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

Noii, Nima; Khodadadian, Amirreza; Ulloa, Jacinto; Aldakheel, Fadi; Wick, Thomas; François, Stijn; Wriggers, Peter

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.

Citation

Noii, N., Khodadadian, A., Ulloa, J., Aldakheel, F., Wick, T., François, S., & Wriggers, P. (2022). Bayesian Inversion with Open-Source Codes for Various One-Dimensional Model Problems in Computational Mechanics. Archives of Computational Methods in Engineering, 29(6), 4285-4318. https://doi.org/10.1007/s11831-022-09751-6

• Journal Article Type: Article
• Acceptance Date: Mar 21, 2022
• Online Publication Date: May 7, 2022
• Publication Date: 2022-10
• Deposit Date: Feb 25, 2025
• Journal: Archives of Computational Methods in Engineering
• Print ISSN: 1134-3060
• Electronic ISSN: 1886-1784
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 29
• Issue: 6
• Pages: 4285-4318
• DOI: https://doi.org/10.1007/s11831-022-09751-6
• Public URL: https://keele-repository.worktribe.com/output/1079463
• Publisher URL: https://link.springer.com/article/10.1007/s11831-022-09751-6
• Additional Information: Received: 10 November 2021; Accepted: 21 March 2022; First Online: 7 May 2022; : ; : The authors declare no conflict of interest.