报告人：周涛研究员

报告题目：Some numerical issues regarding deep neural network approximations for PDEs.

报告摘要：

(1) Deep neural networks have been widely used for solving PDEs in recently years. In this talk, we shall discuss some numerical issues for such approaches. In particular, we shall present some recent ideas for dealing with essential boundary conditions, nonlocal operators and effective sampling strategies on unbounded domains. 

(2)Randomize-then-optimize (RTO) is widely used for sampling from posterior distributions in Bayesian inverse problems. However, RTO can be computationally intensive for complexity problems due to repetitive evaluations of the expensive forward model and its gradient. In this work, we present a novel goal-oriented deep neural networks (DNN) surrogate approach to substantially reduce the computation burden of RTO. In particular, we propose to draw the training points for the DNN-surrogate from a local approximated posterior distribution. We present a Bayesian inverse problem governed by elliptic PDEs to demonstrate the computational accuracy and efficiency of our DNN-RTO approach.

报告时间：2022年5月28日10:00-13:00

报告形式：腾讯会议；会议号：624-964-167

报告人简介：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、随机最优控制以及时间并行算法等。在国际权威期刊如SIAM Review、SINUM、JCP等发表论文60余篇。2018年获自然科学基金委“优秀青年科学基金”资助。现担任SIAM J. Sci. Comput.、Commun. Comput. Phys、J. Sci. Comput.等国际期刊编委，国际不确定性量化期刊（International Journal for UQ）副主编。