Learning and correcting non-Gaussian model errors

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.

References in corpus (5)

• Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations
• Solving ill-posed inverse problems using iterative deep neural networks
• Discovering physical concepts with neural networks
• Binary black hole merger dynamics and waveforms
• Convergence rates and structure of solutions of inverse problems with imperfect forward models

Cited by in corpus (4)

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