U ^p -Net

a generic deep learning-based time stepper for parameterized spatio-temporal dynamics

authored by: 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.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Technische Universität Berlin
Hamburg University of Technology (TUHH)
Kyoto University
University of Sydney
Imperial College London
Type: Article
Journal: Computational mechanics
Volume: 71
Pages: 1227–1249
No. of pages: 23
ISSN: 0178-7675
Publication date: 06.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/s00466-023-02295-x (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{b78f93b6e75941caadc0b892452c54ce,
title = "U p -Net: a generic deep learning-based time stepper for parameterized spatio-temporal dynamics",
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",
author = "Merten Stender and Jakob Ohlsen and Hendrik Geisler and Amin Chabchoub and Norbert Hoffmann and Alexander Schlaefer",
note = "Funding Information: J. Ohlsen was supported by the Hamburg University of Technology initiative (funding ID T-LP-E01- WTM-1801-02).",
year = "2023",
month = jun,
doi = "10.1007/s00466-023-02295-x",
language = "English",
volume = "71",
pages = "1227–1249",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "6",
}

U p -Net

a generic deep learning-based time stepper for parameterized spatio-temporal dynamics

U ^p -Net