# Physics-informed Neural Networks with Unknown Measurement Noise

arXiv: https://arxiv.org/abs/2211.15498 · HTML: https://mlsanity.com/paper/2211.15498/

## 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 (most cited first, 17 of 17)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks](https://mlsanity.com/paper/2207.10289/) (2022)
- [Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism](https://mlsanity.com/paper/2009.04544/) (2020)
- [Probabilistic Regression for Visual Tracking](https://mlsanity.com/paper/2003.12565/) (2020)
- [Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems](https://mlsanity.com/paper/2111.02801/) (2021)
- [Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons](https://mlsanity.com/paper/2201.07766/) (2022)
- [Physics-informed learning of governing equations from scarce data](https://mlsanity.com/paper/2005.03448/) (2020)
- [Respecting causality is all you need for training physics-informed neural networks](https://mlsanity.com/paper/2203.07404/) (2022)
- [Bayesian Neural Networks: An Introduction and Survey](https://mlsanity.com/paper/2006.12024/) (2020)
- [On the Anatomy of MCMC-Based Maximum Likelihood Learning of Energy-Based Models](https://mlsanity.com/paper/1903.12370/) (2019)
- [The Old and the New: Can Physics-Informed Deep-Learning Replace Traditional Linear Solvers?](https://mlsanity.com/paper/2103.09655/) (2021)
- [How to Train Your Energy-Based Model for Regression](https://mlsanity.com/paper/2005.01698/) (2020)
- [Recipes for when Physics Fails: Recovering Robust Learning of Physics Informed Neural Networks](https://mlsanity.com/paper/2110.13330/) (2021)

## Built on by (most cited first, 7 of 7)

- [Repulsive Ensembles for Bayesian Inference in Physics-informed Neural Networks](https://mlsanity.com/paper/2505.17308/) (2025)
- [naPINN: Noise-Adaptive Physics-Informed Neural Networks for Recovering Physics from Corrupted Measurement](https://mlsanity.com/paper/2602.02547/) (2026)
- [Deep Learning based Spatially Dependent Acoustical Properties Recovery](https://mlsanity.com/paper/2310.10970/) (2023)
- [Dynamics-Encoded Deep Learning for Robust System Identification and Parameter Estimation](https://mlsanity.com/paper/2410.04299/) (2024)
- [PINNing Cerebral Blood Flow: Analysis of Perfusion MRI in Infants using Physics-Informed Neural Networks](https://mlsanity.com/paper/2410.19759/) (2024)
- [Physics-guided denoiser network for enhanced additive manufacturing data quality](https://mlsanity.com/paper/2508.02712/) (2025)
- [Impact of Multiple Non-Invasive Biosignals on Cardiovascular Biomarker Estimation via Simulation-Based Inference](https://mlsanity.com/paper/2609.11969/) (2026)

## 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.