报告题目：Adaptive trajectories sampling for solving PDEs with deep learning methods

报 告 人：邹青松教授，中山大学计算机学院

报告时间：2023年9月18日（星期一）下午16：00-17：00

报告地点：龙洞行政楼610报告厅

主持人：陈学松

摘要：In this paper, we propose a novel adaptive technique, named {\it adaptive trajectories sampling} (ATS), to select training points for learning the solution of partial differential equations (PDEs). By the ATS, the training points are selected adaptively according to an empirical-value-type instead of residual-type error indicator from trajectories which are generated by a PDE-related stochastic process. We incorporate the ATS into three known deep learning solvers for PDEs, namely, the adaptive physics-informed neural network method (ATS-PINN), the adaptive derivative-free-loss method (ATS-DFLM), and the adaptive temporal-difference method for forward-backward stochastic differential equations (ATS-FBSTD).Our numerical experiments demonstrate that the ATS remarkably improves the computational accuracy and efficiency of the original deep learning solvers for the PDEs. In particular, for some specific high-dimensional PDEs, the ATS can even improve the accuracy of the PINN by two orders of magnitude.

个人简介：邹青松，中山大学计算机学院教授，科学计算系主任，广东省计算数学学会理事长。长期从事科学计算领域研究工作。在传统科学计算领域，主要研究有限体积法和有限元方法。在人工智能科学计算（科学智算）领域，主要研究偏微分方程的深度学习算法和基于AI的分子性质预测，并涉及AI科学计算多学科领域的评测。发表SCI期刊论文60多篇，多篇发表在SIAM J Numer Anal，Numer Math，Math Comp，J Comp Physics等知名刊物。主持国家自然科学基金项目5项，参与科技部重点研发项目2项（课题负责人1项）。获2020年度广东省自然科学二等奖（排名第一）。