报告题目：Deep adaptive sampling for numerical PDEs
主讲人：周涛研究员（中国科学院数学与系统科学研究院）
时间：2023年3月9日（周四）15:30 p.m.
地点：北院卓远楼305会议室
主办单位：统计与数学学院
摘要：Adaptive computation is of great importance in numerical simulations. The ideas for adaptive computations can be dated back to adaptive finite element methods in 1970s. In this talk, we shall first review some recent development for adaptive method with applications. Then, we shall propose a deep adaptive sampling method for solving PDEs where deep neural networks are utilized to approximate the solutions. In particular, we propose the failure informed PINNs (FI-PINNs), which can adaptively refine the training set with the goal of reducing the failure probability. Compared to the neural network approximation obtained with uniformly distributed collocation points, the developed algorithms can significantly improve the accuracy, especially for low regularity and high-dimensional problems.
主讲人简介：
周涛，中国科学院数学与系统科学研究院研究员。曾于瑞士洛桑联邦理工大学从事博士后研究。主要研究方向为不确定性量化、偏微分方程数值方法以及时间并行算法等。在国际权威期刊SIAM Review、SINUM、JCP等发表论文70余篇。2016年获CSIAM青年科技奖，2018年获优秀青年科学基金资助，2022年获中组部高层次人才专项资助，并获得第三届王选杰出青年学者奖。2018年曾担任国防科工局《核挑战专题》不确定性量化方向首席科学家，并在2021年被授予“挑战英才”称号。现担任SIAM J Sci Comput、J Sci Comput、Commun. Comput. Phys. 等多个国际权威期刊编委，国际不确定性量化期刊（International Journal for UQ）副主编。周涛研究员目前担任东亚工业与应用数学学会副主席，并担任学会期刊East Asian Journal on Applied Mathematics主编。
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