PhD Comprehensive Exam | Yun Su, Developing Data-Driven Neural Network Approaches for Solving High-Dimensional Hamilton-Jacobi-Bellman Equations

MC 5501

Candidate

Yun Sui | Applied Mathematics, University of Waterloo

Title

Developing Data-Driven Neural Network Approaches for Solving High-Dimensional Hamilton-Jacobi-Bellman Equations

Abstract

This study presents novel data-driven neural network methodologies for solving high-dimensional Hamilton-Jacobi-Bellman (HJB) equations, central to optimal control theory and dynamic programming. Traditional approaches to solving HJB equations often struggle with the curse of dimensionality, limiting their applicability in complex systems. Our approach combines data-driven loss term to Physics-Informed Neural Networks, utilizing the structure of HJB equations to guide network training and architecture design, thereby enhancing solution accuracy and computational efficiency. Empirical assessments of our approach reveal its capacity to tackle Hamilton-Jacobi-Bellman (HJB) equations in high dimensions. This breakthrough paves the way for novel applications in fields such as finance, robotics, and autonomous decision-making systems.