Learning and correcting non-Gaussian model errors

TL;DR

This paper introduces a neural network method to accurately approximate and correct non-Gaussian, nonlinear modeling errors in numerical models, enhancing prediction and inverse problem solutions across various physical systems.

Contribution

It presents a novel neural network approach specifically designed to address complex non-Gaussian model errors in augmented direct and inverse problems.

Findings

Effective correction of non-Gaussian errors demonstrated on simulated data

Improved model confidence and quantitative results shown with experimental data

Method applicable to diverse physical systems and inverse problems

Abstract

All discretized numerical models contain modelling errors - this reality is amplified when reduced-order models are used. The ability to accurately approximate modelling errors informs statistics on model confidence and improves quantitative results from frameworks using numerical models in prediction, tomography, and signal processing. Further to this, the compensation of highly nonlinear and non-Gaussian modelling errors, arising in many ill-conditioned systems aiming to capture complex physics, is a historically difficult task. In this work, we address this challenge by proposing a neural network approach capable of accurately approximating and compensating for such modelling errors in augmented direct and inverse problems. The viability of the approach is demonstrated using simulated and experimental data arising from differing physical direct and inverse problems.