strong\u003e(\u003cstrong\u003ea-b\u003c/strong\u003e) Dimensional reductions of (\u003cstrong\u003ea\u003c/strong\u003e) WAXS and (\u003cstrong\u003eb\u003c/strong\u003e) SAXS profiles of PLA were conducted using PCA and NMF. In the case of PCA, only each dimension in PCA space was recovered to original space. For NMF, each basic vector in the factorized matrix was plotted. In all profiles, intensities of the profiles were unified using min-max normalizations.\u003c/p\u003e","description":"","filename":"Picture4.png","url":"https://assets-eu.researchsquare.com/files/rs-8066698/v1/22e506ca5e0377d077b7bd4b.png"},{"id":96920282,"identity":"2a2f59a9-bdd4-4af4-987b-12479df9b094","added_by":"auto","created_at":"2025-11-27 14:15:01","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":93049,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePCA\u0026amp;NMF–property relationships using LASSO and RF regressions and visualization of important components. \u003c/strong\u003e(\u003cstrong\u003ea\u003c/strong\u003e-\u003cstrong\u003ec\u003c/strong\u003e) Parity plots of (\u003cstrong\u003ea\u003c/strong\u003e) degradation (deg.) weights, (\u003cstrong\u003eb\u003c/strong\u003e) yield stress, and (\u003cstrong\u003ec\u003c/strong\u003e) hypervolume in LASSO and RF regressions. (\u003cstrong\u003ee\u003c/strong\u003e-\u003cstrong\u003eg\u003c/strong\u003e) Most significant 5 components via PCA\u0026amp;NMD of WAXS and SAXS profiles for the properties: (\u003cstrong\u003ee\u003c/strong\u003e) degradation weight, (\u003cstrong\u003ef\u003c/strong\u003e) yield stress, and (\u003cstrong\u003eg\u003c/strong\u003e) hypervolume. Orders from top to bottom were determined using the average of the coefficient in LASSO and importance in the RFR.\u003c/p\u003e","description":"","filename":"Picture5.png","url":"https://assets-eu.researchsquare.com/files/rs-8066698/v1/36de0bc72a94420fef31c219.png"},{"id":96920462,"identity":"83b33e82-136d-411b-9438-27e4fd9d5d2a","added_by":"auto","created_at":"2025-11-27 14:15:11","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":60911,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eBayesian optimization based on Gaussian process regression using property and surrogate variables. \u003c/strong\u003e(\u003cstrong\u003ea\u003c/strong\u003e) Direct multi-objective optimization of process conditions for degradability and toughness. Candidate points on the Pareto frontier (degradation weight vs. yield stress), selected from 660 process combinations by Gaussian process regression, were experimentally validated in triplicate. Randomly selected process conditions were also evaluated for comparison. (\u003cstrong\u003eb\u003c/strong\u003e–\u003cstrong\u003ed\u003c/strong\u003e) Bayesian optimization using PCA- and NMF-derived surrogate variables instead of actual properties, applied to known 122 samples. (\u003cstrong\u003eb\u003c/strong\u003e) Optimization using a surrogate variable as a proxy for degradation weight. (\u003cstrong\u003ec\u003c/strong\u003e, \u003cstrong\u003ed\u003c/strong\u003e) Optimization based on hypervolume metrics, where (\u003cstrong\u003ec\u003c/strong\u003e) shows the maximum hypervolume obtained in each trial, and (\u003cstrong\u003ed\u003c/strong\u003e) shows the cumulative hypervolume across all selected samples. Horizontal gray lines indicate the maximum values among the 122 samples.\u003c/p\u003e","description":"","filename":"Picture6.png","url":"https://assets-eu.researchsquare.com/files/rs-8066698/v1/ff10a673a5f9d265f2469a62.png"},{"id":96921013,"identity":"e02efd22-9bf8-4f2d-b900-68b4dd11090a","added_by":"auto","created_at":"2025-11-27 14:15:35","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":70347,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eHierarchical modeling of PSP relationship for prediction of X-ray profiles and property.\u003c/strong\u003e(\u003cstrong\u003ea\u003c/strong\u003e) Parity plots of degradation (deg.) weights in PSP hierarchical modeling, where LASSO or RF regression was utilized in process–structure relationship and LASSO was applied in structure–property relationship. (\u003cstrong\u003eb\u003c/strong\u003e-\u003cstrong\u003ed\u003c/strong\u003e) Representative regenerated profiles recovered using inverse transforms of PCA and NMF utilizing predicted values of structure data in the process-structure relationship by employing RFR.\u003c/p\u003e","description":"","filename":"Picture7.png","url":"https://assets-eu.researchsquare.com/files/rs-8066698/v1/49503a527a0689c59232bb37.png"},{"id":96923218,"identity":"1529a72f-f5d1-4412-a150-e14da25f9992","added_by":"auto","created_at":"2025-11-27 14:21:12","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1597471,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8066698/v1/07d73782-e9d0-4953-88c4-6fb06f22d7ce.pdf"},{"id":96904200,"identity":"7b76fad9-8cd3-4b79-b59e-0f9940e9bdd9","added_by":"auto","created_at":"2025-11-27 12:01:43","extension":"mov","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":22737361,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryVideo1.mov","url":"https://assets-eu.researchsquare.com/files/rs-8066698/v1/f4f0306301a4069bc185a179.mov"}],"financialInterests":"No competing interests reported.","formattedTitle":"Data-Driven Process–Structure–Property Framework for the Design, Understanding, and Prediction of Sustainable Polymers","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eThe