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.
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Publication details
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- Open access
- Green open access
Cite this article
APA 7
Ren, Y., Liu, X., Hajij, M., Liò, P., & Wei, G. W. (2026). Mathematical Invariant-Enabled Topological Neural Networks for Molecular and Materials Property Prediction. https://omanscience.com/en/articles/mathematical-invariant-enabled-topological-neural-networks-for-molecular-and-materials-property-prediction
MLA 9
Ren, Yiming, et al. "Mathematical Invariant-Enabled Topological Neural Networks for Molecular and Materials Property Prediction." https://omanscience.com/en/articles/mathematical-invariant-enabled-topological-neural-networks-for-molecular-and-materials-property-prediction.
Chicago (author–date)
Ren, Yiming, Xiang Liu, Mustafa Hajij, Pietro Liò, and Guo-Wei Wei. 2026. "Mathematical Invariant-Enabled Topological Neural Networks for Molecular and Materials Property Prediction." https://omanscience.com/en/articles/mathematical-invariant-enabled-topological-neural-networks-for-molecular-and-materials-property-prediction.
Harvard
Ren, Y., Liu, X., Hajij, M., Liò, P. and Wei, G. W. (2026) 'Mathematical Invariant-Enabled Topological Neural Networks for Molecular and Materials Property Prediction', Available at: https://omanscience.com/en/articles/mathematical-invariant-enabled-topological-neural-networks-for-molecular-and-materials-property-prediction.
Vancouver
Ren Y, Liu X, Hajij M, Liò P, Wei GW. Mathematical Invariant-Enabled Topological Neural Networks for Molecular and Materials Property Prediction. https://omanscience.com/en/articles/mathematical-invariant-enabled-topological-neural-networks-for-molecular-and-materials-property-prediction
IEEE
Y. Ren, X. Liu, M. Hajij, P. Liò, and G. W. Wei, "Mathematical Invariant-Enabled Topological Neural Networks for Molecular and Materials Property Prediction," https://omanscience.com/en/articles/mathematical-invariant-enabled-topological-neural-networks-for-molecular-and-materials-property-prediction.