RBF-MGN:Solving spatiotemporal PDEs with Physics-informed Graph Neural Network

Zixue, Xiang,; Wei, Ping; Wen, Yuh‐Sheng

doi:10.48550/arxiv.2212.02861

Cited by 1 publication

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“…This issue prevents the use of the Physics-Informed framework for complex geometries, this is why there is a clear lack of work in this direction. There are ways to overcome this issue, for instance, [14] approximated the spatial derivatives with finite differences, allowing to tackle three dimensional problems. However, this approach does not generalize well for irregular problems, since it is known from classical numerical analysis that finite differences are not accurate enough.…”

Section: Building Pde Residuals On Complex Geometriesmentioning

confidence: 99%

Physics-Informed Graph Convolutional Networks: Towards a generalized framework for complex geometries

Chenaud,

Magoules,

Alves

Civil-Comp Conferences

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Since the seminal work of [9] and their Physics-Informed neural networks (PINNs), many efforts have been conducted towards solving partial differential equations (PDEs) with Deep Learning models. However, some challenges remain, for instance the extension of such models to complex three-dimensional geometries, and a study on how such approaches could be combined to classical numerical solvers. In this work, we justify the use of graph neural networks for these problems, based on the similarity between these architectures and the meshes used in traditional numerical techniques for solving partial differential equations. After proving an issue with the Physics-Informed framework for complex geometries, during the computation of PDE residuals, an alternative procedure is proposed, by combining classical numerical solvers and the Physics-Informed framework. Finally, we propose an implementation of this approach, that we test on a three-dimensional problem on an irregular geometry.

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Section: Building Pde Residuals On Complex Geometriesmentioning

confidence: 99%