@Article{CiCP-34-2,
author = {Yu, Nguwi, Jiang and Penent, Guillaume and Privault, Nicolas},
title = {Numerical Solution of the Incompressible Navier-Stokes Equation by a Deep Branching Algorithm},
journal = {Communications in Computational Physics},
year = {2023},
volume = {34},
number = {2},
pages = {261--289},
abstract = {<p style="text-align: justify;">We present an algorithm for the numerical solution of systems of fully nonlinear PDEs using stochastic coded branching trees. This approach covers functional
nonlinearities involving gradient terms of arbitrary orders, and it requires only a boundary condition over space at a given terminal time $T$ instead of Dirichlet or Neumann
boundary conditions at all times as in standard solvers. Its implementation relies on
Monte Carlo estimation, and uses neural networks that perform a meshfree functional
estimation on a space-time domain. The algorithm is applied to the numerical solution of the Navier-Stokes equation and is benchmarked to other implementations in
the cases of the Taylor-Green vortex and Arnold-Beltrami-Childress flow.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2022-0140},
url = {https://global-sci.com/article/79367/numerical-solution-of-the-incompressible-navier-stokes-equation-by-a-deep-branching-algorithm}
}