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

verfasst von: 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.
Organisationseinheit(en): Institut für Kontinuumsmechanik
Institut für Angewandte Mathematik
PhoenixD: Simulation, Fabrikation und Anwendung optischer Systeme
Externe Organisation(en): KU Leuven
Swansea University
Universität Paris-Saclay
Typ: Artikel
Journal: Archives of Computational Methods in Engineering
Band: 29
Seiten: 4285-4318
Anzahl der Seiten: 34
ISSN: 1134-3060
Publikationsdatum: 10.2022
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Angewandte Informatik, Angewandte Mathematik
Elektronische Version(en): https://doi.org/10.1007/s11831-022-09751-6 (Zugang: Offen)
: Details im Forschungsportal „Research@Leibniz University“

BibTeX

@article{58d182a6e3c54d1ab1bbad82982dceee,
title = "Bayesian Inversion with Open-Source Codes for Various One-Dimensional Model Problems in Computational Mechanics",
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.",
author = "Nima Noii and Amirreza Khodadadian and Jacinto Ulloa and Fadi Aldakheel and Thomas Wick and Stijn Fran{\c c}ois and Peter Wriggers",
note = "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{\textquoteright}s Excellence Strategy within the Cluster of Excellence PhoenixD, EXC 2122 (project number: 390833453).",
year = "2022",
month = oct,
doi = "10.1007/s11831-022-09751-6",
language = "English",
volume = "29",
pages = "4285--4318",
journal = "Archives of Computational Methods in Engineering",
issn = "1134-3060",
publisher = "Springer Netherlands",
number = "6",
}