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.

通过结合经典数值解法和物理感知框架的方法，本研究在三维非规则几何体上测试了基于图神经网络的解决偏微分方程问题的可行性。