DS-GPS : A Deep Statistical Graph Poisson Solver (for faster CFD simulations)

11/21/2022

∙

This paper proposes a novel Machine Learning-based approach to solve a Poisson problem with mixed boundary conditions. Leveraging Graph Neural Networks, we develop a model able to process unstructured grids with the advantage of enforcing boundary conditions by design. By directly minimizing the residual of the Poisson equation, the model attempts to learn the physics of the problem without the need for exact solutions, in contrast to most previous data-driven processes where the distance with the available solutions is minimized.

READ FULL TEXT

DS-GPS : A Deep Statistical Graph Poisson Solver (for faster CFD simulations)

Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions

SailFFish: A Lightweight, Parallelised Fast Poisson Solver Library

A C^0 finite element algorithm for the sixth order problem with simply supported boundary conditions

Enforcing Dirichlet boundary conditions in physics-informed neural networks and variational physics-informed neural networks

Boundary Graph Neural Networks for 3D Simulations

Towards a Machine-Learned Poisson Solver for Low-Temperature Plasma Simulations in Complex Geometries

Poisson CNN: Convolutional Neural Networks for the Solution of the Poisson Equation with Varying Meshes and Dirichlet Boundary Conditions

DS-GPS : A Deep Statistical Graph Poisson Solver (for faster CFD simulations)

Related Research

Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions

SailFFish: A Lightweight, Parallelised Fast Poisson Solver Library

A C^0 finite element algorithm for the sixth order problem with simply supported boundary conditions

Enforcing Dirichlet boundary conditions in physics-informed neural networks and variational physics-informed neural networks

Boundary Graph Neural Networks for 3D Simulations

Towards a Machine-Learned Poisson Solver for Low-Temperature Plasma Simulations in Complex Geometries

Poisson CNN: Convolutional Neural Networks for the Solution of the Poisson Equation with Varying Meshes and Dirichlet Boundary Conditions