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2022

Failure-informed adaptive sampling for PINNs

Gao, Zhiwei, Yan, Liang, Zhou, Tao

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Physics-informed neural networks (PINNs) have emerged as an effective technique for solving PDEs in a wide range of domains.

It is noticed, however, the performance of 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 work an adaptive strategy, termed the failure-informed PINNs (FI-PINNs), which is inspired by the viewpoint of reliability analysis.

Failure-informed adaptive sampling for PINNs · Around

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Christopher M Bishop and Nasser M Nasrabadi
2006
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Léon Bottou
2012
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Diederik P Kingma and Jimmy Ba
Original
2014
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Weinan E and Bing Yu
2018
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Justin Sirignano and Konstantinos Spiliopoulos
2018
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Maziar Raissi, Paris Perdikaris, and George E Karniadakis
2019
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Weinan E
2020
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Levi McClenny and Ulisses Braga-Neto
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2020
Earlier work this paper cites.
Yaohua Zang, Gang Bao, Xiaojing Ye, and Haomin Zhou
2020
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