Diffusion Model Driven Airfoil Design: From Geometry Encoding to Practical Applications

TL;DR

This work systematically compares three geometry encodings—PCA latent weights, ordered coordinate contours, and 2D signed distance functions (SDF)—for diffusion-model-based inverse airfoil design under broad flow conditions ($AOA$, $Re$, $Ma$). Using the elucidating diffusion model backbone with a shared U-Net, the coordinate-based representation consistently delivers the best accuracy, robustness, and extrapolation ability, while PCA tradeoffs design freedom and SDF suffers from data density and resolution limits yet remains a promising path toward 3D diffusion. The study demonstrates both single-target and multi-target design workflows, leveraging the stochastic nature of diffusion to generate diverse feasible geometries that satisfy aerodynamic targets, and shows practical deployment considerations including XFOIL validation and design-trial budgets. Collectively, the results establish a principled, generalizable framework for diffusion-based airfoil inverse design and provide a concrete path toward extension to 3D geometries and more complex engineering constraints. The approach potentially accelerates design cycles by enabling rapid generation of constraint-satisfying candidates across wide operating envelopes.

Abstract

Diffusion model, the state-of-the-art generative machine learning architecture, has shown promising results airfoil inverse designs. In this study, we implemented and trained a series of diffusion models on three different airfoil geometry data encoding formats -- principal component weights, ordered $x$-$y$ coordinates, and 2D signed distance functions (SDF) -- to generate 2D airfoils. By systematically comparing the performance of diffusion models trained on different data structures, it is found that for 2D airfoil design problems, the diffusion model performs the best when directly trained with coordinates. Training with latent space (PCA weights in this study) limits the model's design freedom, and decreases the training effectiveness. Although the 2D SDF data appears to result in the least performing model, it proves its feasibility in aerodynamic shape generation, paving the way towards 3D problems where SDF is more favored. This study also investigated deploying the diffusion model in practical engineering applications. A multi-target optimization procedure is proposed based on the stochastic nature of the diffusion process, which drastically simplifies the procedure compared to conventional methods. The extrapolation performance of the model is also investigated by tasking the model with both aerodynamic and flow condition labels that are extrapolated beyond the training set boundaries.

Figures (13)

• Figure 1: Workflow of Diffusion Model Training and Deployment
• Figure 2: The Diffusion Model Dataset Distribution
• Figure 3: Different data structures to encode the airfoil geometry.
• Figure 4: PCA Accuracy
• Figure 5: Neural Network Architecture: U-Net with ResNet blocks