Machine Learning Models for Predicting Mechanical Properties of Glass Based on Experiments, Molecular Dynamics Simulations and QSPR Analysis

Silicate glass is a versatile material widely used in architectural windows, electronics, optics, and nuclear waste storage. As science and technology advance, demand grows for high-performance glass materials. The mechanical properties, which directly impact service life, safety, and functionality, have attracted much attention. Conventional glass development relies on empirical experience and trial-and-error methods, which are slow and limited in scope. In addition, the amorphous nature and broad compositional range of glass materials make designing tailored materials challenging, requiring composition optimization, cost reduction, and process assurance. Recent advancements on computational modeling, machine learning (ML), and materials informatics offer promising solutions. ML models can predict glass properties and accelerate the discovery of high-performance compositions via leveraging high-dimensional compositional data and integrating computational and experimental insights. However, ML effectiveness depends on dataset quality—availability, completeness, consistency, accuracy, and representativeness. In this work, three ML-based models were constructed from three distinct sources, and datasets were sourced from SciGlass (density), molecular dynamics simulations (Young’s modulus), and a QSPR model (hardness). This approach could provide an innovative dataset construction strategy for advancing glass composition design.

In this study, ML models were developed to predict the density, Young’s modulus, and hardness of silicate glasses. The dataset comprised 425 density values and 43 hardness values selected from the SciGlass database, 425 Young’s modulus values obtained through MD simulations, and 50 hardness values predicted using a QSPR model. In the MD simulations, the Teter potential was employed, while the QSPR modeling incorporated descriptors was related to electronegativity. This work focused on six-component borosilicate glasses composed of SiO₂-B₂O₃-Al₂O₃-MgO-CaO-Na₂O. For initial data collection, a data preprocessing step was conducted, which included outlier removal, elimination of duplicate entries, and normalization of the compositional variables. A multilayer perceptron (MLP) neural network was used to model the relationship between glass composition and properties. The neural network architecture consisted of an input layer, several hidden layers, and an output layer, with weighted connections between neurons. The input features were the molar percentages of the oxide components, while the outputs were the corresponding physical properties. Non-linearity was introduced through the use of the rectified linear unit (ReLU) activation function in the hidden layers, enabling the model to capture complex nonlinear relationships. The output layer used a linear activation function to provide direct predictions of glass properties. To train and validate the models, the dataset was split into training and test sets in a ratio of 9:1. This partitioning ensured sufficient training data, while reserving a subset for independent evaluation of model generalization. Model performance was assessed using mean squared error (MSE) and the coefficient of determination (R²). The trained models were subsequently used to predict the density, Young’s modulus, and hardness of silicate glasses. Finally, nine formulations and corresponding properties were predicted from the models and experimentally verified.

The compositions of the dataset are widely distributed. The density of the glass varies between 2.3 g/cm³ and 2.8 g/cm³, Young’s modulus is primarily distributed between 82 GPa and 115 GPa, and hardness values range from 5.0 GPa to 7.0 GPa. The QSPR model related to hardness demonstrates a good linear correlation between hardness and the F_net descriptor, with the R² value of greater than 0.80, indicating good model fitting and predictive performance. In this study, three ML models are developed to predict the density, Young’s modulus, and hardness of silicate glasses. The R² values of the models show clear differences. The density-related model shows a relatively low predictive accuracy, with an R² of only 0.30 on the test set, the model for Young’s modulus achieves an R² of approximately 0.70 and the hardness-related model exhibits the maximum performance, with R² of > 0.95. However, the predictive accuracy of all three models was satisfactory. The maximum relative error for density prediction is only 2.67%. The predictions of Young’s modulus are overestimated by approximately 10 GPa, mainly due to the limitations associated with empirical interatomic potentials. The prediction error for hardness ranges from approximately 0.05 GPa to 0.40 GPa. The SHAP analysis is further used to investigate the contributions of individual oxide components to the properties. The results reveal that SiO₂ and Al₂O₃ contents positively affect both Young’s modulus and hardness, while Na₂O negatively affects the glass density. As a result, the use of MD simulations and QSPR method represents a promising alternative in the absence of abundant high-quality experimental data for model training.

This study presented a comprehensive, multi-source modeling framework for predicting the mechanical properties of silicate glasses by integrating experimental data, MD simulations, and QSPR-based data augmentation. A total of 425 experimental density values, 425 MD-derived Young’s modulus values, and 93 hardness values (43 experimental, 50 QSPR-predicted) were used to train three distinct ML models. Nine formulations were predicted and experimentally verified for three properties (i.e., density, Young’s modulus and hardness) based on the three models above. The experimental results exhibited small relative errors, indicating a reasonable agreement with model predictions. The results of Young's modulus took into account the effect of errors introduced by simulation. The data quality could become a critical factor affecting the accuracy of predictive models as using ML method. This work incorporated homologous glass property data obtained from MD simulations and employed QSPR method for rapid data augmentation based on experimentally acquired data. This strategy could address the limitations commonly encountered in conventional database construction, including inconsistent data quality and slow acquisition of experimental measurements. It could provide a novel approach toward establishing a data-driven paradigm for glass materials research.