# Curriculum Learning for Mesh-based simulations

arXiv: https://arxiv.org/abs/2509.13138 · HTML: https://mlsanity.com/paper/2509.13138/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 27 references that are in the map.
- First posted on arXiv 16 Sep 2025.

## Builds on (most cited first, 9 of 9)

- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [Efficient Learning of Mesh-Based Physical Simulation with BSMS-GNN](https://mlsanity.com/paper/2210.02573/) (2022)
- [Simulating Continuum Mechanics with Multi-Scale Graph Neural Networks](https://mlsanity.com/paper/2106.04900/) (2021)
- [Transfer Learning on Multi-Fidelity Data](https://mlsanity.com/paper/2105.00856/) (2021)
- [MG-GNN: Multigrid Graph Neural Networks for Learning Multilevel Domain Decomposition Methods](https://mlsanity.com/paper/2301.11378/) (2023)
- [Multi-Grid Graph Neural Networks with Self-Attention for Computational Mechanics](https://mlsanity.com/paper/2409.11899/) (2024)
- [MeshMask: Physics-Based Simulations with Masked Graph Neural Networks](https://mlsanity.com/paper/2501.08738/) (2025)

## Built on by (most cited first, 1 of 1)

- [Graph Deep Learning for Intracranial Aneurysm Blood Flow Simulation and Risk Assessment](https://mlsanity.com/paper/2512.09013/) (2025)

## Abstract (arXiv)

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 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.