Project Grant 2610704

The National Science Foundation Division of Mathematical Sciences awarded Louisiana State University $299,847 on August 15, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop mathematical foundations for machine learning applied to complex stochastic systems. Work performance runs through July 31, 2029, at Baton Rouge, Louisiana.

The project addresses learning and inference challenges for systems that evolve over time in the presence of randomness, with interacting components operating on different time scales and partially observable behavior. Part I develops likelihood-based methods for learning multiscale stochastic differential equations from observations of slow components alone, using conditional normalizing flows and Bayesian nonparametric methods based on normalized Lévy process priors, with theoretical analysis providing principled estimation and uncertainty quantification of averaged drift functions for high-dimensional multiscale SDEs. Part II develops a statistical framework for offline reinforcement learning and inverse reinforcement learning for controlled SDEs with unknown dynamics, applying large deviation theory to derive exponentially accurate confidence bounds for long-run cost functionals and optimize policies with rigorous performance guarantees. The project supports training of students in theoretical, computational, and data-science skills.