TopoGeoNet: A Scalable Topological and Geometric Learning Framework for Spatial Graph

Zhishang Luo, Zhili Xiong, Samantha Chen, David Z. Pan, Yusu Wang

Keywords: Spatial Graph Learning, Graph Neural Networks, Geometric Deep Learning

TL;DR: TopoGeoNet is a hybrid GNN–U-Net architecture that jointly learns topology and geometry in spatial graphs, enabling state-of-the-art performance on million-node-level problems like chip congestion prediction and terrain shortest-path estimation.

Abstract:

Spatial graphs – graphs whose nodes are associated with geometric coordinates – arise in diverse domains including 3d point clouds, molecular structures, chip circuits and geospatial terrains. Different from generic graphs, learning on spatial graphs requires capturing both topological structure (graph connectivity) and the geometric context (spatial layout).
We propose TopoGeoNet, a scalable hybrid architecture that integrates graph neural networks (GNNs) for local message passing with a multi-scale convolutional U-Net over spatial grids. This heterogeneous design allows the model to jointly learn topological and geometric information while effectively capturing long-range interactions.
We apply TopoGeoNet to two challenging large-scale spatial graph problems, chip circuits congestion prediction and terrain shortest path distance prediction, using graph ranging from 62,500 to about one million nodes. We showed that TopoGeoNet achieves state-of-the-art accuracy on both tasks compared to various other architectures, demonstrating the power of unified geometric-topological learning in large-scale spatial graphs.

Submission Type: Extended abstract (max 4 main pages).

Software: https://github.com/luckyjackluo/TopoGeoNet

Submission Number: 41