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  4. Up-Net : a generic deep learning-based time stepper for parameterized spatio-temporal dynamics
 
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Up-Net : a generic deep learning-based time stepper for parameterized spatio-temporal dynamics

Citation Link: https://doi.org/10.15480/882.5173
Publikationstyp
Journal Article
Date Issued
2023-03-24
Sprache
English
Author(s)
Stender, Merten  orcid-logo
Ohlsen, Jakob  
Geisler, Hendrik  
Chabchoub, Amin  
Hoffmann, Norbert  orcid-logo
Schlaefer, Alexander  
Institut
Strukturdynamik M-14  
Medizintechnische und Intelligente Systeme E-1  
TORE-DOI
10.15480/882.5173
TORE-URI
http://hdl.handle.net/11420/15389
Journal
Computational Mechanics  
Volume
71
Issue
6
Start Page
1227
End Page
1249
Citation
Computational Mechanics 71 (6): 1227-1249 (2023)
Publisher DOI
10.1007/s00466-023-02295-x
Scopus ID
2-s2.0-85150650970
Publisher
Springer
In the age of big data availability, data-driven techniques have been proposed recently to compute the time evolution of spatio-temporal dynamics. Depending on the required a priori knowledge about the underlying processes, a spectrum of black-box end-to-end learning approaches, physics-informed neural networks, and data-informed discrepancy modeling approaches can be identified. In this work, we propose a purely data-driven approach that uses fully convolutional neural networks to learn spatio-temporal dynamics directly from parameterized datasets of linear spatio-temporal processes. The parameterization allows for data fusion of field quantities, domain shapes, and boundary conditions in the proposed Up-Net architecture. Multi-domain Up-Net models, therefore, can generalize to different scenes, initial conditions, domain shapes, and domain sizes without requiring re-training or physical priors. Numerical experiments conducted on a universal and two-dimensional wave equation and the transient heat equation for validation purposes show that the proposed Up-Net outperforms classical U-Net and conventional encoder–decoder architectures of the same complexity. Owing to the scene parameterization, the Up-Net models learn to predict refraction and reflections arising from domain inhomogeneities and boundaries. Generalization properties of the model outside the physical training parameter distributions and for unseen domain shapes are analyzed. The deep learning flow map models are employed for long-term predictions in a recursive time-stepping scheme, indicating the potential for data-driven forecasting tasks. This work is accompanied by an open-sourced code.
Subjects
Machine learning
Partial differential equations
Representation learning
Sensor data fusion
Time integration
Wave propagation
MLE@TUHH
DDC Class
004: Informatik
530: Physik
Funding(s)
I3 initiative (funding ID T-LP-E01- WTM-1801-02)  
Publication version
publishedVersion
Lizenz
https://creativecommons.org/licenses/by/4.0/
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