by Dmitry I. Kabanov, Luis Espath, Jonas Kiessling & Raul F. Tempone
This repo contains the paper based on the talk given at the 91st Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2021).
The paper is accepted for publication in the Proceedings in Applied Mathematics and Mechanics.
We apply neural networks to the problem of estimating divergence-free velocity flows from given sparse observations. Fol- lowing 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.
Comparison of prediction errors for two models. Left: without divergence-free regularization. Right: with divergence-free regularization.
To cite the article, please use the following BibTeX data:
@Article{KabanovEtAl2021a,
author = {Kabanov, Dmitry I. and Espath, Luis and Kiessling, Jonas and Tempone, Raul},
journal = {Proceedings in Applied Mathematics \& Mechanics},
title = {Estimating divergence-free flows via neural networks},
year = {2021},
doi = {10.1002/pamm.202100173},
}
The manuscript text is not open source. The authors reserve the rights to the article content. See LICENSE.