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Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck Equations
Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck Equations
组织者
演讲者
时间
2024年05月15日 15:00 至 15:30
地点
理科楼A-304
摘要
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.
演讲者介绍
焦小沛，于2017年本科毕业于上海交通大学致远学院（物理班），2022年博士毕业于清华大学数学科学系，师从丘成栋教授（IEEE fellow，前美国伊利诺伊大学芝加哥分校终身教授）。先后在北京雁栖湖应用数学研究院，荷兰特文特大学从事博士后工作（导师Johannes Schmidt-Hieber教授，国际数理统计学会会士）。现研究方向包括控制理论，数值偏微分方程，生物信息学。获得2025年国家青年科学基金[C类]资助。