growing environmental impact of conventional plastics and rubbers has fueled demand for high-performance, sustainable polymeric materials. \u003csup\u003e1-6\u003c/sup\u003e For instance, in the field of biodegradable plastics, numerous polymers have been developed with degradation rates tailored to specific environmental conditions. \u003csup\u003e7-10\u003c/sup\u003e In line with circular economy initiatives, composite technologies play a critical role in producing recycled materials with properties comparable to those of virgin polymers. \u003csup\u003e11-14\u003c/sup\u003e Because key properties often exhibit trade-offs, such as toughness versus degradability, achieving the desired balance requires careful control over both primary and higher-order polymer structures. \u003csup\u003e15,16\u003c/sup\u003e However, as material systems become increasingly complex, conventional trial-and-error approaches struggle to achieve optimal results efficiently. This underscores the need for digital research platforms that enable automated analysis, mechanism discovery, and experimental recommendation toward the development of sustainable polymers.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eData-driven science has emerged as a powerful strategy in polymer science for both material development and mechanistic understanding. \u003csup\u003e17-20\u003c/sup\u003e Advanced computational techniques can extract key patterns from complex, high-dimensional datasets and automate analysis without human bias, \u003csup\u003e21-23\u003c/sup\u003e leading to increasing applications in polymer science. \u003csup\u003e24,25\u003c/sup\u003e Additionally, machine learning models have been used to design polymeric materials, including biodegradable polymers, by exploring chemical structure/process\u0026ndash;property relationships. \u003csup\u003e26-29\u003c/sup\u003e Among them, a Bayesian optimization framework employing surrogate objective variables rather than directly measured properties has been developed, \u003csup\u003e29\u003c/sup\u003e since experimental evaluation of sustainable polymer properties such as degradation tests often requires long periods. Explainable artificial intelligence (XAI) techniques have helped uncover the higher-order structure\u0026ndash;property relationships behind target property predictions. \u003csup\u003e28-31\u003c/sup\u003e Despite these advances, most studies have focused on single-variable relationships or isolated stages within the research workflow\u0026shy;\u0026ndash;as exemplified by the above two relationships\u0026ndash;which limits their ability to address the inherently multi-process, multitask, and hierarchical nature of real-world polymer systems. To overcome these limitations, a more comprehensive framework is required.\u003c/p\u003e\n\u003cp\u003eThe process\u0026ndash;structure\u0026ndash;property (PSP) relationship is a core conceptual framework in materials science, where processing conditions determine structural characteristics in mesoscale, which in turn govern material properties. \u003csup\u003e32,33\u003c/sup\u003e PSP modeling has recently gained attention in data-driven research involving additives and metal alloys. \u003csup\u003e34-37\u003c/sup\u003e However, the structural \u0026ldquo;S\u0026rdquo; component\u0026mdash;typically represented by high-dimensional data such as spectra or images\u0026mdash;remains a bottleneck for effective machine learning integration. A major challenge in PSP modeling is the development of an integrated and automated framework that supports design, interpretation, and property prediction in a unified manner. While PSP relationships have long been studied in polymer science\u003csup\u003e38-42\u003c/sup\u003e\u0026mdash;such as in vulcanization, conductivity, and composites\u0026mdash;applications of data-driven PSP modeling remain limited. Some efforts have been made in areas like polypropylene injection molding and reactor alloy design, \u003csup\u003e43,44\u003c/sup\u003e but a comprehensive, data-driven framework for sustainable polymers has rarely been reported.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eHere, we propose a data-driven modeling approach to elucidate the PSP relationships in polylactic acid (PLA), a representative sustainable polymer (Fig. 1). Our framework comprises three interconnected components: (1) Design \u0026ndash; Single- and Multi-objective Bayesian optimization using surrogate objective variables derived from structural data are employed to identify optimal process and composition parameters; (2) Understanding \u0026ndash; Dimensionality reduction and XAI are applied to analyze measurement data and reveal key structural features underlying the structure\u0026ndash;property relationships; (3) Prediction \u0026ndash; Hierarchical PSP modeling enables the regeneration of high-dimensional structural data (e.g., X-ray scattering profiles) from process conditions and subsequent prediction of material properties.