主講人：閆亮 東南大學(xué)副教授

時(shí)間：2022年12月9日19：00

地點(diǎn)：騰訊會(huì)議 871 210 436

舉辦單位：數(shù)理學(xué)院

主講人介紹：閆亮，副教授、博士生導(dǎo)師。主要從事不確定性量化、貝葉斯反問(wèn)題理論與算法的研究。2017年入選江蘇省高?！扒嗨{(lán)工程”優(yōu)秀青年骨干教師培養(yǎng)對(duì)象，2018年入選東南大學(xué)首批“至善青年學(xué)者”（A層次）支持計(jì)劃。2019年在第十一屆反問(wèn)題年會(huì)上獲得“優(yōu)秀青年學(xué)術(shù)獎(jiǎng)”。已經(jīng)在《SIAM J. Sci. Comput.》、《Inverse Problems》、《J. Comput. Phys.》等國(guó)內(nèi)外刊物上發(fā)表30多篇學(xué)術(shù)論文。

內(nèi)容介紹：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.