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

• URL: http://arxiv.org/abs/2602.02547v1
• Date: Fri, 30 Jan 2026 06:03:33 GMT
• Title: naPINN: Noise-Adaptive Physics-Informed Neural Networks for Recovering Physics from Corrupted Measurement
• Authors: Hankyeol Kim, Pilsung Kang,
• Abstract summary: We propose the Noise-Adaptive Physics-Informed Neural Network (naPINN), which robustly recovers physical solutions from corrupted measurements.<n>naPINN embeds an energy-based model into the training loop to learn the latent distribution of prediction residuals.<n>We demonstrate the efficacy of naPINN on various benchmark partial differential equations corrupted by non-Gaussian noise and varying rates of outliers.
• Score: 3.450547277166974
• License: http://creativecommons.org/licenses/by-sa/4.0/
• 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.

Related papers

• Unlearning Noise in PINNs: A Selective Pruning Framework for PDE Inverse Problems [11.570920716097552]
  Physics-informed neural networks (PINNs) provide a promising framework for solving inverse problems governed by partial differential equations (PDEs)<n>The ill-posed nature of PDE inverse problems makes them highly sensitive to noise.<n>We propose P-PINN, a selective pruning framework designed to unlearn the influence of corrupted data in a pretrained PINN.
  arXiv  Detail & Related papers  (2026-02-23T15:29:50Z)
• APRIL: Auxiliary Physically-Redundant Information in Loss - A physics-informed framework for parameter estimation with a gravitational-wave case study [0.0]
  Physics-Informed Neural Networks (PINNs) embed the partial differential equations governing the system under study directly into the training of Neural Networks.<n>We present a complementary approach by including auxiliary physically-redundant information in loss.<n>We mathematically demonstrate that these terms preserve the true physical minimum while reshaping the loss landscape.
  arXiv  Detail & Related papers  (2025-10-15T15:34:19Z)
• PEEL the Layers and Find Yourself: Revisiting Inference-time Data Leakage for Residual Neural Networks [64.90981115460937]
  This paper explores inference-time data leakage risks of deep neural networks (NNs)<n>We propose a novel backward feature inversion method, textbfPEEL, which can effectively recover block-wise input features from the intermediate output of residual NNs.<n>Our results show that PEEL outperforms the state-of-the-art recovery methods by an order of magnitude when evaluated by mean squared error (MSE)
  arXiv  Detail & Related papers  (2025-04-08T20:11:05Z)
• Deep Neural Networks Tend To Extrapolate Predictably [51.303814412294514]
  neural network predictions tend to be unpredictable and overconfident when faced with out-of-distribution (OOD) inputs. We observe that neural network predictions often tend towards a constant value as input data becomes increasingly OOD. We show how one can leverage our insights in practice to enable risk-sensitive decision-making in the presence of OOD inputs.
  arXiv  Detail & Related papers  (2023-10-02T03:25:32Z)
• Learning Provably Robust Estimators for Inverse Problems via Jittering [51.467236126126366]
  We investigate whether jittering, a simple regularization technique, is effective for learning worst-case robust estimators for inverse problems. We show that jittering significantly enhances the worst-case robustness, but can be suboptimal for inverse problems beyond denoising.
  arXiv  Detail & Related papers  (2023-07-24T14:19:36Z)
• On the uncertainty analysis of the data-enabled physics-informed neural network for solving neutron diffusion eigenvalue problem [4.0275959184316825]
  We investigate the performance of DEPINN in calculating the neutron diffusion eigenvalue problem from several perspectives. In order to reduce the effect of noise and improve the utilization of the noisy prior data, we propose innovative interval loss functions. This paper confirms the feasibility of the improved DEPINN for practical engineering applications in nuclear reactor physics.
  arXiv  Detail & Related papers  (2023-03-15T08:59:03Z)
• Implicit Stochastic Gradient Descent for Training Physics-informed Neural Networks [51.92362217307946]
  Physics-informed neural networks (PINNs) have effectively been demonstrated in solving forward and inverse differential equation problems. PINNs are trapped in training failures when the target functions to be approximated exhibit high-frequency or multi-scale features. In this paper, we propose to employ implicit gradient descent (ISGD) method to train PINNs for improving the stability of training process.
  arXiv  Detail & Related papers  (2023-03-03T08:17:47Z)
• Robust Regression with Highly Corrupted Data via Physics Informed Neural Networks [4.642273921499256]
  Physics-informed neural networks (PINNs) have been proposed to solve two main classes of problems. We show the generalizability, accuracy and efficiency of the proposed algorithms for recovering governing equations from noisy and corrupted measurement data.
  arXiv  Detail & Related papers  (2022-10-19T15:21:05Z)
• Robust Learning of Physics Informed Neural Networks [2.86989372262348]
  Physics-informed Neural Networks (PINNs) have been shown to be effective in solving partial differential equations. This paper shows that a PINN can be sensitive to errors in training data and overfit itself in dynamically propagating these errors over the domain of the solution of the PDE.
  arXiv  Detail & Related papers  (2021-10-26T00:10:57Z)
• Non-Singular Adversarial Robustness of Neural Networks [58.731070632586594]
  Adrial robustness has become an emerging challenge for neural network owing to its over-sensitivity to small input perturbations. We formalize the notion of non-singular adversarial robustness for neural networks through the lens of joint perturbations to data inputs as well as model weights.
  arXiv  Detail & Related papers  (2021-02-23T20:59:30Z)
• The Implicit Biases of Stochastic Gradient Descent on Deep Neural Networks with Batch Normalization [44.30960913470372]
  Deep neural networks with batch normalization (BN-DNNs) are invariant to weight rescaling due to their normalization operations. We investigate the implicit biases of gradient descent (SGD) on BN-DNNs to provide a theoretical explanation for the efficacy of weight decay.
  arXiv  Detail & Related papers  (2021-02-06T03:40:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.