Heteroscedastic Uncertainty Quantification in Physics-Informed Neural Networks
Abstract
Physics-informed neural networks (PINNs) provide a machine learning framework to solve differential equations. However, PINNs do not inherently consider measurement noise or model uncertainty. In this paper, we propose the UQ-PINN which is an extension of the PINN with additional outputs to approximate the additive noise. The multi-output architecture enables approximation the mean and standard deviation over data using negative Gaussian log-likelihood loss. The performance of the UQ-PINN is demonstrated on the Poisson equation with additive noise.
Cite
Text
Claessen et al. "Heteroscedastic Uncertainty Quantification in Physics-Informed Neural Networks." ICLR 2024 Workshops: AI4DiffEqtnsInSci, 2024.Markdown
[Claessen et al. "Heteroscedastic Uncertainty Quantification in Physics-Informed Neural Networks." ICLR 2024 Workshops: AI4DiffEqtnsInSci, 2024.](https://mlanthology.org/iclrw/2024/claessen2024iclrw-heteroscedastic/)BibTeX
@inproceedings{claessen2024iclrw-heteroscedastic,
title = {{Heteroscedastic Uncertainty Quantification in Physics-Informed Neural Networks}},
author = {Claessen, Olivier and Shapovalova, Yuliya and Heskes, Tom},
booktitle = {ICLR 2024 Workshops: AI4DiffEqtnsInSci},
year = {2024},
url = {https://mlanthology.org/iclrw/2024/claessen2024iclrw-heteroscedastic/}
}