TY - JOUR

T1 - Bayesian Inversion with Open-Source Codes for Various One-Dimensional Model Problems in Computational Mechanics

AU - Noii, Nima

AU - Khodadadian, Amirreza

AU - Ulloa, Jacinto

AU - Aldakheel, Fadi

AU - Wick, Thomas

AU - François, Stijn

AU - Wriggers, Peter

N1 - Funding Information: The corresponding author F. Aldakheel appreciates the scientific support of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) in the Priority Program SPP 2020 within its second funding phase. T. Wick and P. Wriggers were funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy within the Cluster of Excellence PhoenixD, EXC 2122 (project number: 390833453).

PY - 2022/10

Y1 - 2022/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85129484284&partnerID=8YFLogxK

U2 - 10.1007/s11831-022-09751-6

DO - 10.1007/s11831-022-09751-6

M3 - Article

AN - SCOPUS:85129484284

VL - 29

SP - 4285

EP - 4318

JO - Archives of Computational Methods in Engineering

JF - Archives of Computational Methods in Engineering

SN - 1134-3060

IS - 6

ER -