Gaussian Process Regression-based Knowledge Distillation Framework for Simultaneous Prediction of Physical and Mechanical Properties of Epoxy Polymers

Gaussian Pro cess Regression-based Kno wledge Distillation F ramew ork for Sim ultaneous Prediction of Ph ysical and Mec hanical Prop erties of Ep o xy P olymers Sindu B.S. a and Jan Hamaek ers b a Sp ecial and Multifunctional Structures Lab oratory , CSIR-Structural Engineering Research Centre, T aramani, Chennai, T amil Nadu, India - 600113. b F raunhofer Institute for Algorithms and Scientific Computing SCAI, Schloss Birlinghov en, 53757 Sankt Augustin, German y Marc h 19, 2026 Abstract Ep o xy p olymers are widely used due to their multifunctional prop erties, but machine learning (ML) applications remain limited o wing to their complex 3D molecular structure, m ulti-comp onent nature, and lack of curated datasets. Existing ML studies are largely restricted to simulation data, sp ecific prop- erties, or narro w constituent ranges. T o address these limitations, we developed an informed Gaussian Pro cess Regression-based Knowledge Distillation (GPR-KD) framew ork for predicting multiple ph ysi- cal (glass transition temp erature, density) and mec hanical prop erties (elastic mo dulus, tensile strength, compressiv e strength, flexural strength, fracture energy , adhesive strength) of thermoset epoxy polymers. The mo del was trained on exp erimental literature data cov ering div erse monomer classes (9 resins, 40 hardeners). Individual GPR mo dels serve as teacher mo dels capturing nonlinear feature-prop ert y rela- tionships, while a unified neural netw ork student mo del learns distilled kno wledge across all prop erties sim ultaneously . By enco ding the target property as an input feature, the student model lev erages cross- prop ert y correlations. Molecular-level descriptors extracted from SMILES representations using RDKit create a physics-informed mo del. The framew ork combines GPR in terpretability and robustness with deep learning scalability and generalization. Comparative analysis demonstrates superior prediction ac- curacy ov er con ven tional ML mo dels. Simultaneous m ulti-prop ert y prediction further improv es accuracy through information sharing across correlated prop erties. The prop osed framework enables accelerated design of no vel ep o xy polymers with tailored prop erties. 1 In tro duction Ep o xy p olymers are thermoset materials exhibiting with multi-functional prop erties such as high strength, excellen t adhesion, effectiv e electrical insulation, lo w shrink age, c hemical and solv ent resistance, etc. They are widely used in several industries like aerospace, marine, automotive, infrastructure, electrical and electronics for sp ecific functional requiremen t. F or instance, adhesiv e strength, fracture toughness and w eight are the ma jor requirements for use in aerospace applications [1]; resistance to moisture, salinit y and v aried temp erature cycles is the ma jor requirement in marine applications; viscosit y , lo w shrink age and corrosion resistance are the requirements for its application in paint and coatings [1]; insulation resistance is the ma jor requiremen t for electrical applications [2]; adhesiv e strength, durability , tensile and fracture prop erties are the requirements for infrastructural applications [3]. Hence, care should b e taken to design ep o xy p olymers with required functionalities so that it can be used for the intended purp oses. The basic constituents of epoxy p olymers are resin and hardener. When these tw o compounds undergo an irreversible reaction, a dense, three 1 dimensional netw ork is formed. How ev er, the functionalities and the prop erties of ep o xy p olymers dep end up on several factors like the constituen t resin and hardener types, their composition, curing conditions and degree of polymerization. The conv en tional trial-and-error-based exp erimen tal inv estigations limit the dev elopment of high p erformance epoxy p olymers with m ulti-functional characteristics. A few nov el approaches w ere developed in the recent times to establish constituent-structure-property relationship of epoxy p olymers and to predict its prop erties which can enric h the design pro cess. Results from exp erimen tal nanoinden tation [4, 5] tests and scratch induced deformation tests [6] were used to establish a correlation with the intrinsic mechanical prop erties. Computational molecular dynamics (MD) simulations w ere p erformed to determine the mechanical, ph