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

TL;DR

This work tackles the asynchronous limitations of energy-based physics guidance in generative aerodynamic design by introducing Dflow-SUR, a differentiable, decoupled framework that optimizes the final physics objective via gradients backpropagated to the initial noise in a flow-matching CNF. By separating flow inference from physical loss optimization, Dflow-SUR eliminates gradient conflicts, reduces surrogate uncertainty, and enhances robustness to hyperparameters, achieving dramatic improvements in physical loss reduction and computational efficiency on 2D airfoil and 3D wing cases. The approach yields more aerodynamically coherent designs, with higher mean L/D and tighter performance distributions, validated against CFD surrogates and generation benchmarks. Overall, Dflow-SUR provides a scalable, high-fidelity front-end for physics-informed design exploration that complements, rather than replaces, high-fidelity CFD-based optimization.

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.

Figures (12)

• Figure 1: Four physical guidance generation strategies: a. conditional guidance during flow matching training; b and c represent energy-based approach with different $t_c$ setting; d is the newly developed Dflow-SUR. Strategies shown in b, c, and d involve physical guidance during flow matching inference.
• Figure 2: Asynchronous dynamics between flow-matching denoising and physical loss optimization. $\mathcal{L}_{\text{uncon}}$ denotes the final physical loss from unconditional generation, $\mathcal{L}_{\text{achieved}}$ represents the final physical loss under energy-based guidance, and $\mathcal{L}_{\text{desired}}$ indicates the target physical constraint imposed on the generative model.
• Figure 3: The mean loss curves fo energy-based approaches, when $t_c = 0.0, 0.2, 0.6, 0.8$, $T=1000$ (gray dashed lines represent pseudo‐loss curves).
• Figure 4: Performance comparison between the energy-based approach and Dflow‐SUR in three metrics.
• Figure 5: The gradient alignment score of energy-based approach when $t_c = 0.0$, $T=1000$.