Recent Advances in Graph-based Neural PDE Solvers
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Interest in learned simulators has increased in recent years due to their fast inference times. Among these approaches, message-passing Graph Neural Networks have gained particular popularity because of their strong formal resemblance to mesh-based methods (finite elements, finite volumes, and finite differences) and their ability to generalize to previously unseen meshes. However, these models suffer from a fundamental limitation: poor scalability. Their memory consumption is generally high, making state-of-the-art meshes increasingly difficult to handle. In this work, we investigate alternatives to classical MeshGraphNet architectures and propose promising solutions to the aforementioned limitations.
