Adaptive sampling with failure-informed enrichment scheme for PINNs

讲座时间 Datetime: 2022年9月16日，星期五，10:00-11:00

地点 Venue: 腾讯线上会议：937-988-588

主持人 Host：时聪

报告人 Speaker: 闫亮 

单位 Affiliation: 东南大学

报告摘要 Abstract:

_{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.  Utilizing a failure-informed enrichment strategy, FI-PINNs incrementally adds new collocation points to the training set with the goal of finely partitioning significant sub-regions where the collocation points significantly affect the failure probability.  The accuracy of the PINNs model is then improved using the new collocation points. The loop is sequential and complementary up until the convergence criteria is met. When compared to the conventional PINN 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.}