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Seminar on Control Theory and Nonlinear Filtering
Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck Equations
Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck Equations
Organizer
Speaker
Time
Wednesday, May 15, 2024 3:00 PM - 3:30 PM
Venue
理科楼A-304
Abstract
The Fokker-Planck (FP) equation is crucial in stochastic processes with Brownian motions, but handling high-dimensional FP equations is challenging due to the curse of dimensionality (CoD). Wang et al propose a novel approach using a score-based solver to fit the score function in stochastic differential equations (SDEs), introducing three fitting methods: Score Matching (SM), Sliced Score Matching (SSM), and Score-PINN. Their results demonstrate the stability, speed, and effectiveness of the score-based SDE solver, suggesting its potential as a CoD solution for high-dimensional FP equations.
Speaker Intro
Jiao Xiaopei graduated with a bachelor's degree from the Zhi Yuan College of Shanghai Jiao Tong University (Physics Department) in 2017 and obtained his PhD from the Department of Mathematical Sciences at Tsinghua University in 2022, under the guidance of Professor Stephen Shing-Toung Yau (IEEE Fellow, former tenured professor at the University of Illinois at Chicago). He has conducted postdoctoral research at the Beijing Institute of Mathematica Science and Application and at the University of Twente in the Netherlands (under the guidance of Professor Johannes Schmidt-Hieber, Fellow of the Institute of Mathematical Statistics). His current research interests include control theory, numerical partial differential equations, and bioinformatics.