Curriculum learning for mesh-based simulations

Graph neural networks (GNNs) have emerged as powerful surrogates for mesh-based computational fluid dynamics, but training them on high-resolution unstructured meshes with hundreds of thousands of nodes remains prohibitively expensive. We study a coarse-to-fine curriculum that accelerates convergence by first training on very coarse meshes and then progressively introducing medium and high resolutions (up to 3×105 nodes). Unlike multiscale GNN architectures, the model itself is unchanged; only the fidelity of the training data varies over time. We achieve comparable generalization accuracy while reducing total wall-clock time by up to 50%. Furthermore, on datasets where our model lacks the capacity to learn the underlying physics, using curriculum learning enables it to break through plateaus.

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Publication Details

Journal
Physics of Fluids
Published
2026-02-01
DOI
https://doi.org/10.1063/5.0316165
Primary Topic
Model Reduction and Neural Networks
Type
article
Field-Weighted Citation Impact
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article

Curriculum learning for mesh-based simulations

Vincent Lannelongue, Paul Garnier, Elie HACHEM
Physics of Fluids
Model Reduction and Neural Networks
article

Curriculum learning for mesh-based simulations

Vincent Lannelongue, Paul Garnier, Elie HACHEM
article en

Abstract

Graph neural networks (GNNs) have emerged as powerful surrogates for mesh-based computational fluid dynamics, but training them on high-resolution unstructured meshes with hundreds of thousands of nodes remains prohibitively expensive. We study a coarse-to-fine curriculum that accelerates convergence by first training on very coarse meshes and then progressively introducing medium and high resolutions (up to 3×105 nodes). Unlike multiscale GNN architectures, the model itself is unchanged; only the fidelity of the training data varies over time. We achieve comparable generalization accuracy while reducing total wall-clock time by up to 50%. Furthermore, on datasets where our model lacks the capacity to learn the underlying physics, using curriculum learning enables it to break through plateaus.

Physics of FluidsVol. 38(2)
Centre National de la Recherche Scientifique (FR), Université Paris Sciences et Lettres (FR), Centre de Mise en Forme des Matériaux (FR)
Quality Education
Openalex Percentile: Top 54%
Model Reduction and Neural Networks
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