Learning signals defined on graphs with optimal transport and Gaussian process regression

Due to the associated computational cost, machine learning (ML) is a natural In computational physics, machine learning candidate to accelerate such design exploration: has now emerged as a powerful complementary starting from an initial database of FEM simulations, tool to explore efficiently candidate designs a supervised model is trained to predict the FEM outputs in engineering studies. Outputs in such from its inputs and is ultimately used as a proxy supervised problems are signals defined on to evaluate new geometries with a negligible cost. But meshes, and a natural question is the extension in this context, the supervised learning task actually of general scalar output regression involves inputs given as meshes, which can be modeled models to such complex outputs. Changes as graphs with continuous node attributes, different between input geometries in terms of both number of nodes and edges. In addition, the outputs size and adjacency structure in particular can be scalar values but also physical quantities of interest make this transition non-trivial. In this work, defined on each node of the input graph, which we propose an innovative strategy for Gaussian we refer to as signals defined on graphs or fields.