Curriculum Learning for Mesh-based simulations

2025-09-16

AI Summary

Training graph neural networks (GNNs) as surrogates for high-fidelity computational fluid dynamics (CFD) simulations on high-resolution unstructured meshes (hundreds of thousands of nodes) incurs prohibitive computational cost and often suffers from training stagnation. Method: We propose a “coarse-to-fine” curriculum learning strategy that progressively increases input mesh resolution and data fidelity—without altering the GNN architecture—to systematically control training difficulty. Contribution/Results: This approach significantly accelerates convergence and overcomes training bottlenecks even with low-capacity GNNs. Experiments demonstrate a 50% reduction in total training time while maintaining comparable generalization accuracy across diverse flow regimes. Moreover, it enhances both training efficiency and stability on complex, multi-scale unstructured flow datasets. To our knowledge, this is the first systematic application of curriculum learning to GNN training for unstructured-mesh physics-based simulation, establishing a new paradigm for efficient and scalable scientific machine learning.

Technology Category

• Machine Learning: Structured Learning
• Natural Language Processing: Learning & Optimization for NLP
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Graph neural networks (GNNs) have emerged as powerful surrogates for mesh-based computational fluid dynamics (CFD), but training them on high-resolution unstructured meshes with hundreds of thousands of nodes remains prohibitively expensive. We study a emph{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 imes10^5) 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.

Problem

• Accelerating GNN training for high-resolution CFD simulations
• Reducing computational cost of mesh-based surrogate models
• Overcoming learning plateaus in physics simulation tasks

Innovation

• Coarse-to-fine curriculum learning approach
• Training on progressively refined mesh resolutions
• Unchanged GNN architecture with varying data fidelity