Stochastic particle method for high-dimensional PDEs

报告题目: Stochastic particle method for high-dimensional PDEs

报告人：熊云丰讲师北京师范大学数学科学学院

报告时间：2025年5月22日下午15:00

报告地点：红瓦楼726

报告内容简介：Numerical resolution of moderately high-dimensional nonlinear PDEs remains a huge challenge due to the curse of dimensionality for the classical numerical methods including finite difference, finite element and spectral methods. In this talk, we discuss a stochastic particle method (SPM) by tracking the deterministic motion, random jump, resampling and reweighting of particles. Real-valued weighted particles are adopted by SPM to approximate the high-dimensional solution, which automatically adjusts the point distribution to intimate the relevant feature of the solution. A piecewise constant reconstruction with virtual uniform grid is employed to evaluate the nonlinear terms, which fully exploits the intrinsic adaptive characteristic of SPM. Combining both, SPM can achieve the goal of adaptive sampling in time. Numerical experiments on the 6-D Allen-Cahn equation, 7D Hamiltonian-Jacobi-Bellman equation and 1000000-D linear fractional diffusion equation demonstrate the potential of SPM in solving moderately high-dimensional nonlinear PDEs efficiently while maintaining an acceptable accuracy.

报告人简介：熊云丰目前为北京师范大学数学科学学院讲师，他2020年毕业于北京大学获理学博士学位，主要研究方向为高维问题的数值方法，包括谱方法和随机粒子方法在高维偏微分方程、随机系统中的应用。目前在国际权威期刊SIAM Journal on Numerical Analysis，SIAM Journal on Scientific Computing, Journal of Computational Physics，PLOS Computational Biology上发表论文多篇，获国家自然基金委青年科学基金项目、中国博士后科学基金会等资助，并参与国家重点研发项目。

报告邀请人：盛长滔