\u003c/p\u003e"},{"header":"RESULTS ","content":"\u003cp\u003e\u003cstrong\u003ePreparation and evaluation of PLA films\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003ePolylactic acid (PLA), a widely studied biodegradable and bio-based polymer, was selected as a representative sustainable polymer. \u003csup\u003e45,46\u003c/sup\u003e PLA was isothermally crystallized under various conditions by systematically varying four processing parameters: (i) crystallization temperature (\u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e), (ii) crystallization time (\u003cem\u003et\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e), (iii) the ratio of poly(L-lactic acid) (PLLA) to poly(D-lactic acid) (PDLA) (\u003cem\u003er\u003c/em\u003e\u003csub\u003eP(L/D)LA\u003c/sub\u003e), and (iv) the presence or absence of a nucleating agent. This design resulted in 80 combinations (5 × 2 × 4 × 2) and 8 quenched films, as illustrated in Fig. 1b. The crystalline structures of the resulting PLA films were characterized using wide-angle X-ray scattering (WAXS) and small-angle X-ray scattering (SAXS) measurements (Fig. 2a–b). For pure PLLA (\u003cem\u003er\u003c/em\u003e\u003csub\u003eP(L/D)LA\u003c/sub\u003e = 100/0), α′-form crystals were observed at \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e = 90 °C (Fig. 2a, top). \u003csup\u003e47\u003c/sup\u003e As \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e increased, peaks corresponding to the α-form became apparent and persisted up to \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e = 160 °C. These peaks disappeared at \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e = 180 °C, close to the melting temperature (\u003cem\u003eT\u003c/em\u003e\u003csub\u003em\u003c/sub\u003e) of PLLA (~175 °C). In the SAXS profiles, long-period structure derived from lamellar crystals were evident, with the scattering vector \u003cem\u003eq\u003c/em\u003e decreasing with increasing \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e (Fig. 2b, 120 and 140 °C), indicating an increase in lamellar thickness. For equimolar blends of PLLA and PDLA (\u003cem\u003er\u003c/em\u003e\u003csub\u003eP(L/D)LA\u003c/sub\u003e = 50/50), additional peaks corresponding to stereocomplex PLA (scPLA) emerged at \u003cem\u003eq\u003c/em\u003e = 8.4 and 14.7 nm⁻¹ (Fig. 2a, bottom). \u003csup\u003e48,49\u003c/sup\u003e At \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e = 180 °C, only scPLA peaks remained, owing to its higher \u003cem\u003eT\u003c/em\u003e\u003csub\u003em\u003c/sub\u003e (~220 °C), attributed to its helical double-stranded structure. SAXS profiles under these conditions showed peaks at lower \u003cem\u003eq\u003c/em\u003e values, indicating long-period structures. However, under the current processing conditions, equimolar blends did not form fully developed scPLA structures, but rather mixtures of PLLA, PDLA, and scPLA, as evidenced by dual melting peaks in DSC measurements. These findings demonstrate that variations in \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e and PLLA/PDLA ratio lead to distinct crystalline structure.\u003c/p\u003e\n\u003cp\u003eThese structural differences influence the material properties. Enzymatic degradation and tensile tests were conducted to characterize biodegradability and mechanical strength, respectively. In the degradation tests, films were immersed in a buffer containing proteinase K for 2 days, and weight loss was measured. Quenched samples (with negligible crystallinity) showed the least degradation at \u003cem\u003er\u003c/em\u003e\u003csub\u003eP(L/D)LA\u003c/sub\u003e = 50/50 (Fig. 2c, 0 °C), consistent with reports that PDLA degrades more slowly than PLLA. \u003csup\u003e50,51\u003c/sup\u003e At \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e = 140 °C, degradation decreased, likely due to increased crystallinity. Interestingly, samples crystallized at \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e = 180 °C showed higher degradation, particularly at \u003cem\u003er\u003c/em\u003e\u003csub\u003eP(L/D)LA\u003c/sub\u003e = 50/50, possibly due to the presence of residual amorphous regions (Fig. 2a,c). Tensile tests conducted at 55 °C (below the \u003cem\u003eT\u003c/em\u003e\u003csub\u003eg\u003c/sub\u003e of PLLA and PDLA) revealed that yield stress increased with crystallinity, following a trend opposite to degradation (Fig. 2d). These results confirm that the mechanical and degradative properties of PLA films are closely linked to both the processing conditions and the resulting crystalline structure.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDirect process/X-ray profile–property relationships\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn conventional data-driven approaches, material properties are predicted directly from either processing parameters or structural data such as X-ray profiles using machine learning models. To explore this, we applied two representative regression techniques: Least absolute shrinkage and selection operator (LASSO, linear) and random forest regression (RFR, non-linear), to model (A) process–property and (B) X-ray profile–property relationships (Fig. 1b). For process–property modeling, RF regression exhibited higher predictive performance than LASSO, as indicated by the coefficient of determination (Fig. 3a). This suggests that the property responses to process variations are non-linear and better captured by RFR. In contrast, both methods performed well in modeling the X-ray profile–property relationship (Fig. 3b), indicating a relatively straightforward, possibly linear relationship between structure and properties. It is worth noting that conventional approaches treat processing and structural data separately, without capturing the full process–structure–property (PSP) hierarchy that materials scientists intuitively rely on.