naPINN: 用于从损坏测量中恢复物理的噪声自适应物理信息神经网络
naPINN: Noise-Adaptive Physics-Informed Neural Networks for Recovering Physics from Corrupted Measurement
AI总结：
提出噪声自适应物理信息神经网络(naPINN)，通过嵌入能量模型学习残差分布并自适应过滤异常值，从非高斯噪声和离群点损坏的测量中鲁棒恢复物理解。
摘要：
物理信息神经网络(PINNs)是解决逆问题和从观测数据中发现控制方程的有效方法。然而，在复杂测量噪声和严重离群点下，其性能显著下降。为解决此问题，我们提出了噪声自适应物理信息神经网络(naPINN)，该网络无需噪声分布先验知识，即可从损坏测量中鲁棒恢复物理解。naPINN在训练循环中嵌入一个基于能量的模型，以学习预测残差的潜在分布。利用学习到的能量景观，一个可训练的可靠性门自适应地过滤具有高能量的数据点，同时拒绝代价正则化防止丢弃有效数据导致的平凡解。我们在被非高斯噪声和不同比例离群点损坏的各种基准偏微分方程上展示了naPINN的有效性。结果表明，naPINN显著优于现有的鲁棒PINN基线，成功隔离离群点并在严重数据损坏下准确重建动力学。
英文摘要：
Physics-Informed Neural Networks (PINNs) are effective methods for solving inverse problems and discovering governing equations from observational data. However, their performance degrades significantly under complex measurement noise and gross outliers. To address this issue, we propose the Noise-Adaptive Physics-Informed Neural Network (naPINN), which robustly recovers physical solutions from corrupted measurements without prior knowledge of the noise distribution. naPINN embeds an energy-based model into the training loop to learn the latent distribution of prediction residuals. Leveraging the learned energy landscape, a trainable reliability gate adaptively filters data points exhibiting high energy, while a rejection cost regularization prevents trivial solutions where valid data are discarded. We demonstrate the efficacy of naPINN on various benchmark partial differential equations corrupted by non-Gaussian noise and varying rates of outliers. The results show that naPINN significantly outperforms existing robust PINN baselines, successfully isolating outliers and accurately reconstructing the dynamics under severe data corruption.
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