ysical and transp ort prop erties of ep o xy p olymers [7]. MD sim ulations using Reactive Interface F orce Field (IFF-R) w ere used to determine the prop erties of ep o xy p olymers when sub jected to large deformations [8]; to get the exp erimen tal results that can b e obtained using Differential Scanning Calorimetry (DSC) [9] b y utilizing information such as heat of formation and activ ation energy . MD sim ulations were also used to identify the influence of certain molecular interactions on mechanical and transp ort prop erties of p olymers [9, 10], to correlate the functionality of monomers (di-, tri-, tetra-) with the mechanical prop erties lik e yield stress, elastic mo dulus and P oisson’s ratio [11]. ML-based approac hes are b eing widely used for design, optimization and property prediction of homopoly- mers and cop olymers due to the a v ailability of large databanks [12 – 15]. Ho wev er, their use in thermoset ep o xy p olymers is v ery limited due to the in volv ement of tw o or more constituen t ingredien ts, complex three-dimensional structure and lac k of large curated datasets. Recently , attempts are b eing made for com- p osition optimization, prop ert y prediction and design of high p erformance ep o xy p olymers using ML-based approac hes. Results from MD simulations in conjunction with Neural Netw orks (NNs) w as used to optimize the composition of epoxy p olymers with p erformance c haracteristics like elastic modulus, tensile strength, elongation at break, glass transition temperature (Tg ) [16] and self-healing prop erties [17]. The composition of shape memory ep o xy p olymers (SMP) was also optimized using NNs using the results from exp erimen tal in vestigations [18]. Unified ML mo del based on Supp ort V ector Regression (SVR) w as prop osed to pre- dict the Tg of homo-, hetero- and cross linked ep o xy- p olymers based on the constituent monomers and its descriptors [19]. ML ensem ble model based on Gradien t Boosting Regression (GBR) and Kernel Ridge Regression (KRR) w as used to predict the Tg of epoxy polymers by correlating the molecular descriptors of resin (16 t yp es) and hardener (19 types) with exp erimen tal (94 com binations) DMT A measuremen ts and the most imp ortan t descriptors affecting the Tg were further iden tified using Lasso regression [20]. Materials genome approach in conjunction with attention- and gate-augmented graph conv olutional net works, mul- tila yer p erceptrons and transfer learning was used to identify the gene structures resp onsible for different prop erties and to design ep o xy p olymers with high strength, mo dulus and toughness [21]. Similarly , ML- based approach w as developed to predict the elastic mo dulus and yield strength of ep o xy p olymers using the basic structural features of monomers, thereb y , enabling feature-based prediction of their prop erties [22]. ML-based conv olutional mo del was emplo yed for discov ery of new thermoset SMPs with high recov ery stress from a newly constituted comp ositional space [23, 24]. Though several attempts hav e b een made to use ML for design of ep o xy p olymer or prediction of prop- erties, most of the approaches seem to b e limited as the data for the mo del are obtained from computational sim ulations or the mo del has b een dev elop ed to predict a sp ecific prop ert y of ep o xy p olymers or with very limited set of constituen ts. With this in mind, we develop a ML mo del which can b e used to predict mul- tiple physical (glass transition temp erature and density) and mechanical (elastic mo dulus, tensile strength, compressiv e strength, flexural strength, fracture energy and adhesive strength) properties of t wo-component, thermoset epoxy polymers merely with the help of its constituen t ingredients (t ype of resin and hardener and its prop ortion). W e develop a GPR-based knowledge distillation framework (GPR-KD) for this purp ose in whic h individual GPR mo dels are trained as teacher mo dels for each target prop erty , and the the knowledge learned from these teachers is distilled into a unified studen t mo del for property prediction. The constituent resin and hardener are first enco ded using a lab el enco ding scheme to numerically represent their chemical iden tities. These enco ded v ariables are then used together with the relev ant pro cess parameters as inputs to the model, allowing it to learn correlations b et w een material comp osition, processing conditions, and the resulting ph ysical and mechanical prop erties (cf. Section 2.1). W e then conv ert it into an informed ML 2 mo del [25] by including information ab out the intrinsic features of the monomeric constituen ts extracted from an op en source, c heminformatics to ol (cf. Section 2.2). The data for training the mo del was collected from sev eral exp erimen tal data from literature. W e also compared the p erformance of the mo del with other con ven tional approac hes and found that our mo del is able to predict the prop erties more accurately (cf. Section 3.1). The ma jor adv an tage of this mo del is that a single mo del can b e used to predict m ultiple ph ysical and mechanical prop erties of ep o xy p olymers. The mo del also extracts the benefits of learning from one another as it has b een trained with different properties. This has also b een witnessed by improv ed pre- diction accuracy while multiple prop erties are predicted together (cf. Section 3.2). The mo del thus pa ves the path for designing nov el ep o xy p olymers with exceptional prop erties whic h would only b e p ossible through lab orious experimental trials. 2 ML mo del for prediction of prop erties In order to predict the physical and mechanical prop erties of ep o xy p olymers, we develop a GPR-based kno wledge distillation framew ork. The data for training the ML mo del is provided from the experimental results in the literature. A total of 236 data p oin ts spread across several properties such as glass transition temp erature (Tg ), density , elastic mo dulus, compressiv e strength, tensile strength, flexural strength and adhesiv e strength for differen t types of ep o xy p olymers are collected for this purp ose [26 – 51]. The data spans across diverse resin (9) and hardener (40) classes; several pro cess parameters (stoic hiometric ratio b et w een the resin and hardener, curing temp erature) and test parameters (strain rate, test temp erature). The distribution of datap oin ts across different ep o xy combinations and the range of individual physical and mec hanical prop erties collected from literature is presented in Figure 1. 2.1 Basic arc hitecture of the mo del The basic input used for prediction of epoxy p olymers properties using the prop osed GPR-KD framework are the constituen t ingredient (resin and hardener) ty p es, their proportion and other process parameters. Firstly , w e con vert the categorical data (resin type, hardener t yp e and property to be predicted) into numerical lab els using lab el enco der. Then, this enco ded information along with the molecular weigh t of individual monomers, pro cess parameters and test parameters are selected as input features for the mo del. F or each target property , an independent GPR model is dev eloped and emplo y ed as a high-fidelity teacher within the prop osed knowledge distillation framework. F or training eac h teac her mo del, only the subset of the dataset comprising data p oints asso ciated with the target prop ert y is used. The dataset is then normalized to a uniform scale so as to remov e bias arising from differences in feature scales. The av ailable data are partitioned into training and testing sets using an 80:20 split. Then, h yp erparameter optimization is carried out on training dataset using five-fold cross-v alidation. A grid search strategy is employ ed to explore an extensiv e kernel space constructed from linear (DotPro duct), radial basis function (RBF), Mat ´ ern, and constan t kernels, including their additive com binations, together with the noise regularization parameter. Mo del selection is based on minimization of the mean absolute error (MAE), ensuring robust p erformance across folds while a voiding ov erfitting. Once the optimal h yp erparameter configuration is iden tified, the best- p erforming GPR mo del is retained for final ev aluation and kno wledge transfer. The trained teacher mo del is used to generate predictions on the full normalized input space to pro duce prop ert y-sp ecific soft targets for subsequen t knowledge distillation. These GPR teacher mo dels th us provide accurate non-linear mappings b et w een the input features and target prop erties, yielding physically consistent predictiv e resp onses that are w ell suited for guiding the training of a unified student neural netw ork. The student mo del is implemen ted as a fully connected feed-forw ard neural netw ork with an input la yer, t wo hidden lay ers, and an output lay er. The input to the studen t net work is formed by concatenating the normalized feature v ector with a one-hot