Dmitry I. Kabanov
Estimating divergence‐free flows via neural networks
Kabanov, Dmitry I.; Espath, Luis; Kiessling, Jonas; Tempone, Raul F.
Authors
Abstract
We apply neural networks to the problem of estimating divergence-free velocity flows from given sparse observations. Following the modern trend of combining data and models in physics-informed neural networks, we reconstruct the velocity flow by training a neural network in such a manner that the network not only matches the observations but also approximately satisfies the divergence-free condition. The assumption is that the balance between the two terms allows to obtain the model that has better prediction performance than a usual data-driven neural network. We apply this approach to the reconstruction of truly divergence-free flow from the noiseless synthetic data and to the reconstruction of wind velocity fields over Sweden.
Citation
Kabanov, D. I., Espath, L., Kiessling, J., & Tempone, R. F. (2021). Estimating divergence‐free flows via neural networks. PAMM, 21(1), Article e202100173. https://doi.org/10.1002/pamm.202100173
Journal Article Type | Conference Paper |
---|---|
Acceptance Date | Dec 14, 2021 |
Online Publication Date | Dec 14, 2021 |
Publication Date | 2021-12 |
Deposit Date | Dec 6, 2022 |
Publicly Available Date | Dec 8, 2022 |
Journal | PAMM |
Electronic ISSN | 1617-7061 |
Publisher | Wiley |
Peer Reviewed | Peer Reviewed |
Volume | 21 |
Issue | 1 |
Article Number | e202100173 |
DOI | https://doi.org/10.1002/pamm.202100173 |
Keywords | Electrical and Electronic Engineering; Atomic and Molecular Physics, and Optics |
Public URL | https://nottingham-repository.worktribe.com/output/7711301 |
Publisher URL | https://onlinelibrary.wiley.com/doi/10.1002/pamm.202100173 |
Files
Proc Appl Math Mech - 2021 - Kabanov - Estimating divergence‐free flows via neural networks
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Publisher Licence URL
https://creativecommons.org/licenses/by-nc-nd/4.0/
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