Learning and correcting non-Gaussian model errors

JOURNAL OF COMPUTATIONAL PHYSICS

卷:432

Article

Smyl, Danny¹  Tallman, Tyler N.²  Black, Jonathan A.¹  Hauptmann, Andreas^3,4  Liu, Dong^5,6,7,8 

[1] Univ Sheffield, Dept Civil & Struct Engn, Sheffield, S Yorkshire, England

[2] Purdue Univ, Sch Aeronaut & Astronaut, W Lafayette, IN 47907 USA

[3] Univ Oulu, Res Unit Math Sci, Oulu, Finland

[4] UCL, Dept Comp Sci, London, England

[5] Univ Sci & Technol China USTC, CAS Key Lab Microscale Magnet Resonance, Hefei 230026, Peoples R China

[6] Univ Sci & Technol China USTC, Dept Modern Phys, Hefei 230026, Peoples R China

[7] USTC, Hefei Natl Lab Phys Sci Microscale, Hefei, Peoples R China

[8] USTC, Synerget Innovat Ctr Quantum Informat & Quantum P, Hefei, Peoples R China

关键词: Finite element method;    Inverse problems;    Model errors;    Neural networks;    Non-linearity;    Tomography;   

DOI  :  10.1016/j.jcp.2021.110152

来源: Elsevier

【 摘 要 】

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. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free