U p -Net
a generic deep learning-based time stepper for parameterized spatio-temporal dynamics
- verfasst von
- Merten Stender, Jakob Ohlsen, Hendrik Geisler, Amin Chabchoub, Norbert Hoffmann, Alexander Schlaefer
- Abstract
In the age of big data availability, data-driven techniques have been proposed recently to compute the time evolution of spatiotemporal 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 UpNet 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.
- Organisationseinheit(en)
-
Institut für Kontinuumsmechanik
- Externe Organisation(en)
-
Technische Universität Berlin
Technische Universität Hamburg (TUHH)
Kyoto University
Universität Sydney
Imperial College London
- Typ
- Artikel
- Journal
- Computational mechanics
- Band
- 71
- Seiten
- 1227–1249
- Anzahl der Seiten
- 23
- ISSN
- 0178-7675
- Publikationsdatum
- 06.2023
- Publikationsstatus
- Veröffentlicht
- Peer-reviewed
- Ja
- ASJC Scopus Sachgebiete
- Numerische Mechanik, Meerestechnik, Maschinenbau, Theoretische Informatik und Mathematik, Computational Mathematics, Angewandte Mathematik
- Elektronische Version(en)
-
https://doi.org/10.1007/s00466-023-02295-x (Zugang:
Offen)
