Learning signals defined on graphs with optimal transport and Gaussian process regression - Centre de mathématiques appliquées (CMAP)
Pré-Publication, Document De Travail Année : 2024

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

Résumé

In computational physics, machine learning has now emerged as a powerful complementary tool to explore efficiently candidate designs in engineering studies. Outputs in such supervised problems are signals defined on meshes, and a natural question is the extension of general scalar output regression models to such complex outputs. Changes between input geometries in terms of both size and adjacency structure in particular make this transition non-trivial. In this work, we propose an innovative strategy for Gaussian process regression where inputs are large and sparse graphs with continuous node attributes and outputs are signals defined on the nodes of the associated inputs. The methodology relies on the combination of regularized optimal transport, dimension reduction techniques, and the use of Gaussian processes indexed by graphs. In addition to enabling signal prediction, the main point of our proposal is to come with confidence intervals on node values, which is crucial for uncertainty quantification and active learning. Numerical experiments highlight the efficiency of the method to solve real problems in fluid dynamics and solid mechanics.
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Dates et versions

hal-04740924 , version 1 (18-10-2024)

Identifiants

  • HAL Id : hal-04740924 , version 1

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Raphaël Carpintero Perez, Sébastien da Veiga, Josselin Garnier, Brian Staber. Learning signals defined on graphs with optimal transport and Gaussian process regression. 2024. ⟨hal-04740924⟩
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