Estimating divergence-free flows via neural networks

Dmitry I. Kabanov, Luis Espath, Jonas Kiessling, Raul Tempone

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish (US)
JournalPAMM: Proceedings in Applied Mathematics & Mechanics
Issue number1
StatePublished - Dec 14 2021

Bibliographical note

KAUST Repository Item: Exported on 2022-01-18
Acknowledgements: The authors greatfully acknowledge research funding from the Alexander von Humboldt Foundation. Open access funding enabled and organized by Projekt DEAL.


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