Improving pseudo-time stepping convergence for cfd simulations with neural networks
A Zandbergen, T van Noorden, A Heinlein - arXiv preprint arXiv …, 2023 - arxiv.org
Computational fluid dynamics (CFD) simulations of viscous fluids described by the Navier-
Stokes equations are considered. Depending on the Reynolds number of the flow, the …
Stokes equations are considered. Depending on the Reynolds number of the flow, the …
Convergence Framework of Deep Learning-based Hybrid Iterative Methods and the Application to Designing a Fourier Neural Solver for Parametric PDEs
C Cui, K Jiang, Y Liu, S Shu - arXiv preprint arXiv:2408.08540, 2024 - arxiv.org
Recently, deep learning-based hybrid iterative methods (DL-HIM) have emerged as a
promising approach for designing fast neural solvers to tackle large-scale sparse linear …
promising approach for designing fast neural solvers to tackle large-scale sparse linear …
Toward Improving Boussinesq Flow Simulations by Learning with Compressible Flow
N Mangnike, D Hyde - Proceedings of the Platform for Advanced …, 2024 - dl.acm.org
In computational fluid dynamics, the Boussinesq approximation is a popular model for the
numerical simulation of natural convection problems. Although using the Boussinesq …
numerical simulation of natural convection problems. Although using the Boussinesq …
A neural-preconditioned poisson solver for mixed Dirichlet and Neumann boundary conditions
We introduce a neural-preconditioned iterative solver for Poisson equations with mixed
boundary conditions. Typical Poisson discretizations yield large, ill-conditioned linear …
boundary conditions. Typical Poisson discretizations yield large, ill-conditioned linear …
A Neural Multigrid Solver for Helmholtz Equations with High Wavenumber and Heterogeneous Media
C Cui, K Jiang, S Shu - arXiv preprint arXiv:2404.02493, 2024 - arxiv.org
Solving high-wavenumber and heterogeneous Helmholtz equations presents a long-
standing challenge in scientific computing. In this paper, we introduce a deep learning …
standing challenge in scientific computing. In this paper, we introduce a deep learning …
Variational operator learning: A unified paradigm marrying training neural operators and solving partial differential equations
T Xu, D Liu, P Hao, B Wang - Journal of the Mechanics and Physics of …, 2024 - Elsevier
Neural operators as novel neural architectures for fast approximating solution operators of
partial differential equations (PDEs), have shown considerable promise for future scientific …
partial differential equations (PDEs), have shown considerable promise for future scientific …
Accelerating PDE Data Generation via Differential Operator Action in Solution Space
Recent advancements in data-driven approaches, such as Neural Operator (NO), have
demonstrated their effectiveness in reducing the solving time of Partial Differential Equations …
demonstrated their effectiveness in reducing the solving time of Partial Differential Equations …
Neural Krylov Iteration for Accelerating Linear System Solving
Solving large-scale sparse linear systems is essential in fields like mathematics, science,
and engineering. Traditional numerical solvers, mainly based on the Krylov subspace …
and engineering. Traditional numerical solvers, mainly based on the Krylov subspace …