学术报告

题      目：Adaptive trajectories sampling for solving PDEs with deep learning methods

报  告  人：邹青松   教授  (邀请人：钟柳强 )

                                    中山大学

时      间：3月25日  10：00-11：00

地     点：数科院西楼二楼会议室

报告人简介:

         邹青松，中山大学计算机学院教授，博士生导师，数据科学系主任，广东省计算数学学会理事长,期刊International Journal of Numerical Analysis and Modelling编委。长期从事科学计算方面的研究工作，在包括SIAM J Numer Anal, Math Comp, Numer Math, J Comp Phy等在内的知名国际发表论文60多局。主要研究方向包括高阶高精度有限体积法，偏微分方程深度学习算法，和来自生物，医学，金融，材料等领域的应用问题的人工智能科学计算。

摘      要：

        In this paper, we propose a new adaptive technique, named {\it adaptive trajectories sampling} (ATS), which is used to select training points for the numerical solution of partial differential equations (PDEs) with deep learning methods. The key feature of the ATS is that all training points are adaptively selected from trajectories which are generated according to a  PDE-related stochastic process. We incorporate the ATS into three known deep learning solvers for PDEs, namely the adaptive derivative-free-loss method (ATS-DFLM), the adaptive physics-informed neural network method (ATS-PINN), and the adaptive temporal-difference method for forward-backward stochastic differential equations (ATS-FBSTD).Our numerical experiments demonstrate that the ATS  markedly 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.