Physics-guided generative design with gradient-based source-space optimization on flow matching

Abstract Generative design can rapidly propose diverse, constraint-satisfying candidates for real-time analysis and closed-loop optimization under expensive physics evaluations. However, reliable generation requires effective incorporation of physical constraints by means of physics-guided generation. In many state-of-the-art physics-guided flow-based methods, physical optimization cannot fully converge within the generative time schedule, leading to limited constraint-satisfaction accuracy in the generated samples. We refer to this issue as the asynchronicity . This phenomenon arises when an energy-based objective is used as the physical loss in denoising generative paradigms, such as diffusion models and flow matching models. To address it, we propose Dflow-SUR , a new physics-guided flow matching framework that performs surrogate-based, gradient-driven optimization directly in the initial source space used to initialize the flow inference. Compared with existing physics-guided schemes, Dflow-SUR improves physical-loss minimization by four to six orders of magnitude, yielding samples that better satisfy physical constraints and, for 3D wing design, produce smoother spanwise pressure distributions. Moreover, Dflow-SUR reduces wall-clock time by 74% on a 2D airfoil case and improves the mean lift-to-drag ratio by 11.8% over Latin hypercube sampling on a 3D wing case. Overall, Dflow-SUR offers three practical advantages: superior guidance controllability, reduced sensitivity to surrogate uncertainty induced by noisy samples, and robustness to hyperparameter choices. The efficiency and robustness demonstrated by the results presented in this paper demonstrate that Dflow-SUR can enable accurate, efficient, and physically consistent generative design, which can effectively support design and analysis processes that require expeditious evaluations of a physical system, such as optimization and digital twins.