arXiv Machine Learning By Pochinapeddi Sai Bhargav, Nithin Somasekharan, Rohit Sunil Kanchi, Sicheng He, Shaowu Pan

How Does Distribution Shift Shape Pretraining Gains in Neural PDE Surrogates?

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The study investigates how distribution shift influences the benefits of pretraining neural PDE surrogates for computational fluid dynamics. Researchers pretrained a model on 254,909 RANS solutions from one airfoil family and fine‑tuned it on a new family under two target settings—identical Spalart‑Allmaras (SA) modeling and SA with added $e^N$ transition modeling—while keeping freestream ranges matched. Results show that at 1,000 fine‑tuning samples, the pretrained model matches a from‑scratch model trained on 3.25× more data for the same‑SA target and 2.58× more for the transition‑modeled target; by 5,000 samples the advantage reverses. Additionally, increasing the number of distinct airfoils in the fine‑tuning set reduces error for both targets, but the improvement is significant only for the same‑SA case.

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