Failure-informed adaptive sampling for PINNs

主讲人：周涛 中国科学院数学与系统科学研究院研究员

时间：2022年10月28日10：00

地点：腾讯会议 855 981 699

举办单位：数理学院

主讲人介绍：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70余篇。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。

内容介绍：Deep neural networks have emerged as an effective tool for solving PDEs. Recent research has demonstrated, however, that the performance of DNNs-based approaches (such as PINNs) can vary dramatically with different sampling procedures. For instance, a fixed set of (prior chosen) training points may fail to capture the effective solution region (especially for problems with singularities). To overcome this issue, we present in this talk an adaptive strategy -- failure-informed PINNs (FI-PINNs), which is inspired by the viewpoint of re-liability analysis. The basic idea is to define a failure probability by using the residual. Then, with the aim of placing more samples in the failure region, the proposed FI-PINNs employs a failure-informed enrichment technique to incrementally add new collocation points to the training set adaptively. Compared to the conventional PINNs, FI-PINNs can significantly improve the accuracy. We prove rigorous bounds on the error incurred by FI-PINNs and illustrate its perfor-mance through several problems。