\u003c/p\u003e\n\u003cp\u003eBoth LASSO and RF can also provide feature importance metrics, such as regression coefficients and feature importance scores, respectively—tools that fall under the umbrella of XAI for global interpretability. In the process–property model, \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e emerged as the most influential parameter in RFR (Fig. 3c). For the X-ray profile–property model, LASSO highlighted diffraction peaks at \u003cem\u003eq\u003c/em\u003e ≈ 11.7–11.9 nm⁻¹ (α-form), with negative coefficients suggesting that decreased crystallinity enhances degradability (Fig. 3d, top). RFR, on the other hand, emphasized non-diffraction regions—suggesting that amorphous halo contributions were more important for predicting degradation (Fig. 3d, bottom). These differences highlight the strengths and limitations of different regression algorithms in handling high-dimensional data. However, it also emphasizes the challenge: humans often interpret X-ray data using simplified abstractions, making direct analysis of structural data difficult when integrating “S” into hierarchical PSP models.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDimensionality reduction of X-ray profiles \u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eX-ray diffraction and scattering profiles typically contain intensity information over hundreds or thousands of \u003cem\u003eq\u003c/em\u003e-values, making them high-dimensional and computationally intensive to analyze. To address this, we applied principal component analysis (PCA) and non-negative matrix factorization (NMF) to reduce the dimensionality of the WAXS (1465 \u003cem\u003eq\u003c/em\u003e-values) and SAXS (528 \u003cem\u003eq\u003c/em\u003e-values) datasets down to 10 components. The cumulative contribution of the first 10 PCA components exceeded 99%. In total, 122 samples were considered, including the initial 88, additional samples suggested via Gaussian process regression (GPR) in section 3.9, and randomly selected samples from an expanded processing space.\u003c/p\u003e\n\u003cp\u003eIn PCA, each low-dimensional component can be inversely transformed into the original high-dimensional space, allowing direct interpretation. For WAXS_PCA1 and WAXS_PCA2 corresponded to α-form and α′-form crystalline peaks, respectively, based on slight differences in peak positions (Fig. 4a). WAXS_PCA3 aligned with features of scPLA, while PCA5 emphasized peak shoulders, potentially capturing crystallite disorder or peak width. In NMF, the basis vectors are inherently non-negative, enabling clearer interpretation of peak shapes. In WAXS data, WAXS_NMF1, NMF3, and NMF4 captured α-form, α′-form, and scPLA peaks, respectively (Fig. 4a). Notably, WAXS_NMF2 corresponded to the amorphous phase. For SAXS data, both PCA and NMF identified dominant signals at low \u003cem\u003eq\u003c/em\u003e values near the beam center, likely due to high-intensity scattering unrelated to crystalline order (Fig. 4b). However, SAXS components SAXS_PCA5 and SAXS_NMF5 revealed long-range periodic peaks, indicating successful feature separation. These results demonstrate that both PCA and NMF can effectively extract and separate meaningful structural features from high-dimensional X-ray profiles.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eUnderstanding of structural importance by XAI\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eDimensionality-reduced X-ray data were used to predict the enzymatic degradation weight and yield stress of the 122 PLA samples. Each sample was represented by 40 structural features: 10 components from both PCA and NMF for WAXS and SAXS data. These features served as input for predictive models built using nested cross-validation (10-fold outer loop for testing, 5-fold inner loop for hyperparameter tuning) (Fig. 1b, (C)). Both LASSO and RFR achieved high coefficients of determination (\u003cem\u003eR\u003c/em\u003e²) for degradation weight and yield stress predictions (Fig. 5a–b). Additionally, we evaluated prediction performance in terms of Pareto optimization using the hypervolume metric defined over the two objectives (degradation weight and yield stress). In this case, predictive accuracy declined; LASSO showed minimal performance, while RFR still yielded moderate \u003cem\u003eR\u003c/em\u003e² values (Fig. 5c). These results suggest that PCA- and NMF-derived structural features effectively capture linear property relationships. However, the Pareto front, involving trade-offs between objectives, reflects more complex, nonlinear dependencies—better handled by non-linear models such as RF.