Neural Networks-based Random Vortex Methods for Modelling Incompressible Flows
<|reference_start|>Neural Networks-based Random Vortex Methods for Modelling Incompressible Flows: 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.<|reference_end|>
@article{cherepanov2024neural,
    title={Neural Networks-based Random Vortex Methods for Modelling Incompressible
  Flows},
    author={Vladislav Cherepanov and Sebastian W. Ertel},
    journal={arXiv preprint arXiv:2405.13691},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.13691},
    primaryClass={physics.flu-dyn cs.NA math.NA math.PR stat.ML}
}