Gaussian process regression with Sliced Wasserstein Weisfeiler-Lehman graph kernels
This work addresses the challenge of handling large-scale graph data in computational physics, such as fluid dynamics and solid mechanics, with a novel kernel that improves efficiency, though it is incremental in the context of graph kernel methods.
The authors tackled the problem of supervised learning on large, sparse graphs with continuous node attributes in computational physics by introducing the Sliced Wasserstein Weisfeiler-Lehman (SWWL) graph kernel for Gaussian process regression, which achieved positive definiteness and drastic complexity reduction, enabling processing of datasets with tens of thousands of nodes previously impossible to handle.
Supervised learning has recently garnered significant attention in the field of computational physics due to its ability to effectively extract complex patterns for tasks like solving partial differential equations, or predicting material properties. Traditionally, such datasets consist of inputs given as meshes with a large number of nodes representing the problem geometry (seen as graphs), and corresponding outputs obtained with a numerical solver. This means the supervised learning model must be able to handle large and sparse graphs with continuous node attributes. In this work, we focus on Gaussian process regression, for which we introduce the Sliced Wasserstein Weisfeiler-Lehman (SWWL) graph kernel. In contrast to existing graph kernels, the proposed SWWL kernel enjoys positive definiteness and a drastic complexity reduction, which makes it possible to process datasets that were previously impossible to handle. The new kernel is first validated on graph classification for molecular datasets, where the input graphs have a few tens of nodes. The efficiency of the SWWL kernel is then illustrated on graph regression in computational fluid dynamics and solid mechanics, where the input graphs are made up of tens of thousands of nodes.