Failure-informed adaptive sampling for PINNs

主讲人：闫亮 东南大学副教授

时间：2022年12月9日19：00

地点：腾讯会议 871 210 436

举办单位：数理学院

主讲人介绍：闫亮，副教授、博士生导师。主要从事不确定性量化、贝叶斯反问题理论与算法的研究。2017年入选江苏省高校“青蓝工程”优秀青年骨干教师培养对象，2018年入选东南大学首批“至善青年学者”（A层次）支持计划。2019年在第十一届反问题年会上获得“优秀青年学术奖”。已经在《SIAM J. Sci. Comput.》、《Inverse Problems》、《J. Comput. Phys.》等国内外刊物上发表30多篇学术论文。

内容介绍：Physics-informed neural networks (PINNs) have emerged as an effective technique for solving PDEs in a wide range of domains. Recent research has demonstrated, however, that the performance of PINNs can vary dramatically with different sampling procedures, and that using a fixed set of training points can be detrimental to the convergence of PINNs to the correct solution. In this talk, we present an adaptive approach termed failure-informed PINNs(FI-PINNs), which is inspired by the viewpoint of reliability analysis. The basic idea is to define a failure probability by using the residual, which represents the reliability of the PINNs. With the aim of placing more samples in the failure region and fewer samples in the safe region, FI-PINNs employs a failure-informed enrichment technique to incrementally add new collocation points to the training set adaptively. The failure probability, similar to classical adaptive finite element methods, acts as an error indicator that guides the refinement of the training set. When compared to the conventional PINNs method and the residual-based adaptive refinement method, the developed algorithm can significantly improve accuracy, especially for low regularity and high-dimensional problems. We prove rigorous bounds on the error incurred by the proposed FI-PINNs and illustrate its performance through several problems.