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

TL;DR

This paper explores the use of diffusion models for airfoil design, comparing different data encodings, and demonstrates their potential in practical engineering applications including multi-target optimization and extrapolation beyond training data.

Contribution

It systematically compares diffusion model performance on various airfoil data formats and introduces a multi-target optimization approach leveraging the stochastic nature of diffusion models.

Findings

Coordinates-based diffusion models outperform other data formats.

Latent space training reduces design flexibility and effectiveness.

Diffusion models can be used for multi-target optimization and extrapolation tasks.

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.