Mathematical AI for Molecular Sciences

Abstract

Artificial intelligence (AI) based Molecular Sciences have begun to gain momentum due to the great advancement in experimental data, computational power and learning models. However, a major issue that remains for all these AI-based learning models is the efficient molecular representations and featurization. Here we propose advanced mathematics-based molecular representations and featurization. Molecular structures and their interactions are represented by high-order topological and algebraic models (including Rips complex, Alpha complex, Neighborhood complex, Dowker complex, Hom-complex, Tor-algebra, etc). Mathematical invariants (from persistent homology, persistent Ricci curvature, persistent spectral, R-Torsion, etc) are used as molecular descriptors for learning models. Further, we develop geometric and topological deep learning models to systematically incorporate molecular high-order, multiscale, and periodic information, and use them for analysing molecular data from chemistry, biology, and materials.