Computer-aided drug design (CADD), including structure-based virtual screening of a large number of available compounds (ligands) for a given drug target, has become an essential component of modern drug discovery. The actual value of the virtual screening relies on the accuracy of the target-ligand binding affinity prediction. It is recognized as a grand challenge for the virtual screening to accurately predict the target-ligand binding structures (molecular geometries) and binding affinities associated with diverse and massive datasets. This project aims to address the grand challenge in development of machine-learning (ML)-CADD models by introducing new, more effective mathematical representations of molecular geometries with the ability to track molecular geometry changes via Ricci curvatures and their associated spectral information. The outcomes of this project will furnish novel, more reliable computational approaches in essential areas of computational drug design, biomolecular modeling, data analysis, dimensionality reduction, and mathematical biology. Moreover, this project will provide graduate and undergraduate students with training in data analysis, biological modeling, algorithm development, and computational drug design. The enhancement of curricula from this project is planned as a continuation of the investigators' teaching-research practice. The new mathematical framework and deep learning architectures are directly integrated into computer software packag