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

2026-01-30

AI Summary

This work addresses the challenge of accurately recovering underlying physical laws using physics-informed neural networks (PINNs) in the presence of complex non-Gaussian noise and a high proportion of outliers. To this end, we propose naPINN, a novel approach that integrates an energy-based model with an adaptive data filtering mechanism. The energy-based model learns the residual distribution, while a trainable reliability gate dynamically identifies and removes high-energy outliers. A rejection-cost regularization term is introduced to prevent the erroneous removal of valid data points. Notably, naPINN requires no prior knowledge of the noise characteristics and consistently outperforms existing robust PINN variants across multiple benchmark partial differential equations contaminated with non-Gaussian noise and varying outlier ratios, achieving precise anomaly detection and accurate reconstruction of the physical fields.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Natural Language Processing: Safety and Robustness
• Intelligent Robots: State Estimation

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Physics-Informed Neural Networks
• measurement noise
• outliers
• inverse problems
• data corruption

Innovation

• noise-adaptive
• physics-informed neural networks
• energy-based model
• outlier rejection
• robust inverse problems