用粗到细的训练策略，让神经网络更快学会流体模拟。
Curriculum Learning for Mesh-based simulations
- 先用低分辨率网格训练，逐步增加精度
- 相同精度下训练时间减少50%，效果相当
- 帮助模型突破学习瓶颈，适合物理仿真任务
图神经网络（GNN）已成为网格化计算流体动力学（CFD）的强大替代模型，但在包含数十万节点的高分辨率非结构化网格上训练仍极其耗时。本文研究了一种从粗到精的课程学习策略：先在极低分辨率网格上训练，再逐步引入中等和高分辨率数据（最高达3×10⁵个节点）。与多尺度架构不同，模型本身保持不变，仅训练数据的保真度随时间变化。实验表明，在达到相近泛化精度的前提下，总壁钟时间最多减少50%。此外，当模型能力不足时，课程学习仍能帮助其突破学习平台。
原文摘要 · Abstract (English)
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 \(3\times10^5\) 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.
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