Project Grant 2307115

The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $300,000 Project Grant to the University of Massachusetts (UMass) for the project "Regularized Divergences and their Gradient Flows, Generative Modeling and Structure-Preserving Learning" under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The 3-year project aims to develop new mathematical tools and machine learning algorithms to improve the reliability and capabilities of generative models, which are critical for applications in areas such as medical imaging, drug discovery, and cosmology. Key aspects include designing Lipschitz-regularized probability divergences to handle scarce or expensive data, and incorporating physical constraints and symmetries into generative algorithms. The research will also apply these new methods to merge disparate cancer study datasets, addressing a challenge in data integration. The project will train graduate students in this cutting-edge field of research.