Towards Multi-Fidelity Scaling Laws of Neural Surrogates in CFD

TL;DR

This paper investigates how neural surrogate models for CFD scale with data and compute, revealing optimal fidelity trade-offs and providing empirical scaling laws for multi-fidelity datasets in scientific machine learning.

Contribution

It introduces the first empirical scaling laws for multi-fidelity neural surrogates in CFD, analyzing the trade-offs between fidelity, data, and compute.

Findings

Identify compute-performance scaling behavior.

Show budget-dependent optimal fidelity mixes.

Provide practical guidelines for efficient dataset generation.

Abstract

Scaling laws describe how model performance grows with data, parameters and compute. While large datasets can usually be collected at relatively low cost in domains such as language or vision, scientific machine learning is often limited by the high expense of generating training data through numerical simulations. However, by adjusting modeling assumptions and approximations, simulation fidelity can be traded for computational cost, an aspect absent in other domains. We investigate this trade-off between data fidelity and cost in neural surrogates using low- and high-fidelity Reynolds-Averaged Navier-Stokes (RANS) simulations. Reformulating classical scaling laws, we decompose the dataset axis into compute budget and dataset composition. Our experiments reveal compute-performance scaling behavior and exhibit budget-dependent optimal fidelity mixes for the given dataset configuration. These findings provide the first study of empirical scaling laws for multi-fidelity neural surrogate datasets and offer practical considerations for compute-efficient dataset generation in scientific machine learning.