Gaussian process regression with Sliced Wasserstein Weisfeiler-Lehman graph kernels

Raphaël Carpintero Perez, Sébastien Da Veiga, Josselin Garnier, Brian Staber
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:1297-1305, 2024.

Abstract

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.

Cite this Paper


BibTeX
@InProceedings{pmlr-v238-carpintero-perez24a, title = { {G}aussian process regression with Sliced {W}asserstein {W}eisfeiler-{L}ehman graph kernels }, author = {Carpintero Perez, Rapha\"{e}l and Da Veiga, S\'{e}bastien and Garnier, Josselin and Staber, Brian}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {1297--1305}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/carpintero-perez24a/carpintero-perez24a.pdf}, url = {https://proceedings.mlr.press/v238/carpintero-perez24a.html}, abstract = { 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. } }
Endnote
%0 Conference Paper %T Gaussian process regression with Sliced Wasserstein Weisfeiler-Lehman graph kernels %A Raphaël Carpintero Perez %A Sébastien Da Veiga %A Josselin Garnier %A Brian Staber %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-carpintero-perez24a %I PMLR %P 1297--1305 %U https://proceedings.mlr.press/v238/carpintero-perez24a.html %V 238 %X 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.
APA
Carpintero Perez, R., Da Veiga, S., Garnier, J. & Staber, B.. (2024). Gaussian process regression with Sliced Wasserstein Weisfeiler-Lehman graph kernels . Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:1297-1305 Available from https://proceedings.mlr.press/v238/carpintero-perez24a.html.

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