Dflow-SUR: Enhancing Generative Aerodynamic Inverse Design using Differentiation Throughout Flow Matching

2025/12/09 by Yang, Aobo, Wei, Zhen, Liem, Rhea +1
#Computational Engineering #FOS: Computer and information sciences #Finance #and Science (cs.CE)

paper · doi:10.48550/arxiv.2512.08336

Abstract

Generative inverse design requires incorporating physical constraints to ensure that generated designs are both reliable and accurate. However, we observe that current state-of-the-art energy-based methods suffer from an asynchronous phenomenon, where the optimization of the physical loss is constrained by the flow matching inference process. To overcome this limitation, we introduce Dflow-SUR, a differentiation strategy that separates the optimization of the physical loss from the flow matching inference. Compared to the most advanced energy-based baseline, Dflow-SUR achieves a reduction in physical loss by four orders of magnitude, while also cutting wall-clock time by 74% on the airfoil case. Additionally, it increases the mean lift-to-drag ratio by 11.8% over traditional Latin-hypercube sampling in wing design. Beyond improvements in accuracy and efficiency, Dflow-SUR offers three additional practical advantages: (i) enhanced control over guidance, (ii) lower surrogate uncertainty, and (iii) greater robustness to hyper-parameter tuning. Together, these results demonstrate that Dflow-SUR is a highly promising framework, providing both scalability and high fidelity for generative aerodynamic design.

Citations

• Rapid aerodynamic prediction of swept wings via physics-embedded transfer learning
• D-Flow: Differentiating through Flows for Controlled Generation
• Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generation
• Automatic Parameterization for Aerodynamic Shape Optimization via Deep Geometric Learning
• Contrastive Energy Prediction for Exact Energy-Guided Diffusion Sampling in Offline Reinforcement Learning
• Flow Matching for Generative Modeling
• Diffusion Models Beat GANs on Topology Optimization
• Score-Based Generative Modeling through Stochastic Differential Equations
• Airfoil Design Parameterization and Optimization using Bézier Generative Adversarial Networks
• Denoising Diffusion Probabilistic Models
• Geodesic Convolutional Shape Optimization
• Comparison of surrogate-based uncertainty quantification methods for computationally expensive simulators
• Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning

Related

• Generative Inverse Design: From Single Point Optimization to a Diverse Design Portfolio via Conditional Variational Autoencoders
• AFBench: A Large-scale Benchmark for Airfoil Design
• Parametric Generative Schemes with Geometric Constraints for Encoding and Synthesizing Airfoils
• AeroDiT: Diffusion Transformers for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows
• Compositional Generative Inverse Design