\u003c/p\u003e\n\u003cp\u003eThe most important structural features were identified via LASSO coefficients and RFR feature importances. For both degradation weight and yield stress, WAXS_NMF2 and WAXS_PCA1 were consistently highlighted as key contributors (Fig. 5d–e). WAXS_NMF2 corresponds to the amorphous phase, while WAXS_PCA1 represents the α- form of PLA. Notably, the LASSO coefficient for WAXS_NMF2 was positive for degradation weight (0.630) and negative for yield stress (-0.785), illustrating the trade-off between degradability and mechanical strength. Conversely, WAXS_PCA1 exhibited the opposite trend (-0.153 for degradation, 0.064 for yield stress). These trends reaffirm that increasing crystallinity reduces enzymatic degradability while enhancing toughness—an established phenomenon in PLA materials. This validates that the data-driven structure–property models provide physically interpretable insights from high-dimensional structural data. The same analysis was extended to the Pareto solutions. Feature contributions for hypervolume prediction were generally lower than for individual property predictions (Fig. 5f), suggesting increased complexity. Nonetheless, SAXS_NMF5 (related to lamellar thickness), WAXS_NMF4, and WAXS_PCA4 (associated with scPLA crystal lattice) were prominent, implying that stereocomplex formation contributes positively to overcoming property trade-offs. It should be noted that the use of dimensionality reduction enables capturing the overall shapes of X-ray profiles, making them more interpretable to humans.\u003c/p\u003e\n\u003cp\u003eTo provide local explanations for individual samples, SHAP (SHapley Additive exPlanations) analysis was performed using the RF regression models. \u003csup\u003e52,53\u003c/sup\u003e SHAP values confirmed that WAXS_NMF2 and WAXS_PCA1 were the most significant features across most samples for both degradation weight and yield stress—consistent with global model results (Supplementary Video 1). However, for Pareto solutions, which involve nonlinear dependencies, the most influential features varied between samples. For instance, WAXS_NMF3 and WAXS_NMF7 (corresponding to α′- and α-forms of PLA) emerged as key contributors depending on the sample location in feature space. These findings highlight the effectiveness of XAI methods in elucidating complex and localized structure–property relationships in nonlinear systems, where the contribution of each feature varies across individual samples.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMaterials design by Bayesian optimization \u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn biodegradable polymers, degradability and mechanical strength often exhibit a trade-off relationship. \u003csup\u003e15,16,28\u003c/sup\u003e Consistent with this, enzymatic degradation and yield stress in PLA samples showed strong negative correlation (Spearman’s \u003cem\u003eρ\u003c/em\u003e = −0.89, \u003cem\u003ep\u003c/em\u003e \u0026lt; 0.01, Fig. 6a). To address this conflict, Bayesian Optimization (BO) was employed using Gaussian process regression (GPR). \u003csup\u003e54-56\u003c/sup\u003e The BO model was trained on the original 88 samples. The design space was then expanded to include 660 process parameter combinations (11 × 5 × 6 × 2; see Fig. 1b). New candidate points were suggested based on multi-objective optimization by maximizing Expected Hypervolume Improvement (EHVI) or Hypervolume-based Probability of Improvement (HVPI) (Fig. 1b, (D)). \u003csup\u003e28,57,58\u003c/sup\u003e Several new samples were identified on or near the Pareto front, showing moderate yield stress (\u0026gt;14 MPa) and high degradation (\u0026gt;0.7 mg) (Fig. 6a). While dramatic breakthroughs were limited—likely due to a constrained design space—this approach demonstrates potential for optimizing difficult trade-offs. \u003csup\u003e28\u003c/sup\u003e \u003c/p\u003e\n\u003cp\u003eMore recently, surrogate optimization strategies have emerged, wherein easily measurable intermediate variables are used in place of expensive or difficult-to-measure objective properties. \u003csup\u003e29\u003c/sup\u003e In the context of PSP modeling, this suggests the possibility of optimizing structure, rather than final properties (Fig. 1b, (E)). Thus, we performed BO simulations using selected PCA and NMF features (e.g., WAXS_NMF3, NMF8) as surrogate objectives—identified as important contributors via XAI analysis (Fig. 5d, 5f). Remarkably, BO targeting WAXS_NMF8 achieved similar or even superior early performance in degradation prediction compared to property-based BO (Fig. 6b). This advantage was even more pronounced for multi-objective optimization (hypervolume) where BO using WAXS_NMF3 matched or exceeded direct optimization (Fig. 6c–d). These results support the feasibility of structure-based BO, effectively bypassing costly experimental tests such as degradation assays or mechanical evaluations. This surrogate-variable approach holds significant promise for sustainable materials research, where resource-intensive evaluations (e.g., degradation, recyclability, mechanical strength) often limit experimental throughput.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eHierarchical modeling for prediction of X-ray profiles and property\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn previous sections, we separately modeled process–property and structure–property relationships. However, the hierarchical nature of the PSP framework suggests that integrated models—where process data predict structure, which in turn predicts properties—may offer more robust, interpretable, and generalizable insights. As a first step toward such hierarchical modeling, we constructed regression models from process parameters to individual structural features (from PCA/NMF), and then from these structural features to target properties using LASSO (Fig. 1b, (F)). For the process–structure step, LASSO regression yielded low \u003cem\u003eR\u003c/em\u003e² values, indicating poor performance (Fig. 7a). In contrast, RF regression significantly improved \u003cem\u003eR\u003c/em\u003e² values, suggesting that the process–structure mapping is inherently nonlinear. Using the predicted structural features, we then attempted to reconstruct the full X-ray profiles via inverse transformation of the PCA or NMF components. The regenerated WAXS and SAXS profiles showed good agreement with the original data across a wide range of crystalline morphologies, including amorphous, α-form PLLA, and scPLA samples (Fig. 7b–d). Simultaneously, material properties were also predicted from the reconstructed structural features. These results demonstrate the viability of hierarchical PSP modeling, where processing conditions can be used to predict not only properties but also high-dimensional structural data—supporting both design and mechanistic understanding in a unified framework.