Mathematical models improve predicting molecules and materials properties
Mathematical Invariant-Enabled Topological Neural Networks for Molecular and Materials Property Prediction
Machine Learning
Summary
Predicting the properties of molecules and materials is hard because of their complex 3D structures. This paper introduces a new system that uses several mathematical perspectives, like topology and geometry, to better understand these structures. The authors show that combining these mathematical features with special neural networks improves prediction accuracy. Their method works well on tasks like drug binding, material properties, and toxicity prediction.
What this means in practice
- •For drug development teams: Predict binding between proteins and potential drug molecules using mathematically enhanced neural networks for better accuracy.
- •For materials engineering teams: Improve prediction of metal-organic framework properties by integrating multiple mathematical descriptors into machine learning models.
Authors
Yiming Ren, Xiang Liu, Mustafa Hajij, Pietro Liò, Guo-Wei Wei
Abstract
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.