中国科学院数学与系统科学研究院

科研进展与学术交流报告会

（第119期）

报告人：邓伟华 教授（兰州大学）

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

摘  要：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.

时  间：2025.9.26(星期五), 10:40-11:50

地  点：南楼204会议室，腾讯会议907-5908-5643