\u003c/p\u003e"},{"header":"DISCUSSION","content":"\u003cp\u003eIn this study, we have established a comprehensive data-driven framework for modeling process–structure–property (PSP) relationships in sustainable polymers, exemplified by polylactic acids (PLA). By systematically varying crystallization processing conditions, we characterized the resulting crystalline structures and their corresponding material properties via X-ray diffraction/scattering, enzymatic degradation assays, and tensile testing. Leveraging single- and multi-objective Bayesian optimization, we successfully identified new Pareto-optimal processing parameters that effectively balance the trade-off between degradability and mechanical toughness using structure parameters as surrogate objective variables. To gain structural insights, dimensionality reduction techniques combined with explainable AI (XAI) were employed, revealing key diffraction features closely linked to material performance. Furthermore, we developed hierarchical PSP models that enable the sequential prediction of both structural profiles and functional properties directly from processing inputs.\u003c/p\u003e\n\u003cp\u003eThe development of sustainable polymers typically involves navigating complex, multivariate process-structure-property spaces, where conventional trial-and-error experimentation is inefficient and costly. Existing materials informatics approaches often address isolated problems—such as single-property prediction or feature extraction—and thus fall short in handling the inherently multimodal, multiscale, multitask, and multi-process nature of polymer design. Our integrated PSP modeling framework demonstrates the power of data-driven science to unify these disparate tasks into a coherent platform for automated and holistic analysis, similar to human performance. We envision this approach as a foundational step toward the creation of generalized materials models that can accelerate discovery and optimization across diverse polymer systems, ultimately advancing sustainable materials technologies.\u003c/p\u003e"},{"header":"METHODS","content":"\u003cp\u003e\u003cstrong\u003eMolding of PLA\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003ePLA films were prepared via hot pressing. PLA and the nucleator (Ecopromote® TF) were supplied by Teijin Limited and Nissan Chemical Corporation, respectively. The mixture of poly L-lactic acid (PLLA) and/or poly D-lactic acid (PDLA) (5 wt.%) in the present/absence of the nucleator (0.1 wt.% for PLA) were dissolved in dioxane and stirred for 18 h at 60 °C. The solution was then freeze-dried using FDU-506 (EYELA) and heated at 100 °C for 15 h under vacuum. The obtained white solids were placed between a silicon wafer treated with \u003cem\u003en\u003c/em\u003e-octadecyl trimethoxy silane and melted at 240 °C for 10 min at 10 MPa using a hot-press machine (Imoto Machinery Co., Ltd.). Crystallization was conducted at a specific temperature (90-180 °C) for 5 or 20 min at 5 MPa in different pre-heated hot press machines (Imoto Machinery Co., Ltd.). The crystallization of PLA was quenched in ice water to obtain a film of approximately 150 mm in thickness. For original samples, eighty crystallized samples (five crystalline temperatures (90, 120, 140, 160, and 180 °C), two crystallization times (5 and 20 min), four ratios of PLLA/PDLA (\u003cem\u003er\u003c/em\u003e\u003csub\u003eP(L/D)LA\u003c/sub\u003e = 100/0, 90/10, 70/30, and 50/50), and two concentrations of nucleator (0 and 0.1 wt.%)) and eight quenched samples (four ratios of PLLA/PDLA and two concentrations of nucleator) were prepared, obtaining a total of 88 samples.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eX-ray scattering/diffraction measurements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWide-angle X-ray scattering (WAXS) and small-angle X-ray scattering (SAXS) measurements were performed using BL40XU or BL05XU at SPring-8. The PLA films were exposed to X-rays (0.1 nm) for 0.5 s and 5 s, which were detected by SOPHIAS and PILATUS (1 M) with a sample-to-detector distance of 100.3 mm and 3870 mm for WAXS and SAXS, respectively. The beam centers and sample-to-detector distances were estimated using CeO\u003csub\u003e2\u003c/sub\u003e and AgBe as the standard samples for WAXS and SAXS, respectively. The two-dimensional image data were converted to one-dimensional profiles using the FIT2D software, and the profiles were subtracted from the background profiles without samples using any coefficient. The scattering vector was defined as \u003cem\u003eq \u003c/em\u003e= 4π sin(\u003cem\u003eq \u003c/em\u003e/ \u003cem\u003eλ\u003c/em\u003e), where \u003cem\u003eλ\u003c/em\u003e is the wavelength of the X-ray, and 2\u003cem\u003eq\u003c/em\u003e is the scattering angle.