首页|Failure-Informed Adaptive Sampling for PINNs,Part Ⅱ:Combining with Re-sampling and Subset Simulation

Failure-Informed Adaptive Sampling for PINNs,Part Ⅱ:Combining with Re-sampling and Subset Simulation

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This is the second part of our series works on failure-informed adaptive sampling for physic-informed neural networks(PINNs).In our previous work(SIAM J.Sci.Comput.45:A1971-A1994),we have presented an adaptive sampling framework by using the fail-ure probability as the posterior error indicator,where the truncated Gaussian model has been adopted for estimating the indicator.Here,we present two extensions of that work.The first extension consists in combining with a re-sampling technique,so that the new algorithm can maintain a constant training size.This is achieved through a cosine-anneal-ing,which gradually transforms the sampling of collocation points from uniform to adap-tive via the training progress.The second extension is to present the subset simulation(SS)algorithm as the posterior model(instead of the truncated Gaussian model)for estimating the error indicator,which can more effectively estimate the failure probability and generate new effective training points in the failure region.We investigate the performance of the new approach using several challenging problems,and numerical experiments demonstrate a significant improvement over the original algorithm.

Physic-informed neural networks(PINNs)Adaptive samplingFailure probability

Zhiwei Gao、Tao Tang、Liang Yan、Tao Zhou

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School of Mathematics,Southeast University,Nanjing 210096,Jiangsu,China

Division of Science and Technology,BNU-HKBU United International College,Zhuhai 519087,Guangdong,China

Nanjing Center for Applied Mathematics,Nanjing 211135,Jiangsu,China

Institute of Computational Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China

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2024

应用数学与计算数学学报
上海大学

应用数学与计算数学学报

影响因子:0.165
ISSN:1006-6330
年,卷(期):2024.6(3)