Adjoint-Based Aerodynamic Shape Optimization with a Manifold Constraint Learned by Diffusion Models

Fuente: arXiv
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Autori principali: Chen, Long, Oezkaya, Emre, Rottmayer, Jan, Gauger, Nicolas R., Shen, Zebang, Ye, Yinyu
Natura: Preprint
Pubblicazione: 2025
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author Chen, Long
Oezkaya, Emre
Rottmayer, Jan
Gauger, Nicolas R.
Shen, Zebang
Ye, Yinyu
author_facet Chen, Long
Oezkaya, Emre
Rottmayer, Jan
Gauger, Nicolas R.
Shen, Zebang
Ye, Yinyu
contents We introduce an adjoint-based aerodynamic shape optimization framework that integrates a diffusion model trained on existing designs to learn a smooth manifold of aerodynamically viable shapes. This manifold is enforced as an equality constraint to the shape optimization problem. Central to our method is the computation of adjoint gradients of the design objectives (e.g., drag and lift) with respect to the manifold space. These gradients are derived by first computing shape derivatives with respect to conventional shape design parameters (e.g., Hicks-Henne parameters) and then backpropagating them through the diffusion model to its latent space via automatic differentiation. Our framework preserves mathematical rigor and can be integrated into existing adjoint-based design workflows with minimal modification. Demonstrated on extensive transonic RANS airfoil design cases using off-the-shelf and general-purpose nonlinear optimizers, our approach eliminates ad hoc parameter tuning and variable scaling, maintains robustness across initialization and optimizer choices, and achieves superior aerodynamic performance compared to conventional approaches. This work establishes how AI generated priors integrates effectively with adjoint methods to enable robust, high-fidelity aerodynamic shape optimization through automatic differentiation.
format Preprint
id arxiv_https___arxiv_org_abs_2507_23443
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Adjoint-Based Aerodynamic Shape Optimization with a Manifold Constraint Learned by Diffusion Models
Chen, Long
Oezkaya, Emre
Rottmayer, Jan
Gauger, Nicolas R.
Shen, Zebang
Ye, Yinyu
Computational Engineering, Finance, and Science
Machine Learning
Optimization and Control
We introduce an adjoint-based aerodynamic shape optimization framework that integrates a diffusion model trained on existing designs to learn a smooth manifold of aerodynamically viable shapes. This manifold is enforced as an equality constraint to the shape optimization problem. Central to our method is the computation of adjoint gradients of the design objectives (e.g., drag and lift) with respect to the manifold space. These gradients are derived by first computing shape derivatives with respect to conventional shape design parameters (e.g., Hicks-Henne parameters) and then backpropagating them through the diffusion model to its latent space via automatic differentiation. Our framework preserves mathematical rigor and can be integrated into existing adjoint-based design workflows with minimal modification. Demonstrated on extensive transonic RANS airfoil design cases using off-the-shelf and general-purpose nonlinear optimizers, our approach eliminates ad hoc parameter tuning and variable scaling, maintains robustness across initialization and optimizer choices, and achieves superior aerodynamic performance compared to conventional approaches. This work establishes how AI generated priors integrates effectively with adjoint methods to enable robust, high-fidelity aerodynamic shape optimization through automatic differentiation.
title Adjoint-Based Aerodynamic Shape Optimization with a Manifold Constraint Learned by Diffusion Models
topic Computational Engineering, Finance, and Science
Machine Learning
Optimization and Control
url https://arxiv.org/abs/2507.23443