DeepAI AI Chat
Log In Sign Up

Learning and correcting non-Gaussian model errors

by   Danny Smyl, et al.

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.


page 11

page 13

page 18

page 20

page 21


Data-Driven Forward Discretizations for Bayesian Inversion

This paper suggests a framework for the learning of discretizations of e...

Accelerating PDE-constrained Inverse Solutions with Deep Learning and Reduced Order Models

Inverse problems are pervasive mathematical methods in inferring knowled...

An efficient Quasi-Newton method for nonlinear inverse problems via learned singular values

Solving complex optimization problems in engineering and the physical sc...

Physics-informed neural networks for inverse problems in supersonic flows

Accurate solutions to inverse supersonic compressible flow problems are ...

Inverse problems for semiconductors: models and methods

We consider the problem of identifying discontinuous doping profiles in ...

Optimal Experimental Design for Inverse Problems in the Presence of Observation Correlations

Optimal experimental design (OED) is the general formalism of sensor pla...