Numerical Solution of the Incompressible Navier-Stokes Equation by a Deep Branching Algorithm
DOI10.4208/cicp.oa-2022-0140arXiv2212.13010OpenAlexW4386428591MaRDI QIDQ6049610
Nicolas Privault, Jiang Yu Nguwi, Guillaume Penent
Publication date: 15 September 2023
Published in: Communications in Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2212.13010
Navier-Stokes equationsMonte Carlo methodbranching processfully nonlinear PDEsrandom treedeep neural networksystems of PDEs
Monte Carlo methods (65C05) Navier-Stokes equations for incompressible viscous fluids (76D05) Stochastic analysis applied to problems in fluid mechanics (76M35) Applications of branching processes (60J85) Applications of stochastic analysis (to PDEs, etc.) (60H30) Navier-Stokes equations (35Q30) Numerical analysis (65-XX)
Related Items (1)
Cites Work
- Unnamed Item
- Unnamed Item
- A splitting method for fully nonlinear degenerate parabolic PDEs
- Wellposedness of second order backward SDEs
- A probabilistic numerical method for fully nonlinear parabolic PDEs
- Navier-Stokes equations and forward-backward SDEs on the group of diffeomorphisms of a torus
- Stochastic cascades and 3-dimensional Navier-Stokes equations
- Branching diffusion representation of semilinear PDEs and Monte Carlo approximation
- DGM: a deep learning algorithm for solving partial differential equations
- Numerical evaluation of ODE solutions by Monte Carlo enumeration of Butcher series
- A forward-backward probabilistic algorithm for the incompressible Navier-Stokes equations
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- A monotone scheme for high-dimensional fully nonlinear PDEs
- Forward-backward stochastic differential systems associated to Navier-Stokes equations in the whole space
- Navier-Stokes equation and diffusions on the group of homeomorphisms of the torus
- Branching Markov processes. I
- The deep learning Galerkin method for the general Stokes equations
- A fully nonlinear Feynman-Kac formula with derivatives of arbitrary orders
- Vorticity and Incompressible Flow
- Generalized solutions of the Cauchy problem for the Navier-Stokes system and diffusion processes
- Second-order backward stochastic differential equations and fully nonlinear parabolic PDEs
- Application of brownian motion to the equation of kolmogorov-petrovskii-piskunov
- A Multivariate Faa di Bruno Formula with Applications
- Solving high-dimensional partial differential equations using deep learning
- An Approximation Scheme for Semilinear Parabolic PDEs with Convex and Coercive Hamiltonians
- FVCA8 Benchmark for the Stokes and Navier–Stokes Equations with the TrioCFD Code—Benchmark Session
- Branching Diffusion Processes
This page was built for publication: Numerical Solution of the Incompressible Navier-Stokes Equation by a Deep Branching Algorithm
