naPINN: Noise-Adaptive Physics-Informed Neural Networks for Recovering Physics from Corrupted Measurement
This addresses the robustness issue in PINNs for inverse problems and equation discovery, offering a domain-specific improvement for handling corrupted data in physics-based machine learning.
The paper tackled the problem of Physics-Informed Neural Networks (PINNs) degrading under complex noise and outliers by proposing naPINN, which robustly recovers physical solutions from corrupted measurements without prior noise knowledge, significantly outperforming existing baselines on benchmark PDEs with non-Gaussian noise and outliers.
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.