Improved Uncertainty Quantification in Physics-Informed Neural Networks Using Error Bounds and Solution Bundles
By: Pablo Flores , Olga Graf , Pavlos Protopapas and more
Potential Business Impact:
Finds answers to science problems with confidence.
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.
Similar Papers
E-PINNs: Epistemic Physics-Informed Neural Networks
Machine Learning (CS)
Makes AI better at guessing how things work.
Examining the robustness of Physics-Informed Neural Networks to noise for Inverse Problems
Computational Physics
Helps computers solve hard science problems better.
Evidential Physics-Informed Neural Networks for Scientific Discovery
Machine Learning (CS)
Helps computers guess how things work, even when unsure.