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

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.