Data-Driven Design of High-Temperature-Resistant Polyimides Using Hierarchical Gaussian Process Regression

Accurate prediction of Tg for polyimides (PIs) is essential for assessing material performance in high-temperature applications in aerospace, electronics, microelectronics, and flexible display technology. However, experimental measurements remain critically challenging due to the labor-intensive synthesis, conventional instrument limits, and time-consuming characterization processes. Meanwhile, force field limitations, timescale discrepancy, and validation difficulties exist in the prediction of Tg for PIs using molecular dynamic simulation. In this study, we introduce a hierarchical Gaussian process regression machine learning method that integrates prior knowledge to predict Tg for PIs with small-sample data sets. We employ RDKit for molecular descriptor calculation and feature selection. Twenty-one key descriptors are identified, and exceptional model performance with a coefficient of determination R² of 0.98/0.74 on the training/test set is achieved, surpassing conventional machine learning approaches. We further use Shapley additive explanations analysis to study the actionable insights for designing thermally stable PIs. The number of rotatable bonds and minimum partial charge act as dominant factors influencing Tg. Validations through experimental synthesis and molecular dynamics simulations confirm that the prediction errors are below 15%, while a Bayesian update strategy employing a radial basis function kernel corrected systematic underestimation in the high-Tg regime (>270 °C). This work provides a robust, validated Tg prediction tool, elucidates critical structure-property relationships, and establishes a transferable framework for data-driven materials design, advancing the development of high-performance polymers.