研究不同分布偏移对神经PDE代理模型预训练增益的影响
How Does Distribution Shift Shape Pretraining Gains in Neural PDE Surrogates?
这个研究很具体，不是泛泛而谈，而是用真实数据（254,909个样本）和具体模型（RANS解）测试了预训练在神经PDE代理模型中的价值，对做相关研究的人应该有用。
研究团队在254,909个RANS解上预训练一个代理模型，然后在新机翼家族上微调。当目标设置相同（Spalart-Allmaras）时，在N=1000样本下，预训练模型精度与从零开始训练的模型相比，相当于使用了3.25倍的数据量。但当目标设置变为包含e^N过渡建模时，这个倍数下降到2.58倍。随着样本量增加到N=5000，这种关系逆转，预训练优势在过渡建模目标上更大（1.86倍 vs 1.56倍）。研究还发现，采样更多不同机翼形状能降低误差，但对相同SA目标的影响更大（3.3倍到4.0倍）。
How Does Distribution Shift Shape Pretraining Gains in Neural PDE Surrogates?
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.
