Estimating divergence‐free flows via neural networks

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

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. (2022, August). Estimating divergence‐free flows via neural networks. Presented at 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Virtual conference

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)
• Start Date: Aug 15, 2022
• End Date: Aug 19, 2022
• 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-VCH Verlag
• 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