enco ded representation of the prop ert y to b e predicted. This explicit conditioning enables the studen t net work to distinguish among different target properties while sharing a common set of net work parameters, thereby allowing sim ultaneous learning of m ultiple prop erties within a single model architecture. The concatenated input is passed sequentially through t w o hidden 3 (a) (b) (c) (d) Figure 1: Data collected from literature (used for training the ML mo del): (a) Distribution of datapoints for eac h property across different ep o xy com binations (236 com binations in total); Distribution of data across individual (b) resin classes and (c) hardener classes; (d) Range of individual physical and mechanical prop erties. la yers, where weigh ts and biases are learned through non-linear activ ation using the rectified linear unit (ReLU) function. Through these hidden lay ers, the mo del progressively transforms the raw input in to a higher-dimensional latent representation that captures coupled constituent–process–prop ert y relationships, whic h are not directly apparent from the original feature space. The final output lay er maps this latent represen tation to a single scalar corresp onding to the predicted ep oxy p olymers prop ert y . The mo del is trained using PyT orch Lightning [52]. During training, a kno wledge distillation loss function is employ ed, defined as a w eighted sum of the mean squared error b et ween the student predictions and the GPR teacher predictions (soft targets) and the mean squared error with resp ect to the true exp erimen tal v alues. A 4 Figure 2: Architecture of the GPR-KD framework used in this study . w eighting factor of α = 0 . 7 is used, assigning higher importance to matc hing the teacher predictions while retaining direct sup ervision from exp erimen tal data. Accordingly , the ov erall loss function reads as L KD = α MSE( ˆ y , y teacher ) + (1 − α ) MSE( ˆ y , y true ) . A schematic ov erview of the newly developed GPR-KD framework is given in Figure 2 This distillation strategy enables the studen t mo del to inherit the smo oth, physically consistent resp onse c haracteristics of the GPR teac hers while main taining direct consistency with measured data, resulting in a compact and efficient surrogate mo del suitable for large-scale parametric studies and rapid prop ert y prediction. T raining of the student neural netw ork is carried out using the Adam optimizer with a fixed learning rate of 10 − 3 , and a mini-batch size of 32, for a total of 5000 training ep o c hs. 2.2 Informed GPR-KD framew ork In order to further enhance the predictive capability of the prop osed framew ork as a ph ysics-informed mo del, in trinsic molecular-level features of the constituent monomers are incorp orated. Eac h resin and hardener 5 (a) (b) Figure 3: Prediction accuracy of the prop osed (a) Knowledge Distillation F ramew ork; (b) Informed Knowl- edge Distillation F ramework. monomer is represented b y its unique SMILES string [53], which pro vides an ASCI I-based represen tation of the molecular structure. F rom these SMILES strings, atomistic and structural descriptors of the resin and hardener molecules are extracted using the op en-source cheminformatics tool RDKit [54]. A total of 28 features which include the following descriptors are extracted from RDKit using a python script whic h include: • Molecular weigh t • Atom Descriptors (type and count of atoms including heavy atoms) • Bond Descriptors (single/double/triple) • Group count (NH/OH, SP3 fractions) • Ring counts (aromatic/saturated/aliphatic and hetero cycles/carbo cycles) • Electron descriptors (No. of hydrogen acceptors/donors, radical/v alence electrons) In cases where tw o t yp es of hardeners are present in the formulation, descriptors corresp onding to b oth hardeners are included. In the informed GPR-KD framew ork, these molecular descriptors replace the abstract categorical representations used in the uninformed architecture, thereby embedding the resin and hardener 6 molecules directly in their ph ysically meaningful feature space. Since the extracted features span several orders of magnitude, all molecular descriptors are normalized b etw een 0 and 1 using a Min–Max scaler to eliminate bias arising from scale differences. The improv emen t in prediction accuracy , particularly for the glass transition temp erature, achiev ed by em b edding the constituen t molecules in their feature space is demonstrated in Figure 3. 