DeepParticle: learning invariant measure by a deep neural network minimizing Wasserstein distance on data generated from an interacting particle method

报告人：张智文副教授香港大学

时间：2025.03.19上午10:00-12:00

地点：腾讯会议# 801-518-841

报告摘要：

High-dimensional PDEs are hard to compute with traditional mesh-based methods, especially with large gradients or unknown concentrations. Mesh-free methods are more appealing but slow and expensive for long computations. We present DeepParticle, an approach integrating Deep Learning (DL), Optimal Transport (OT), and interacting particle (IP) through a case study of Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) front speeds in incompressible flows. PDE analysis reduces the problem to computing the principal eigenvalue of an advection-diffusion operator. Stochastic representation via Feynman-Kac enables a genetic IP algorithm to evolve particle distribution to a time-invariant measure for front speed extraction. This measure is parameterized by the Peclet number. We learn this family of measures by training a physically parameterized DNN on affordable IP data at moderate Peclet numbers, then predict at larger, more expensive Peclet numbers. Our method extends to learning and generating stochastic particle dynamics in general contexts, e.g., aggregation patterns in Keller-Segel chemotaxis systems.

报告人简介：

Z. Zhang received his B.S. degree and Ph.D. degree in mathematics from Tsinghua University, Beijing, P.R. China, in 2006 and 2011, respectively. After his graduation, he was a postdoctoral scholar at California Institute of Technology from 2011 to 2015. He joined the University of Hong Kong as an Assistant Professor in 2015 and became an Associate Professor in 2021. Dr. Zhang’s research interests are scientific computation. Research topics include uncertainty quantification (UQ) and numerical methods for partial differential equations (PDEs) arising from quantum chemistry, wave propagation, multiscale porous media, nonlinear filtering, data assimilation, and stochastic fluid dynamics. Recently, he has also been working on deep learning methods for solving SDEs and PDEs.。

邀请人：王亚婷 副教授