Title: naPINN: Noise-Adaptive Physics-Informed Neural Networks for Recovering Physics from Corrupted Measurement

Abstract: Physics-Informed Neural Networks (PINNs) have proven to be powerful tools for solving inverse problems and identifying governing equations from observational data. Nevertheless, their effectiveness often diminishes substantially when faced with complex measurement noise and significant outliers. To mitigate this vulnerability, we introduce the Noise-Adaptive Physics-Informed Neural Network (naPINN), a method capable of robustly extracting physical solutions from tainted measurements without requiring prior knowledge of the noise distribution. By integrating an energy-based model into the training process, naPINN learns the latent distribution of prediction residuals. Utilizing this learned energy landscape, a trainable reliability gate dynamically filters out data points characterized by high energy, while a rejection cost regularization term ensures that trivial solutions, such as the discarding of valid data, are avoided. Our evaluation on various benchmark partial differential equations, corrupted by non-Gaussian noise and differing levels of outliers, confirms the efficacy of naPINN. The findings indicate that naPINN markedly surpasses existing robust PINN baselines, effectively isolating outliers and accurately reconstructing dynamics even under conditions of severe data corruption.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC