Mathematical Invariant-Enabled Topological Neural Networks for Molecular and Materials Property Prediction

2026-10-06

AI Summary

This study addresses the bottleneck of existing methods that rely on limited structural representations and struggle to comprehensively capture complex three-dimensional information by proposing a mathematical invariant topological neural network. This work pioneers a mathematical multimodal framework that integrates multiscale complementary invariants from topology, spectral theory, commutative algebra, differential geometry, and discrete curvature, thereby revealing the pairing principles between representations and architectures. Evaluated on tasks including protein–ligand binding and metal-organic framework (MOF) property prediction, the proposed method consistently outperforms both single-model approaches and full-component aggregation baselines. By effectively bridging abstract mathematical structures with deep learning architectures, this research establishes a new paradigm for scientific machine learning.

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.

Problem

• molecular property prediction
• materials property prediction
• structural representation
• 3D structure
• scientific machine learning

Innovation

• Topological Neural Networks
• Mathematical Invariants
• Multimodal Learning
• Molecular Property Prediction
• Scientific Machine Learning