发表机构
Rensselaer Polytechnic Institute; University of Tennessee（伦斯勒理工学院; 田纳西大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究通过预训练神经PDE代理模型，发现预训练收益受目标数据量、覆盖范围及物理建模差异共同影响，且随数据量增加收益顺序反转。
AI 中文摘要
预训练神经PDE代理模型可以在几何或建模物理发生变化时减少所需的新CFD数据量。然而，分布偏移的不同组成部分如何影响这一收益仍不清楚。我们在一个翼型家族的254,909个RANS解上预训练代理模型，并在两个具有匹配自由流范围的目标设置下对新家族进行微调：相同的Spalart-Allmaras（SA）建模和SA加上$e^N$转捩建模。在$N=1000$时，对于相同SA目标，预训练模型达到了从零开始训练于$3.25\ imes$样本量的模型的准确度，但对于转捩建模目标则为$2.58\ imes$。到$N=5000$时，这一顺序反转（$1.56\ imes$对比$1.86\ imes$）。在$N=1000$时，采样更多不同的翼型降低了两个目标的误差，但只有对于相同SA目标，增益增加大于观察到的抽样间变异（$3.3\ imes$到$4.0\ imes$）。这些结果表明，预训练价值共同取决于目标数据预算、目标数据覆盖范围以及源和目标在建模物理上是否不同。
英文摘要
Pretraining a neural PDE surrogate can reduce the amount of new CFD data needed when geometry or modeled physics changes. However, it remains unclear how different components of distribution shift affect this benefit. We pretrain a surrogate on 254,909 RANS solutions from one airfoil family and fine-tune it on a new family under two target settings with matched freestream ranges: the same Spalart-Allmaras (SA) modeling and SA with added $e^N$ transition modeling. At $N=1000$, the pretrained model matches the accuracy of a model trained from scratch on $3.25\times$ as many samples for the same-SA target, but $2.58\times$ as many for the transition-modeled target. By $N=5000$, this ordering reverses ($1.56\times$ versus $1.86\times$). At $N=1000$, sampling more distinct airfoils lowers error on both targets, but only for the same-SA target is the gain increase larger than the observed draw-to-draw variation ($3.3\times$ to $4.0\times$). These results show that pretraining value depends jointly on target-data budget, target-data coverage, and whether source and target differ in modeled physics.
Comments15 pages, 5 figures. Representations for the Physical Sciences Workshop, NeurIPS 2026
