Estimating divergence‐free flows via neural networks

PAMM, vol. 21

Abstract

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.

Authors 4

1. Dmitry I. Kabanov corresponding Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University Pontdriesch 14–16 Aachen 52062 Germany

   Dmitry I. Kabanov

2. Luis Espath Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University Pontdriesch 14–16 Aachen 52062 Germany

3. Jonas Kiessling

   KTH Royal Institute of Technology

   Affiliation as printed

   KTH Royal Institute of Technology SE-100 44 Stockholm Sweden

   KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden

4. Raul F. Tempone Aachen

   King Abdullah University of Science and Technology · RWTH Aachen University

   Affiliation as printed

   King Abdullah University of Science and Technology Thuwal 23955-6900 Saudi Arabia

   RWTH Aachen University Pontdriesch 14–16 Aachen 52062 Germany

   King Abdullah University of Science and Technology, Thuwal, 23955-6900 Saudi Arabia