京师数学前沿论坛 第十二讲
京师数学前沿论坛
报告题目(Title)：Deep Learning for High-dimensional PDEs with Fat-tailed Lévy Measure
报告人(Speaker)：邓伟华教授 （兰州大学）
地点(Place)：后主楼1124
时间(Time)：2025年12月26日上午9:00-10:00
报告摘要
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.
主讲人简介
邓伟华，兰州大学数学与统计学院教授、博士生导师，现任院长。2007年获上海大学博士学位后进入兰州大学工作，2010年晋升教授。研究方向为反常扩散、非局部偏微分方程数值解及随机模型，聚焦于细胞迁移、污染物传播等领域的非遍历动力学建模与分析。曾主持国家杰出青年科学基金项目，获教育部自然科学奖二等奖、霍英东教育基金会青年教师奖，2014-2020年连续入选数学类高被引科学家。兼任中国工业与应用数学会常务理事、中国数学会计算数学分会副理事长，并担任《Computer and Mathematics with Applications》等期刊编委。
