Jose Perea

Sponsor: NSF

Collaborative Research: Machine Learning on Stratified Matrix Manifolds Under Group Actions — Foundations, Algorithms and Applications

Advances in machine learning and AI are transforming science, yet analyzing complex datasets from neuroscience and quantum physics remains difficult. This project develops new theory and algorithms for data reduction and generation, advancing national AI competitiveness while training students through cross-institution seminars and undergraduate research. 

It focuses on machine learning over stratified matrix manifolds under group actions, integrating topology, geometry, and machine learning across three thrusts: mathematical foundations, equivariant algorithms (dimensionality reduction, optimal transport, flow-matching), and scientific applications in computational neuroscience and quantum science. By exploiting stratified manifold structure, it enables analysis of symmetry-constrained, rank-varying data beyond current methods.