Neural Network Algorithms for Stochastic Optimal Control
June 2, 2026
Edinburgh, United Kingdom
This minisymposium talk presents neural network algorithms for high-dimensional stochastic optimal control based on forward-backward SDEs. Training combines the control objective with penalties enforcing the Hamilton–Jacobi–Bellman equation along sampled trajectories, and Pontryagin's maximum principle identifies the optimal controls, concentrating computation on the relevant regions of state space. A central question is how to differentiate neural SDEs in time: the talk analyzes adjoint formulations and their effect on training stability and cost, with findings on benchmarks up to 100 dimensions.
Continuous-Time Deep Learning for Generative AI and High-Dim PDEs
May 19, 2026
University of Tennessee, Knoxville, TN
Continuous-time models — ODEs, SDEs, and transport PDEs — provide a unifying mathematical framework for deep learning. This survey lecture traces a path from residual networks as discretized ODEs through the optimal control view of training to stochastic extensions via Fokker–Planck equations. A high-dimensional PDE perspective unifies continuous normalizing flows, flow matching, and score-based diffusion and builds bridges to dynamic optimal transport. The lecture closes with applications in stochastic optimal control and mean-field games and open problems for the probability and PDE communities.
Understanding Generative AI Through Optimal Transport and PDEs
April 3, 2026
Emory University, Atlanta, GA
Modern generative AI systems such as Stable Diffusion and Sora rest on classical transport PDEs. This plenary talk shows how the continuity equation and the Fokker–Planck equation provide a unified framework for continuous normalizing flows, flow matching, and score-based diffusion. A central theme is the distinction between feasible and optimal transport: state-of-the-art methods succeed by constructing feasible probability paths that are computationally tractable in high dimensions. The talk closes with open problems connecting generative modeling to optimal control and mean-field games.