3 P erformance of the informed GPR-KD framew ork The p erformance of the developed informed GPR–KD framew ork in predicting v arious physical prop erties (glass transition temp erature and density) and mec hanical properties (elastic mo dulus, tensile strength, flexural strength, compressiv e yield strength, compressiv e ultimate strength, adhesive strength, and fracture energy) of ep oxy p olymers is ev aluated using the dataset shown in Figure 1. The results of this ev aluation are presented and discussed in this section. 3.1 Comparison with con ven tional methods T able 1: Hyp erparameter searc h space for different regression mo dels. Mo del Hyp erparameter Searc h space PLS Regression Num b er of comp onen ts 1 to 13 T olerance 10 − 4 , 10 − 6 , 10 − 8 , 10 − 10 Ridge Regression α logspace(-10 to 2) Solv er svd, cholesky , lsqr, sparse cg, sag, saga, lbfgs Kernel Ridge Regression α logspace(-10 to 6) Kernel rbf, linear, p oly , sigmoid Random F orest Maxim um depth [1, 2, 3] Gradien t B oosting Regression Learning rate logspace(-6 to -1) Maxim um depth [1, 2, 3] k-Nearest Neighbour Num b er of neighbours 1 to 7 W eights Uniform, Distance Gaussian Pro cess Regression α logspace(-12 to -1) The predictive capability of the informed GPR–KD framework is assessed by comparing its p erformance with sev eral conv en tional ML mo dels including Partial Least Squares (PLS) Regression, Ridge Regression (RR), Kernel Ridge Regression (KRR), Random F orest (RF), Gradien t Boosting Regression (GBR), k- Nearest Neigh b ours (kNN) and Gaussian Pro cess Regression (GPR). F or all models, the input features comprise of molecular-lev el descriptors (as describ ed in Section 2.2) of the constituen t resin and hardener(s) extracted from cheminformatics tool along with relev ant process and testing parameters, while the target ep o xy prop erty serves as the output v ariable. Prior to mo del training, all contin uous input features are nor- malized using Min–Max scaling to eliminate bias arising from differences in feature magnitudes and to ensure stable optimization across learning algorithms. F or each target prop ert y , the av ailable data are partitioned in to training and testing sets using an 80:20 split. Mo del developmen t and h yp erparameter optimization are p erformed exclusively on the training set. Eac h conv entional mo del inv olves a set of hyperparameters that significan tly influence its predictiv e p erformance. Accordingly , hyperparameter optimization is carried out using a grid searc h strategy combined with five-fold cross-v alidation on the training data. The h yp erparam- eter search spaces for the differen t mo dels are defined individually for each algorithm (presented in T able 1). Mo del selection is based on minimization of the mean absolute error, while the generalization capability of the optimized mo dels is ev aluated using the held-out test set. Figure 4 shows the prediction accuracy of informed GPR-KD framew ork in comparison to con ven tional ML models. It can be found that the informed 7 Figure 4: Prediction accuracy (in terms of R 2 score) of different ph ysical and mec hanical properties using prop osed GPR-based kno wledge distillation framework and conv en tional mo dels. GPR-KD model consistently exhibits higher R 2 scores betw een the true and predicted property v alues than the conv en tional ML mo dels for all the prop erties considered. 3.2 Informed GPR-KD framew ork for sim ultaneous prediction of physical and mec hanical prop erties The informed GPR-KD framework is then used for sim ultaneously predicting multiple physical and mechan- ical prop erties together. It is attempted to predict the prop erties like glass transition temp erature, density , adhesiv e strength, flexural strength, elastic mo dulus, tensile strength, compressive strength and fracture energy all together using the informed GPR-KD framew ork. The prediction accuracy of all the properties (except compressiv e strength) improv ed while predicting them simultaneously as against individually pre- dicting them (cf. Figure 5). The impro vemen t is primarily driv en by the capability of the informed GPR–KD framew ork to capture common gov erning trends and correlated resp onse patterns across different proper- ties. By learning a unified feature space while predicting multiple prop erties sim ultaneously , the framework 8 enables effective sharing of information among related prop erties. This sim ultaneous learning pro cess con- strains the solution space and acts as an implicit regularization mechanism, thereby reducing ov erfitting and impro ving the generalization p erformance of the mo del. Finally , Figure 6 shows the comparison of predicted v alues with the true v alues for v arious physical and mec hanical prop erties predicted sim ultaneously using the informed GPR-KD framework. Figure 5: Prediction accuracy (in terms of R 2 Score) during sim ultaneous prediction of multiple properties. 