Speaker: 邓伟华教授，兰州大学

Inviter: 中国科学院数学院学术报告会组委

Title: Deep Learning for High-dimensional PDEs with Fat-tailed Lévy Measure

Language: Chinese

Time & Venue: 2025.09.26 10:40-11:50 数学院南楼N204（数学院交流报告会）

Abstract: The partial differential equations (PDEs) for jump process with Lévy measure have wide applications. When the measure has fat tails, it will bring big challenges for both computational cost and accuracy. In this work, we develop a deep learning method for high-dimensional PDEs related to fat-tailed Lévy measure, which can be naturally extended to the general case. Building on the theory of backward stochastic differential equations for Lévy processes, our deep learning method avoids the need for neural network differentiation and introduces a novel technique to address the singularity of fat-tailed Lévy measures. The developed method is used to solve four kinds of high-dimensional PDEs: the diffusion equation with fractional Laplacian; the advective diffusion equation with fractional Laplacian; the advective diffusion reaction equation with fractional Laplacian; and the nonlinear reaction diffusion equation with fractional Laplacian.