Download This PaperInterpolation Mesh-Graph Net Using Disconnected Spatial Graphs Of Higher Order Element Based Meshes
31 Pages Posted: 14 Nov 2024
Abstract
The problem of disconnectivity in graph neural networks poses a significant obstacle in the accurate modeling of physical systems. The conventional simulation techniques applied on complex problems often require higher order meshes with many nodes without direct edge connections that cannot be appropriately utilized in the state of the art mesh-graphs models. Existing literature has addressed the problem of isolated nodes in small to medium sized graphs to some extent, but a notable gap remains regarding higher order element based meshes in graph neural networks. This is a crucial issue, as the disconnectivity disrupts the information propagation and compromise the prediction quality, meanwhile the naive solutions are likely to fail on these challenging problems. To close this divide, we propose the Interpolation Mesh- Graph Network that uses higher order mesh based data, meanwhile it maintains the nodal resolution, extends the message passing distance and efficiently uses the computation resources, thereby offering a powerful solution to the disconnectivity challenge in the higher order mesh- graph based modeling of complex physical systems.
Keywords: Mesh-Graph Network, Disconnected spatial graph, Isolated nodes, Neural network, Higher order element
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