University of Oulu

Danny Smyl, Tyler N. Tallman, Jonathan A. Black, Andreas Hauptmann, Dong Liu, Learning and correcting non-Gaussian model errors, Journal of Computational Physics, Volume 432, 2021, 110152, ISSN 0021-9991,

Learning and correcting non-Gaussian model errors

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Author: Smyl, Danny1; Tallman, Tyler N.2; Black, Jonathan A.1;
Organizations: 1Department of Civil and Structural Engineering, University of Sheffield, UK
2School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN, USA
3Research Unit of Mathematical Sciences, University of Oulu, Finland
4Department of Computer Science, University College London, UK
5CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China (USTC), Hefei 230026, China
6Hefei National Laboratory for Physical Sciences at the Microscale, USTC, China
7Synergetic Innovation Center of Quantum Information and Quantum Physics, USTC, China
Format: article
Version: accepted version
Access: embargoed
Persistent link:
Language: English
Published: Elsevier, 2021
Publish Date: 2023-01-29


All discretized numerical models contain modeling errors — this reality is amplified when reduced-order models are used. The ability to accurately approximate modeling 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 modeling 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 modeling 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.

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Series: Journal of computational physics
ISSN: 0021-9991
ISSN-E: 1090-2716
ISSN-L: 0021-9991
Volume: 432
Article number: 110152
DOI: 10.1016/
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
113 Computer and information sciences
214 Mechanical engineering
218 Environmental engineering
Funding: DL was supported by National Natural Science Foundation of China (Grant No. 61871356). This work was partially supported by The Academy of Finland Project 336796 (Finnish Centre of Excellence in Inverse Modelling and Imaging, 2018–2025).
Academy of Finland Grant Number: 336796
Detailed Information: 336796 (Academy of Finland Funding decision)
Copyright information: © 2021 Elsevier Inc. This manuscript version is made available under the CC-BY-NC-ND 4.0 license