Improved Uncertainty Quantification in Physics-Informed Neural Networks Using Error Bounds and Solution Bundles

Pablo Flores, Olga Graf, Pavlos Protopapas, Karim Pichara
5/9/2025
cs.LGcs.AIphysics.comp-ph

No official code found. Best implementation: ptflores1/improved-pinn-uq (3 stars, last commit 2025-07-28).

Abstract

Physics-Informed Neural Networks (PINNs) have been widely used to obtain solutions to various physical phenomena modeled as Differential Equations. As PINNs are not naturally equipped with mechanisms for Uncertainty Quantification, some work has been done to quantify the different uncertainties that arise when dealing with PINNs. In this paper, we use a two-step procedure to train Bayesian Neural Networks that provide uncertainties over the solutions to differential equation systems provided by PINNs. We use available error bounds over PINNs to formulate a heteroscedastic variance that improves the uncertainty estimation. Furthermore, we solve forward problems and utilize the obtained uncertainties when doing parameter estimation in inverse problems in cosmology.

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Code Implementations(1)

ptflores1/improved-pinn-uqCommunity100%

This repository contains the code for the paper "Improved Uncertainty Quantification in Physics-Informed Neural Networks Using Error Bounds and Solution Bundles".

30TeX, JinjaMay 27, 20251 years ago
bayesianpinnuaiuai2025uq

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Cite this paper

@article{flores2025improved,
  title  = {Improved Uncertainty Quantification in Physics-Informed Neural Networks Using Error Bounds and Solution Bundles},
  author = {Pablo Flores and Olga Graf and Pavlos Protopapas and Karim Pichara},
  year   = {2025},
  eprint = {2505.06459},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2505.06459v2}
}

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