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

TL;DR

naPINN introduces a noise-adaptive approach to enhance the robustness of physics-informed neural networks, effectively recovering physical laws from highly corrupted data without prior noise knowledge.

Contribution

It proposes a novel energy-based model integrated into PINNs to adaptively filter outliers and recover accurate physics from corrupted measurements.

Findings

Outperforms existing robust PINN methods on benchmark PDEs

Successfully isolates outliers and reconstructs dynamics under severe noise

Demonstrates effectiveness without prior noise distribution knowledge

Abstract

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.