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

TL;DR

The paper addresses the lack of open multi-fidelity aerodynamic datasets and empirical data-driven scaling guidelines for field surrogates. It delivers an open multi-fidelity dataset for a parametric double-delta wing family (272 geometries, $2448$ LF/HF flow snapshots) and performs an empirical scaling study of the MF-VortexNet GNN surrogate under a fixed computational budget. The results yield a strong power-law relation between test error and training data size, with $\epsilon' \propto D^{-0.6122}$, and estimate an approximately eight-sample-per-dimension optimal sampling density in a six-dimensional design space. These findings inform DOE planning, resource allocation between dataset generation and model training, and demonstrate the practical potential of physics-informed GNN surrogates for rapid preliminary design.

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.

Figures (9)

• Figure 1: Geometry definition and its design variables.
• Figure 2: Illustration of vehicle configurations sampled from the design space. Training samples from the Level 6 set are shown in blue, while samples from the holdout test set are shown in red.
• Figure 3: Design space coverage and design variable distributions of the dataset.
• Figure 4: Surface meshes of a representative geometry used for the mesh sizing study.
• Figure 5: Mesh sizing study: convergence of $C_D$ and $C_M$ with respect to mesh size.