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.
Original language | English (US) |
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Journal | PAMM: Proceedings in Applied Mathematics & Mechanics |
Volume | 21 |
Issue number | 1 |
DOIs | |
State | Published - Dec 14 2021 |