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

TL;DR

This paper introduces DS-GPS, a graph neural network-based solver for Poisson equations that accelerates CFD simulations by learning physics directly from residual minimization, handling unstructured grids and boundary conditions efficiently.

Contribution

The paper presents a novel ML approach using GNNs to solve Poisson problems with mixed boundary conditions, emphasizing physics-based learning without relying on exact solutions.

Findings

Effective processing of unstructured grids

Enforces boundary conditions by design

Reduces computational time for CFD simulations

Abstract

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.