Differential Learning for Robust Prediction of Thermal Stability with Application to Energetic Materials

The discovery of new energetic materials is critical for advancing technologies from defense to private industry. However, experimental approaches remain slow and expensive while computational alternatives require accurate material property inputs that are often costly to obtain, limiting their ability to efficiently predict detonation performance across a vast chemical space. We address this challenge through an active learning strategy that integrates density functional theory calculations, thermochemical modeling, message-passing neural networks, and Bayesian optimization. The resulting high-throughput workflow iteratively expands the training dataset by selecting new molecules in a targeted manner that balances the exploration of broad chemical space with the exploitation of promising high-performing candidates. This approach yields the largest publicly available database of potential CHNO explosives drawn from an initial pool of more than 70 billion candidates and a generalizable surrogate model capable of accurately predicting detonation performance (R$^2$ > 0.98). Feature importance analysis on this largest-to-date dataset reveals that oxygen balance is the dominant driver of detonation performance, complemented by contributions from local electronic structure, density, and the presence of specific functional groups. Cheminformatics analysis highlights how energetic materials with similar performance metrics tend to cluster in distinct chemical spaces offering a clearer direction for future synthesis studies. Together, the surrogate model, database, and resulting chemical insights provide a valuable foundation for high-throughput screening and targeted discovery of new energetic materials spanning diverse and previously unexplored regions of chemical space.

Characterizing crystalline energy landscapes is essential to predicting thermodynamic stability, electronic structure, and functional behavior. While machine learning (ML) enables rapid property predictions, the "black-box" nature of most models limits their utility for generating new scientific insights. Here, we introduce Kolmogorov-Arnold Networks (KANs) as an interpretable framework to bridge this gap. Unlike conventional neural networks with fixed activation functions, KANs employ learnable functions that reveal underlying physical relationships. We developed the Element-Weighted KAN, a composition-only model that achieves state-of-the-art accuracy in predicting formation energy, band gap, and work function across large-scale datasets. Crucially, without any explicit physical constraints, KANs uncover interpretable chemical trends aligned with the periodic table and quantum mechanical principles through embedding analysis, correlation studies, and principal component analysis. These results demonstrate that KANs provide a powerful framework with high predictive performance and scientific interpretability, establishing a new paradigm for transparent, chemistry-based materials informatics.

Existing molecular and materials learning approaches often rely on a limited set of structural representations, which may capture only selected aspects of complex three-dimensional structure. Here, we introduce mathematical invariant-enabled topological neural networks (MITNNs), a framework that represents complex structures through multiple complementary mathematical views and integrates them with topological neural architectures. MITNNs combine multiscale invariants from topology, spectral theory, commutative algebra, differential geometry, and discrete curvature, capturing complementary structural information from the same system. Systematic invariant-subset, architecture-subset, and ensemble analyses show that predictive performance depends on how mathematical representations and neural architectures are paired, with selected combinations outperforming individual models and the aggregation of all available components. Across protein-ligand binding, metal-organic framework properties, mutation-induced protein solubility, and molecular toxicity prediction, MITNN consistently outperforms existing methods. These results establish MITNN as a mathematically multimodal framework for scientific machine learning.