mlsanityData to 14 Oct 2026

Physics-informed Neural Networks with Unknown Measurement Noise

arXiv 2211.15498 ↗First posted 28 Nov 2022stat.ML cs.LGcited by 7

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Abstract (arXiv)

Physics-informed neural networks (PINNs) constitute a flexible approach to both finding solutions and identifying parameters of partial differential equations. Most works on the topic assume noiseless data, or data contaminated with weak Gaussian noise. We show that the standard PINN framework breaks down in case of non-Gaussian noise. We give a way of resolving this fundamental issue and we propose to jointly train an energy-based model (EBM) to learn the correct noise distribution. We illustrate the improved performance of our approach using multiple examples.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 17 of its 41 references that are in the map. First posted on arXiv 28 Nov 2022.

Builds on

17 of 41 references.

References · 17

  1. 2018Neural Ordinary Differential Equationscited by 3,779
  2. 2021Characterizing possible failure modes in physics-informed neural networkscited by 643
  3. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 608
  4. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 473
  5. 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 335
  6. 2022A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networkscited by 236
  7. 2020Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanismcited by 233
  8. 2020Probabilistic Regression for Visual Trackingcited by 231
  9. 2021Gradient-enhanced physics-informed neural networks for forward and inverse PDE problemscited by 222
  10. 2022Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisonscited by 170
  11. 2020Physics-informed learning of governing equations from scarce datacited by 167
  12. 2022Respecting causality is all you need for training physics-informed neural networkscited by 156
5 more
  1. 2020Bayesian Neural Networks: An Introduction and Surveycited by 131
  2. 2019On the Anatomy of MCMC-Based Maximum Likelihood Learning of Energy-Based Modelscited by 105
  3. 2021The Old and the New: Can Physics-Informed Deep-Learning Replace Traditional Linear Solvers?cited by 61
  4. 2020How to Train Your Energy-Based Model for Regressioncited by 23
  5. 2021Recipes for when Physics Fails: Recovering Robust Learning of Physics Informed Neural Networkscited by 18

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 2; 2025: 2; 2026: 2.

7 papers.

  1. 2025Repulsive Ensembles for Bayesian Inference in Physics-informed Neural Networkscited by 1
  2. 2026naPINN: Noise-Adaptive Physics-Informed Neural Networks for Recovering Physics from Corrupted Measurementcited by 1
  3. 2023Deep Learning based Spatially Dependent Acoustical Properties Recoverycited by 0
  4. 2024Dynamics-Encoded Deep Learning for Robust System Identification and Parameter Estimationcited by 0
  5. 2024PINNing Cerebral Blood Flow: Analysis of Perfusion MRI in Infants using Physics-Informed Neural Networkscited by 0
  6. 2025Physics-guided denoiser network for enhanced additive manufacturing data qualitycited by 0
  7. 2026Impact of Multiple Non-Invasive Biosignals on Cardiovascular Biomarker Estimation via Simulation-Based Inferencecited by 0