DS-GPS : A Deep Statistical Graph Poisson Solver (for faster CFD simulations)
Machine Learning
2022-11-23 v1 Artificial Intelligence
Numerical Analysis
Numerical Analysis
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.
Cite
@article{arxiv.2211.11763,
title = {DS-GPS : A Deep Statistical Graph Poisson Solver (for faster CFD simulations)},
author = {Matthieu Nastorg and Marc Schoenauer and Guillaume Charpiat and Thibault Faney and Jean-Marc Gratien and Michele-Alessandro Bucci},
journal= {arXiv preprint arXiv:2211.11763},
year = {2022}
}