DS-GPS : A Deep Statistical Graph Poisson Solver (for faster CFD simulations)
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Abstract (arXiv)
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.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 8 of its 23 references that are in the map. First posted on arXiv 21 Nov 2022.
Builds on
8 of 23 references.
References · 8
- 2020Learning Mesh-Based Simulation with Graph Networkscited by 868
- 2019Deep Equilibrium Modelscited by 615
- 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 473
- 2020Multiscale Deep Equilibrium Modelscited by 151
- 2018Latent-space Physics: Towards Learning the Temporal Evolution of Fluid Flowcited by 97
- 2021Simulating Continuum Mechanics with Multi-Scale Graph Neural Networkscited by 40
- 2019Poisson CNN: Convolutional neural networks for the solution of the Poisson equation on a Cartesian meshcited by 22
- 2021Performance and accuracy assessments of an incompressible fluid solver coupled with a deep Convolutional Neural Networkcited by 8
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Citing papers per year: 2023: 1; 2024: 1.
2 papers.