naPINN: Noise-Adaptive Physics-Informed Neural Networks for Recovering Physics from Corrupted Measurement
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Abstract (arXiv)
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.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 32 of its 55 references that are in the map. First posted on arXiv 30 Jan 2026.
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32 of 55 references.
References · 32
- 2019Benchmarking Neural Network Robustness to Common Corruptions and Perturbationscited by 2,857
- 2016A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networkscited by 2,362
- 2018On the Spectral Bias of Neural Networkscited by 1,321
- 2020Energy-based Out-of-distribution Detectioncited by 1,296
- 2019Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shiftcited by 1,274
- 2018Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labelscited by 1,053
- 2015Automatic differentiation in machine learning: a surveycited by 846
- 2017GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networkscited by 816
- 2020DivideMix: Learning with Noisy Labels as Semi-supervised Learningcited by 691
- 2017MentorNet: Learning Data-Driven Curriculum for Very Deep Neural Networks on Corrupted Labelscited by 652
- 2024KAN: Kolmogorov-Arnold Networkscited by 634
- 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 629
20 more
- 2021Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancycited by 387
- 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 329
- 2022TranAD: Deep Transformer Networks for Anomaly Detection in Multivariate Time Series Datacited by 211
- 2021Towards Robust Vision Transformercited by 137
- 2018Adversarial Uncertainty Quantification in Physics-Informed Neural Networkscited by 120
- 2021Efficient training of physics-informed neural networks via importance samplingcited by 109
- 2019On the Anatomy of MCMC-Based Maximum Likelihood Learning of Energy-Based Modelscited by 105
- 2021Multi-Objective Loss Balancing for Physics-Informed Deep Learningcited by 86
- 2024PirateNets: Physics-informed Deep Learning with Residual Adaptive Networkscited by 70
- 2021Learning in Sinusoidal Spaces with Physics-Informed Neural Networkscited by 61
- 2021Quadratic Residual Networks: A New Class of Neural Networks for Solving Forward and Inverse Problems in Physics Involving PDEscited by 42
- 2023Continual Test-time Domain Adaptation via Dynamic Sample Selectioncited by 35
- 2025Enhancing Time Series Forecasting through Selective Representation Spaces: A Patch Perspectivecited by 34
- 2024RoPINN: Region Optimized Physics-Informed Neural Networkscited by 26
- 2022Is L2 Physics-Informed Loss Always Suitable for Training Physics-Informed Neural Network?cited by 23
- 2024Dual Cone Gradient Descent for Training Physics-Informed Neural Networkscited by 21
- 2023When Model Meets New Normals: Test-time Adaptation for Unsupervised Time-series Anomaly Detectioncited by 17
- 2025Selective Learning for Deep Time Series Forecastingcited by 8
- 2022Physics-informed Neural Networks with Unknown Measurement Noisecited by 7
- 2022Robust Regression with Highly Corrupted Data via Physics Informed Neural Networkscited by 4
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