4 Conclusions In this study , attempt has b een made to develop an informed Gaussian Pro cess Regression based Knowledge Distillation (GPR-KD) framework for prediction of v arious physical (densit y and glass transition temp era- ture) and mechanical prop erties (compressive strength, flexural strength, elastic mo dulus, tensile strength, adhesiv e strength and fracture energy) of thermose t ep o xy p olymers where the lac k of av ailability of data- banks/large curated datasets (as against general p olymers) has limited the application of machine learning for these materials. Data from literature p ertaining to exp erimental in vestigations on ep o xy p olymers cov- ering wide range of resin/hardener classes and different physical and mechanical prop erties ha ve b een used for training the mo del. F ollowing are some of the salien t features of the prop osed GPR–KD framework: • A h ybrid teac her–student arc hitecture in which Gaussian Process Regression (GPR) mo dels serv e as teac her mo dels to guide a neural netw ork student through knowledge distillation. • GPR teachers capture nonlinear structure in limited data regimes and pro vide smo oth, noise-robust predictions that act as informative soft targets for student training. 9 (a) (b) (c) (d) (e) (f ) (g) (h) Figure 6: Comparison of true vs. predicted prop erties during sim ultaneous prediction of m ultiple prop erties using informed enco der-decoder mo del: (a) Glass transition temp erature ( ◦ C); (b) Density (g / cm 3 )); (c) Adhesiv e strength (MPa); (d) Flexural strength (MPa); (e) Elastic mo dulus (GPa); (f) T ensile strength (MP a); (g) F racture energy (kJ / m 2 ); (h) Compressive strength (MP a) • Knowledge distillation enables the studen t netw ork to inherit the generalization capability and regu- larization b eha vior of GPR while ov ercoming its scalability limitations. • The framework explicitly incorp orates characteristic descriptors of constituen t resin and hardener molecules, allowing chemically meaningful learning of comp osition–prop ert y relationships. • Separate embedding represen tations for resin and hardener constituents facilitate discrimination of similarly p erforming c hemical systems and improv e in terpretability of learned trends. • A single distilled student mo del is capable of predicting multiple physical and mechanical prop erties, eliminating the need for separate mo dels for individual targets. • Simultaneous multi-property learning promotes effective transfer of information across correlated prop- erties, leading to enhanced predictive accuracy and stability . 10 • The GPR–KD framew ork demonstrates improv ed prediction accuracy compared to con ven tional stan- dalone machine learning mo dels, particularly in data-scarce regimes. • By combining ph ysics-informed regression with deep learning, the framework achiev es a balance b e- t ween in terpretability , accuracy , and computational efficiency . • The proposed approac h is well suited for high-throughput screening and design of epoxy systems, enabling rapid exploration of comp osition–pro cessing–property relationships. This mo del th us pav es the wa y for design of ep o xy p olymers with desired physical and mec hanical prop erties thereb y leading tow ards sustainable developmen t. Ac kno wledgmen ts The authors would like to thank the help received from Gregor Maier and Rick Oerder while developing the mo del. The first author (B.S.Sindu) ac knowledges the supp ort in the form of Post Do ctoral Industrial F ellowship received from Indo-German Science and T echnology Centre (IGSTC) to carry out research in F raunhofer Institute for Algorithms and Scien tific Computing (SCAI), Germany . References [1] F an-Long Jin, Xiang Li, and So o-Jin P ark. “Syn thesis and application of e poxy resins: A review”. In: Journal of Industrial and Engine ering Chemistry 29 (2015), pp. 1–11. [2] A tsuomi Shundo, Satoru Y amamoto, and Keiji T anak a. “Netw ork formation and physical prop erties of ep o xy resins for future practical applications”. In: JACS Au 2.7 (2022), pp. 1522–1542. 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