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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，本科毕业于上海交通大学致远学院，博士毕业于清华大学数学科学系。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。现研究方向包括有限维滤波理论，丘-丘滤波方法，物理信息神经网络以及生物信息学。研究兴趣主要集中于（1）利用李代数等几何工具进行偏微分方程求解与有限维滤波系统的分类；（2）设计基于物理信息神经网络的新型数值算法。