Sahin, Tarik and von Danwitz, Max and Popp, Alexander (2024) Solving Forward and Inverse Problems of Contact Mechanics using Physics-Informed Neural Networks. Advanced Modeling and Simulation in Engineering Sciences, 11. Springer Nature. doi: 10.1186/s40323-024-00265-3. ISSN 2213-7467.
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Official URL: https://amses-journal.springeropen.com/articles/10.1186/s40323-024-00265-3
Abstract
This paper explores the ability of physics-informed neural networks (PINNs) to solve forward and inverse problems of contact mechanics for small deformation elasticity. We deploy PINNs in a mixed-variable formulation enhanced by output transformation to enforce Dirichlet and Neumann boundary conditions as hard constraints. Inequality constraints of contact problems, namely Karush-Kuhn-Tucker (KKT) type conditions, are enforced as soft constraints by incorporating them into the loss function during network training. To formulate the loss function contribution of KKT constraints, existing approaches applied to elastoplasticity problems are investigated and we explore a nonlinear complementarity problem (NCP) function, namely Fischer-Burmeister, which possesses advantageous characteristics in terms of optimization. Based on the Hertzian contact problem, we show that PINNs can serve as pure partial differential equation (PDE) solver, as data-enhanced forward model, as inverse solver for parameter identification, and as fast-to-evaluate surrogate model. Furthermore, we demonstrate the importance of choosing proper hyperparameters, e.g. loss weights, and a combination of Adam and L-BFGS-B optimizers aiming for better results in terms of accuracy and training time.
Item URL in elib: | https://elib.dlr.de/203753/ | ||||||||||||||||
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Document Type: | Article | ||||||||||||||||
Title: | Solving Forward and Inverse Problems of Contact Mechanics using Physics-Informed Neural Networks | ||||||||||||||||
Authors: |
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Date: | 3 May 2024 | ||||||||||||||||
Journal or Publication Title: | Advanced Modeling and Simulation in Engineering Sciences | ||||||||||||||||
Refereed publication: | Yes | ||||||||||||||||
Open Access: | Yes | ||||||||||||||||
Gold Open Access: | Yes | ||||||||||||||||
In SCOPUS: | Yes | ||||||||||||||||
In ISI Web of Science: | Yes | ||||||||||||||||
Volume: | 11 | ||||||||||||||||
DOI: | 10.1186/s40323-024-00265-3 | ||||||||||||||||
Editors: |
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Publisher: | Springer Nature | ||||||||||||||||
Series Name: | Advances in Machine Learning and Computational Mechanics | ||||||||||||||||
ISSN: | 2213-7467 | ||||||||||||||||
Status: | Published | ||||||||||||||||
Keywords: | Physics-informed neural networks, Mixed-variable formulation, Contact mechanics, Enforcing inequalities, Fischer-Burmeister NCP-function | ||||||||||||||||
HGF - Research field: | other | ||||||||||||||||
HGF - Program: | other | ||||||||||||||||
HGF - Program Themes: | other | ||||||||||||||||
DLR - Research area: | no assignment | ||||||||||||||||
DLR - Program: | no assignment | ||||||||||||||||
DLR - Research theme (Project): | no assignment | ||||||||||||||||
Location: | Rhein-Sieg-Kreis | ||||||||||||||||
Institutes and Institutions: | Institute for the Protection of Terrestrial Infrastructures > Simulation Methods for Digital Twins Institute for the Protection of Terrestrial Infrastructures | ||||||||||||||||
Deposited By: | von Danwitz, Max | ||||||||||||||||
Deposited On: | 17 Apr 2024 16:22 | ||||||||||||||||
Last Modified: | 03 May 2024 15:22 |
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