A Multi-fidelity Double-Delta Wing Dataset and Empirical Scaling Laws for GNN-based Aerodynamic Field Surrogate

TL;DR

This paper introduces a multi-fidelity aerodynamic dataset for double-delta wings, analyzes how dataset size affects GNN surrogate accuracy, and derives empirical scaling laws to optimize data collection and model training.

Contribution

It provides an open-source multi-fidelity aerodynamic dataset and establishes empirical scaling laws linking dataset size to GNN surrogate performance.

Findings

Test error decreases with data size following a power-law with exponent -0.6122.

Optimal sampling density is about eight samples per dimension.

Larger models utilize data more efficiently, indicating a trade-off between data cost and training budget.

Abstract

Data-driven surrogate models are increasingly adopted to accelerate vehicle design. However, open-source multi-fidelity datasets and empirical guidelines linking dataset size to model performance remain limited. This study investigates the relationship between training data size and prediction accuracy for a graph neural network (GNN) based surrogate model for aerodynamic field prediction. We release an open-source, multi-fidelity aerodynamic dataset for double-delta wings, comprising 2448 flow snapshots across 272 geometries evaluated at angles of attack from 11 (degree) to 19 (degree) at Ma=0.3 using both Vortex Lattice Method (VLM) and Reynolds-Averaged Navier-Stokes (RANS) solvers. The geometries are generated using a nested Saltelli sampling scheme to support future dataset expansion and variance-based sensitivity analysis. Using this dataset, we conduct a preliminary empirical scaling study of the MF-VortexNet surrogate by constructing six training datasets with sizes ranging from 40 to 1280 snapshots and training models with 0.1 to 2.4 million parameters under a fixed training budget. We find that the test error decreases with data size with a power-law exponent of -0.6122, indicating efficient data utilization. Based on this scaling law, we estimate that the optimal sampling density is approximately eight samples per dimension in a d-dimensional design space. The results also suggest improved data utilization efficiency for larger surrogate models, implying a potential trade-off between dataset generation cost and model training budget.