Unlearning Noise in PINNs: A Selective Pruning Framework for PDE Inverse Problems

• URL: http://arxiv.org/abs/2602.19967v2
• Date: Sun, 01 Mar 2026 01:40:45 GMT
• Title: Unlearning Noise in PINNs: A Selective Pruning Framework for PDE Inverse Problems
• Authors: Yongsheng Chen, Yong Chen, Wei Guo, Xinghui Zhong,
• Abstract summary: 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.
• Score: 11.570920716097552
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Physics-informed neural networks (PINNs) provide a promising framework for solving inverse problems governed by partial differential equations (PDEs) by integrating observational data and physical constraints in a unified optimization objective. However, the ill-posed nature of PDE inverse problems makes them highly sensitive to noise. Even a small fraction of corrupted observations can distort internal neural representations, severely impairing accuracy and destabilizing training. Motivated by recent advances in machine unlearning and structured network pruning, we propose P-PINN, a selective pruning framework designed to unlearn the influence of corrupted data in a pretrained PINN. Specifically, starting from a PINN trained on the full dataset, P-PINN evaluates a joint residual--data fidelity indicator, a weighted combination of data misfit and PDE residuals, to partition the training set into reliable and corrupted subsets. Next, we introduce a bias-based neuron importance measure that quantifies directional activation discrepancies between the two subsets, identifying neurons whose representations are predominantly driven by corrupted samples. Building on this, an iterative pruning strategy then removes noise-sensitive neurons layer by layer. The resulting pruned network is fine-tuned on the reliable data subject to the original PDE constraints, acting as a lightweight post-processing stage rather than a complete retraining. Numerical experiments on extensive PDE inverse-problem benchmarks demonstrate that P-PINN substantially improves robustness, accuracy, and training stability under noisy conditions, achieving up to a 96.6\% reduction in relative error compared with baseline PINNs. These results indicate that activation-level post hoc pruning is a promising mechanism for enhancing the reliability of physics-informed learning in noise-contaminated settings.

Related papers

• On the Role of Consistency Between Physics and Data in Physics-Informed Neural Networks [2.9455202926636175]
  Physics-informed neural networks (PINNs) have gained significant attention as a surrogate modeling strategy for partial differential equations (PDEs)<n>PINNs are frequently trained using experimental or numerical data that are not fully consistent with the governing equations due to measurement noise, discretization errors, or modeling assumptions.<n>We analyze how data inconsistency limits the attainable accuracy of PINNs.
  arXiv  Detail & Related papers  (2026-02-11T08:00:53Z)
• naPINN: Noise-Adaptive Physics-Informed Neural Networks for Recovering Physics from Corrupted Measurement [3.450547277166974]
  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.
  arXiv  Detail & Related papers  (2026-01-30T06:03:33Z)
• Game-Theoretic Gradient Control for Robust Neural Network Training [0.0]
  Feed-forward neural networks (FFNNs) are vulnerable to input noise, reducing prediction performance.<n>This study aims to enhance FFNN noise robustness by modifying backpropagation, interpreted as a multi-agent game, and exploring controlled target variable noising.
  arXiv  Detail & Related papers  (2025-07-25T10:26:25Z)
• ProPINN: Demystifying Propagation Failures in Physics-Informed Neural Networks [71.02216400133858]
  Physics-informed neural networks (PINNs) have earned high expectations in solving partial differential equations (PDEs)<n>Previous research observed the propagation failure phenomenon of PINNs.<n>This paper provides a formal and in-depth study of propagation failure and its root cause.
  arXiv  Detail & Related papers  (2025-02-02T13:56:38Z)
• 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)
• Failure-informed adaptive sampling for PINNs [5.723850818203907]
  Physics-informed neural networks (PINNs) have emerged as an effective technique for solving PDEs in a wide range of domains. Recent research has demonstrated, however, that the performance of PINNs can vary dramatically with different sampling procedures. We present an adaptive approach termed failure-informed PINNs, which is inspired by the viewpoint of reliability analysis.
  arXiv  Detail & Related papers  (2022-10-01T13:34:41Z)
• Auto-PINN: Understanding and Optimizing Physics-Informed Neural Architecture [77.59766598165551]
  Physics-informed neural networks (PINNs) are revolutionizing science and engineering practice by bringing together the power of deep learning to bear on scientific computation. Here, we propose Auto-PINN, which employs Neural Architecture Search (NAS) techniques to PINN design. A comprehensive set of pre-experiments using standard PDE benchmarks allows us to probe the structure-performance relationship in PINNs.
  arXiv  Detail & Related papers  (2022-05-27T03:24:31Z)
• Physics-Informed Neural Operator for Learning Partial Differential Equations [55.406540167010014]
  PINO is the first hybrid approach incorporating data and PDE constraints at different resolutions to learn the operator. The resulting PINO model can accurately approximate the ground-truth solution operator for many popular PDE families.
  arXiv  Detail & Related papers  (2021-11-06T03:41:34Z)
• 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)
• Revisiting Initialization of Neural Networks [72.24615341588846]
  We propose a rigorous estimation of the global curvature of weights across layers by approximating and controlling the norm of their Hessian matrix. Our experiments on Word2Vec and the MNIST/CIFAR image classification tasks confirm that tracking the Hessian norm is a useful diagnostic tool.
  arXiv  Detail & Related papers  (2020-04-20T18:12:56Z)

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.