Neural Networks-based Random Vortex Methods for Modelling Incompressible Flows

• URL: http://arxiv.org/abs/2405.13691v1
• Date: Wed, 22 May 2024 14:36:23 GMT
• Title: Neural Networks-based Random Vortex Methods for Modelling Incompressible Flows
• Authors: Vladislav Cherepanov, Sebastian W. Ertel,
• Abstract summary: We introduce a novel Neural Networks-based approach for approximating solutions to the (2D) incompressible Navier--Stokes equations. Our algorithm uses a Physics-informed Neural Network, that approximates the vorticity based on a loss function that uses a computationally efficient formulation of the Random Vortex dynamics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper we introduce a novel Neural Networks-based approach for approximating solutions to the (2D) incompressible Navier--Stokes equations. Our algorithm uses a Physics-informed Neural Network, that approximates the vorticity based on a loss function that uses a computationally efficient formulation of the Random Vortex dynamics. The neural vorticity estimator is then combined with traditional numerical PDE-solvers for the Poisson equation to compute the velocity field. The main advantage of our method compared to standard Physics-informed Neural Networks is that it strictly enforces physical properties, such as incompressibility or boundary conditions, which might otherwise be hard to guarantee with purely Neural Networks-based approaches.

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