  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.
