# Towards Multi-Fidelity Scaling Laws of Neural Surrogates in CFD

arXiv: https://arxiv.org/abs/2511.01830 · HTML: https://mlsanity.com/paper/2511.01830/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 46 references that are in the map.
- First posted on arXiv 3 Nov 2025.

## Builds on (most cited first, 23 of 23)

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Scaling Vision Transformers](https://mlsanity.com/paper/2106.04560/) (2021)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [ClimaX: A foundation model for weather and climate](https://mlsanity.com/paper/2301.10343/) (2023)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [Poseidon: Efficient Foundation Models for PDEs](https://mlsanity.com/paper/2405.19101/) (2024)
- [Towards Foundation Models for Scientific Machine Learning: Characterizing Scaling and Transfer Behavior](https://mlsanity.com/paper/2306.00258/) (2023)
- [Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport](https://mlsanity.com/paper/2204.06684/) (2022)
- [AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutions](https://mlsanity.com/paper/2212.07564/) (2022)
- [DrivAerNet++: A Large-Scale Multimodal Car Dataset with Computational Fluid Dynamics Simulations and Deep Learning Benchmarks](https://mlsanity.com/paper/2406.09624/) (2024)
- [Diffusion Models, Image Super-Resolution And Everything: A Survey](https://mlsanity.com/paper/2401.00736/) (2024)
- [Representation Equivalent Neural Operators: a Framework for Alias-free Operator Learning](https://mlsanity.com/paper/2305.19913/) (2023)
- [Boosting Latent Diffusion with Flow Matching](https://mlsanity.com/paper/2312.07360/) (2023)
- [DrivAerML: High-Fidelity Computational Fluid Dynamics Dataset for Road-Car External Aerodynamics](https://mlsanity.com/paper/2408.11969/) (2024)
- [Scaling Law for Time Series Forecasting](https://mlsanity.com/paper/2405.15124/) (2024)
- [Towards Neural Scaling Laws for Time Series Foundation Models](https://mlsanity.com/paper/2410.12360/) (2024)
- [On transfer learning of neural networks using bi-fidelity data for uncertainty propagation](https://mlsanity.com/paper/2002.04495/) (2020)
- [Transfer Learning on Multi-Fidelity Data](https://mlsanity.com/paper/2105.00856/) (2021)
- [GyroSwin: 5D Surrogates for Gyrokinetic Plasma Turbulence Simulations](https://mlsanity.com/paper/2510.07314/) (2025)
- [Computational Optimization, Modelling and Simulation: Recent Trends and Challenges](https://mlsanity.com/paper/1404.0708/) (2014)

## Abstract (arXiv)

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.