U p -Net: a generic deep learning-based time stepper for parameterized spatio-temporal dynamics

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Merten Stender
  • Jakob Ohlsen
  • Hendrik Geisler
  • Amin Chabchoub
  • Norbert Hoffmann
  • Alexander Schlaefer

Research Organisations

External Research Organisations

  • Technische Universität Berlin
  • Hamburg University of Technology (TUHH)
  • Kyoto University
  • University of Sydney
  • Imperial College London
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Details

Original languageEnglish
Pages (from-to)1227–1249
Number of pages23
JournalComputational mechanics
Volume71
Issue number6
Early online date24 Mar 2023
Publication statusPublished - Jun 2023

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.

Keywords

    Machine learning, Partial differential equations, Representation learning, Sensor data fusion, Time integration, Wave propagation

ASJC Scopus subject areas

Cite this

U p -Net: a generic deep learning-based time stepper for parameterized spatio-temporal dynamics. / Stender, Merten; Ohlsen, Jakob; Geisler, Hendrik et al.
In: Computational mechanics, Vol. 71, No. 6, 06.2023, p. 1227–1249.

Research output: Contribution to journal › Article › Research › peer review

Stender M, Ohlsen J, Geisler H, Chabchoub A, Hoffmann N, Schlaefer A. U p -Net: a generic deep learning-based time stepper for parameterized spatio-temporal dynamics. Computational mechanics. 2023 Jun;71(6):1227–1249. Epub 2023 Mar 24. doi: 10.1007/s00466-023-02295-x
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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.",
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AU - Chabchoub, Amin

AU - Hoffmann, Norbert

AU - Schlaefer, Alexander

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