Bayesian Inversion with Open-Source Codes for Various One-Dimensional Model Problems in Computational Mechanics

authored by
Nima Noii, Amirreza Khodadadian, Jacinto Ulloa, Fadi Aldakheel, Thomas Wick, Stijn François, Peter Wriggers
Abstract

The complexity of many problems in computational mechanics calls for reliable programming codes and accurate simulation systems. Typically, simulation responses strongly depend on material and model parameters, where one distinguishes between backward and forward models. Providing reliable information for the material/model parameters, enables us to calibrate the forward model (e.g., a system of PDEs). Markov chain Monte Carlo methods are efficient computational techniques to estimate the posterior density of the parameters. In the present study, we employ Bayesian inversion for several mechanical problems and study its applicability to enhance the model accuracy. Seven different boundary value problems in coupled multi-field (and multi-physics) systems are presented. To provide a comprehensive study, both rate-dependent and rate-independent equations are considered. Moreover, open source codes (https://doi.org/10.5281/zenodo.6451942) are provided, constituting a convenient platform for future developments for, e.g., multi-field coupled problems. The developed package is written in MATLAB and provides useful information about mechanical model problems and the backward Bayesian inversion setting.

Organisation(s)
Institute of Continuum Mechanics
Institute of Applied Mathematics
PhoenixD: Photonics, Optics, and Engineering - Innovation Across Disciplines
External Organisation(s)
KU Leuven
Swansea University
Université Paris-Saclay
Type
Article
Journal
Archives of Computational Methods in Engineering
Volume
29
Pages
4285-4318
No. of pages
34
ISSN
1134-3060
Publication date
10.2022
Publication status
Published
Peer reviewed
Yes
ASJC Scopus subject areas
Computer Science Applications, Applied Mathematics
Electronic version(s)
https://doi.org/10.1007/s11831-022-09751-6 (Access: Open)