Two-Step Bayesian PINNs for Uncertainty Estimation
Abstract
We use a two-step procedure to train Bayesian neural networks that provide uncertainties over the solutions to differential equation (DE) systems provided by Physics-Informed Neural Networks (PINNs). We take advantage of available error bounds over PINNs to formulate a heteroscedastic variance that improves the uncertainty estimation. Furthermore, we solve forward problems and utilize the uncertainties obtained to improve parameter estimation in inverse problems in the fields of cosmology and fermentation.
Cite
Text
Flores et al. "Two-Step Bayesian PINNs for Uncertainty Estimation." NeurIPS 2023 Workshops: DLDE, 2023.Markdown
[Flores et al. "Two-Step Bayesian PINNs for Uncertainty Estimation." NeurIPS 2023 Workshops: DLDE, 2023.](https://mlanthology.org/neuripsw/2023/flores2023neuripsw-twostep/)BibTeX
@inproceedings{flores2023neuripsw-twostep,
title = {{Two-Step Bayesian PINNs for Uncertainty Estimation}},
author = {Flores, Pablo and Graf, Olga and Protopapas, Pavlos and Pichara, Karim},
booktitle = {NeurIPS 2023 Workshops: DLDE},
year = {2023},
url = {https://mlanthology.org/neuripsw/2023/flores2023neuripsw-twostep/}
}