Name: Jiequn Han, Instructor of Mathematics, Department of Mathematics, Princeton University
Date: Thursday, January 21, 2021 at 11:00 am
Solving High-Dimensional PDEs, Controls, and Games with Deep Learning
Developing algorithms for solving high-dimensional partial differential equations, controls, and games has been an exceedingly difficult task for a long time, due to the notorious "curse of dimensionality". In this talk, we introduce a family of deep learning-based algorithms for these problems. The algorithms exploit the mathematical structure of problems and utilize deep neural networks as efficient approximations to high-dimensional functions. Numerical results of a variety of examples demonstrate the efficiency and accuracy of the proposed algorithms in high-dimensions. This opens up new possibilities in economics, engineering, and physics, by considering all participating agents, assets, resources, or particles together at the same time, instead of making ad hoc assumptions on their inter-relationships
Jiequn Han is an Instructor at the Department of Mathematics, Princeton University. He obtained his Ph.D. degree in applied mathematics from the Program in Applied and Computational Mathematics (PACM), Princeton University in 2018. His research draws inspiration from various disciplines of science and is devoted to solving high-dimensional problems arising from scientific computing. His current research topics mainly focus on machine learning based multiscale modeling and solving high-dimensional partial differential equations/stochastic control.