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEnzymatic degradation test\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eEnzymatic degradation tests were performed using proteinase K. The PLA films were cut using an elliptical mold with a length of 14 mm and short axis of 3 mm to obtain nearly identical surface areas. The films were treated with proteinase K (1 mg, Nacalai Tesque) in Tris buffer solution (1 mL, pH 7.4) at 37 °C for 2 d. The solutions were replaced with new solutions after 1 d. After 2 d, the films were washed with pure water and dried under vacuum. The degradation weights were estimated based on the decreased weight of the films before and after the degradation tests, considering the averages of the three tests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTensile test\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTensile tests were performed via the uniaxial elongation of the sample under heating. The samples were cut using a dumbbell-shaped mold with a length of 12 mm and a width of 2 mm. Uniaxial elongations were conducted using a tensile machine (Imoto Machinery Co., Ltd.) at 55 °C at a rate of 10 mm/min. Before the test, samples were maintained under the heating condition for 10 min. The yield stress was evaluated as the highest stress below a strain of 0.3. In some cases, the samples ruptured before reaching the yield points, in which case the stress at break was treated as the yield stress. The elongation at break was estimated as the elongation ratio at which the sample ruptured. Both values were obtained using the average values of three tests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eRegression model by LASSO\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eLeast absolute shrinkage and selection operator (LASSO) was performed using the module in Scikit-learn library. \u003csup\u003e59,60\u003c/sup\u003e Regressions were performed using the \u003cem\u003eLasso\u003c/em\u003e function in the \u003cem\u003elinear_model\u003c/em\u003e module, and predicted values were obtained via nested cross-validation (CV) with 10-fold outer CV for test estimation and 5-fold inner CV for hyperparameter tunning. \u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eRandom forest regression\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eRandom forest regression (RFR) was conducted using \u003cem\u003eRandomForestRegressor\u003c/em\u003e module in scikit-learn. \u003csup\u003e60\u003c/sup\u003e The nested CV was performed, where the hyperparameters max_depth (1, 3, 5, 10, 30 and 50), n_estimators (10, 30, 50, 100, 300), and max_features (sqrt, log2, and None) were determined using 5-fold inner CV, and the predicted values were obtained by the 10-fold outer CV. \u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDimensional reduction of X-ray data by PCA and NMF\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eDimensional reductions were conducted using principal component analysis (PCA) and non-negative matrix factorization (NMF) functions in Scikit-learn. \u003csup\u003e60\u003c/sup\u003e The n_components were set to 20 in both cases, and only the most significant 10 dimensions were used for the next procedure. In PCA, the profiles corresponding to the PCA space were obtained using the \u003cem\u003einverse_transform\u003c/em\u003e function treated with a zero array containing only 1 in a specific component. The profiles separated by NMF were obtained by an attribute of \u003cem\u003ecomponent_\u003c/em\u003e in the function. \u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEvaluation of SHAP values\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSHAP values were evaluated using the SHAP library. \u003csup\u003e52\u003c/sup\u003e Regression models were constructed using a random forest regressor, as explained above. The SHAP values were obtained by the explainer functions in SHAP for test data in the 10-fold outer cross-validation.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eBayesian optimization using Gaussian process regression\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eMulti-objective optimization was performed using COMBO or PHYSBO \u003csup\u003e61\u003c/sup\u003e, a Bayesian optimization library based on a Gaussian process regression (GPR). The molding process of the original 88 combinations was input for multi-objective properties: degradation weight vs. yield stress. Subsequently, the next process conditions were recommended among the expanded combinations of the molding process (\u003cimg width=\"155\" height=\"17\" src=\"data:image/png;base64,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\" alt=\"image\"\u003e combinations, Fig. 1b), with max_num_probes = 1 and num_search_each_prob = 3. The scores of the Pareto solutions were estimated based on the EHVI or HVPI, where a total of four process conditions were adapted for the next step. In addition, three randomly chosen process conditions were used. In the actual procedure, the two multi-objective optimizations proceeded at the same time, where the result of one optimization was reflected in the next input data in the other optimization. Therefore, 11 samples were added to the input data. This cycle was repeated three times with increasing sample numbers.\u003c/p\u003e\n\u003cp\u003eBayesian optimization using surrogate objective variables was carried out on a total of 122 samples obtained by the above procedure. The surrogate variables were determined from the top five most important PCA or NMF structural components based on the feature importances of the RFR model. GPR was performed using the process conditions and the surrogate variables as inputs and objectives, respectively. The initial three samples were selected by random sampling, and subsequently one sample was obtained by GPR for 50 iterations. The results were plotted based on the averages of 100 trials.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eDATA AVAILABILITY\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe datasets used and/or analysed during the current study available from the corresponding author on reasonable request.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCODE AVAILABILITY\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe underlying code for this study is not publicly available but may be made available to qualified researchers on reasonable request from the corresponding author.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eACKNOWLEDGEMENTS\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe synchrotron radiation experiments were performed at the BL40XU and BL05XU beamlines of SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal No. 2020A1525 and 2021B1476).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFUNDING\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was supported by the Cabinet Office, Government of Japan, Cross-ministerial Strategic Innovation Promotion Program (SIP), \u0026ldquo;Technologies for Smart Bio-industry and Agriculture\u0026rdquo; (funding agency: Bio-oriented Technology Research Advancement Institution, NARO). This paper is based on results obtained from a project, JPNP18016, commissioned by the New Energy and Industrial Technology Development Organization (NEDO). This work was also supported by the JSPS Grant-in-Aid for Scientific Research on Innovative Areas, Discrete Geometric Analysis for Materials Design: 20H04644, by the Grant-in-Aid for Scientific Research (B): 20H02800, by Data Creation and Utilization Type Material Research and Development Project Grant Number JPMXP1122683430, JST-Mirai Program Grant Number JPMJMI21EH, JST FOREST program (Grant Number: JPMJFR232U), and by Institute of Mathematics for Industry, Joint Usage/Research Center in Kyushu University (Workshop (II), Reference No. 2023a011, 2024a011, and 2025a041). Y.A. and K.T. acknowledges the financial support of the Grant-in-Aid for RIKEN-Kyushu Univ Science and Technology Hub Collaborative Research Program.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAUTHOR CONTRIBUTIONS\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eY.A. and K.T. conceived the study. Y.A. and H.K. performed the experiments. Y.A. and H.K. analyzed the data. K.K. and A.T. were responsible for the measurements. M.H. and K.H. proposed the use of XAI and sparse modeling, respectively. Y.A. drafted the manuscript, and all authors reviewed and approved the final version.\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\u003eHottle, T. A., Bilec, M. M. \u0026amp; Landis, A. E. 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However, existing approaches are often limited to isolated tasks, hindering their ability to address the complex, multi-process, multitask, and hierarchical nature of sustainable polymers. In this study, we propose an integrated data-driven framework that models the process–structure–property (PSP) relationships of sustainable polymers through three synergisitic components: (1) Design – Bayesian optimization of process conditions to balance multiple material properties using surrogate objective variables derived from structure data; (2) Understanding – extraction of key crystalline features related to single-property and multi-objective axes using dimensionality reduction and XAI on X-ray scattering profiles; and (3) Prediction – hierarchical PSP modeling to regenerate structural X-ray information and predict material properties accurately from processing parameters. This unified framework enables a more systematic and automated approach to sustainable polymer development, reducing dependence on traditional trial-and-error methods and accelerating innovation.","manuscriptTitle":"Data-Driven Process–Structure–Property Framework for the Design, Understanding, and Prediction of Sustainable Polymers","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-27 12:01:37","doi":"10.21203/rs.3.rs-8066698/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"5a81bb1b-404a-4248-90cb-c04049f584d7","owner":[],"postedDate":"November 27th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":58583157,"name":"Physical sciences/Chemistry"},{"id":58583158,"name":"Physical sciences/Engineering"},{"id":58583159,"name":"Physical sciences/Materials science"},{"id":58583160,"name":"Physical sciences/Mathematics and computing"}],"tags":[],"updatedAt":"2025-11-27T12:01:37+00:00","versionOfRecord":[],"versionCreatedAt":"2025-11-27 12:01:37","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8066698","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8066698","identity":"rs-8066698","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}