Towards Multi-Fidelity Scaling Laws of Neural Surrogates in CFD
This addresses the problem of high data generation costs in scientific machine learning, offering practical insights for compute-efficient dataset creation, though it is incremental as it reformulates existing scaling laws for a specific domain.
The paper investigates scaling laws for neural surrogates in computational fluid dynamics by analyzing the trade-off between simulation fidelity and computational cost, finding compute-performance scaling and budget-dependent optimal fidelity mixes in experiments.
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.