Department of Mathematical Sciences PhD Dissertation Defense: Taorui Wang
10:00 a.m. to 12:00 p.m.
Department of Mathematical Sciences
Taorui Wang
Thursday, May 7th, 2026
10:00AM-12:00PM
Stratton Hall 202
Zoom Link:
Speaker: Taorui Wang
Title: Physics-Informed Neural Networks for High Dimensional Partial Differential Equations Arising from Stochastic Dynamics
Abstract: Partial differential equations arising from stochastic dynamics are important in probability, statistical physics, control, reinforcement learning, and optimization. They describe how randomness shapes long-time behavior, control, and search in complex systems. This dissertation studies high-dimensional steady-state Fokker--Planck equations, high-dimensional exploratory Hamilton--Jacobi--Bellman equations, and their use in designing state-dependent temperature controls for Langevin dynamics in non-convex optimization. A common difficulty across these problems is that classical grid-based methods become prohibitively expensive in high dimensions, which motivates neural-network-based solvers such as physics-informed neural networks.
For high-dimensional steady-state Fokker--Planck equations, we develop physics-informed neural network solvers based on tensor neural networks together with numerical-support selection and separable integration for normalization. These methods produce accurate approximations in dimensions up to ten while maintaining normalization. For high-dimensional exploratory HJB equations, we develop physics-informed neural network methods based on continuation in the exploration parameter and stabilized evaluation of the control operator. The resulting framework solves stationary exploratory HJB equations up to six spatial dimensions and finite-horizon exploratory HJB equations up to four spatial dimensions. These computations are then used to construct state-dependent temperatures and the corresponding noise coefficients for Langevin dynamics in non-convex optimization, leading to algorithms that are effective on benchmark minimization problems up to six dimensions.
Committee members: