# Robustness of Physics-Informed Neural Networks to Noise in Sensor Data

arXiv: https://arxiv.org/abs/2211.12042 · HTML: https://mlsanity.com/paper/2211.12042/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 20 references that are in the map.
- First posted on arXiv 22 Nov 2022.

## Builds on (most cited first, 10 of 10)

- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data](https://mlsanity.com/paper/1901.06314/) (2019)
- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [Physics-informed learning of governing equations from scarce data](https://mlsanity.com/paper/2005.03448/) (2020)
- [CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Method](https://mlsanity.com/paper/2110.15832/) (2021)
- [Label-Free Supervision of Neural Networks with Physics and Domain Knowledge](https://mlsanity.com/paper/1609.05566/) (2016)
- [Learning in Sinusoidal Spaces with Physics-Informed Neural Networks](https://mlsanity.com/paper/2109.09338/) (2021)
- [Surrogate Modeling of Fluid Dynamics with a Multigrid Inspired Neural Network Architecture](https://mlsanity.com/paper/2105.03854/) (2021)
- [Physics-Driven Regularization of Deep Neural Networks for Enhanced Engineering Design and Analysis](https://mlsanity.com/paper/1810.05547/) (2018)
- [U-Net-Based Surrogate Model For Evaluation of Microfluidic Channels](https://mlsanity.com/paper/2105.05173/) (2021)

## Built on by (most cited first, 3 of 3)

- [Reliable and efficient inverse analysis using physics-informed neural networks with normalized distance functions and adaptive weight tuning](https://mlsanity.com/paper/2504.18091/) (2025)
- [PE-MHL: Physics-Encoded Modular Hybrid Layers for Scalable Learning of Complex Systems](https://mlsanity.com/paper/2606.04290/) (2026)
- [Overcoming the Limits of Finite Difference Method; Physics-Informed Neural Network for Noisy High-Dimensional Heat Diffusion](https://mlsanity.com/paper/2606.07982/) (2026)

## Abstract (arXiv)

Physics-Informed Neural Networks (PINNs) have been shown to be an effective way of incorporating physics-based domain knowledge into neural network models for many important real-world systems. They have been particularly effective as a means of inferring system information based on data, even in cases where data is scarce. Most of the current work however assumes the availability of high-quality data. In this work, we further conduct a preliminary investigation of the robustness of physics-informed neural networks to the magnitude of noise in the data. Interestingly, our experiments reveal that the inclusion of physics in the neural network is sufficient to negate the impact of noise in data originating from hypothetical low quality sensors with high signal-to-noise ratios of up to 1. The resultant predictions for this test case are seen to still match the predictive value obtained for equivalent data obtained from high-quality sensors with potentially 10x less noise. This further implies the utility of physics-informed neural network modeling for making sense of data from sensor networks in the future, especially with the advent of Industry 4.0 and the increasing trend towards ubiquitous deployment of low-cost sensors which are typically noisier.