الملخص
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.
الكلمات المفتاحية
الموضوع
بيانات النشر
- المجلة
- غير متاح
- وصول مفتوح
- وصول مفتوح أخضر
اقتبس هذه المقالة
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/ar/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/ar/articles/mathematical-invariant-enabled-topological-neural-networks-for-molecular-and-materials-property-prediction.
شيكاغو (المؤلف–التاريخ)
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/ar/articles/mathematical-invariant-enabled-topological-neural-networks-for-molecular-and-materials-property-prediction.
هارفارد
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/ar/articles/mathematical-invariant-enabled-topological-neural-networks-for-molecular-and-materials-property-prediction.
فانكوفر
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/ar/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/ar/articles/mathematical-invariant-enabled-topological-neural-networks-for-molecular-and-materials-property-prediction.