물리 제약을 고려한 고속 역설계 Dflow SUR의 차별화 전략
📝 Abstract
Generative inverse design requires the consideration of physical constraints in exploring new designs to make generation reliable and accurate. We observe that state-of-the-art energy-based approaches exhibit an asynchronous phenomenon in which optimization of the physical loss is throttled by flow matching inference. To address this issue, we introduce Dflow-SUR, a differentiation strategy that decouples physical loss optimization from flow matching inference. Dflow-SUR lowers the physical loss by four orders of magnitude compared with the strongest energy-based baseline while trimming wall-clock time by 74% on airfoil case and boosts the mean lift-to-drag ratio by 11.8% over traditional Latin-hypercube sampling on wing case. In addition to accuracy and speed, Dflow-SUR delivers three practical benefits: (i) superior guidance controllability, (ii) reduced surrogate uncertainty, and (iii) robustness to hyper-parameter tuning. Collectively, these results underscore Dflow-SUR’s promise as a scalable, high-fidelity framework for generative aerodynamic design.
💡 Analysis
Generative inverse design requires the consideration of physical constraints in exploring new designs to make generation reliable and accurate. We observe that state-of-the-art energy-based approaches exhibit an asynchronous phenomenon in which optimization of the physical loss is throttled by flow matching inference. To address this issue, we introduce Dflow-SUR, a differentiation strategy that decouples physical loss optimization from flow matching inference. Dflow-SUR lowers the physical loss by four orders of magnitude compared with the strongest energy-based baseline while trimming wall-clock time by 74% on airfoil case and boosts the mean lift-to-drag ratio by 11.8% over traditional Latin-hypercube sampling on wing case. In addition to accuracy and speed, Dflow-SUR delivers three practical benefits: (i) superior guidance controllability, (ii) reduced surrogate uncertainty, and (iii) robustness to hyper-parameter tuning. Collectively, these results underscore Dflow-SUR’s promise as a scalable, high-fidelity framework for generative aerodynamic design.
📄 Content
Generative aerodynamic inverse design is a data-driven approach that leverages generative models to propose highperformance designs. It has emerged as an alternative to traditional discriminative design, which performs an optimization to find a single optimal solution [1,2] and relies on a surrogate model for performance estimation. This requires a high-quality initial guess, such as conceptual design, which can be difficult to obtain. In contrast, generative design operates without such dependency and enables a broader exploration of the design space. It does so by learning the implicit distribution of valid aerodynamic shapes from existing data, enabling probabilistic sampling of feasible configurations. Some examples in deep generative models include variational autoencoders (VAEs) [3], generative adversarial networks (GANs) [4], and flow-based generative models, which rely on normalizing flows to define expressive probability distributions from which data are generated [5]. With the advancement of flow models for the latter category, such as diffusion models [6,7] and flow matching [8], the denoising paradigm has enabled more controllable and high-fidelity generative processes. Furthermore, physics-based guidance can be provided during shape generation. This steers the generative process towards generating geometrically valid and high-performance aerodynamic shapes. These may feature non-intuitive innovations beyond traditional parameter limits while still meeting performance goals.
Physics can be incorporated into generative models in two ways: via conditional training or through inference-time guidance, depending on when the physics guidance is introduced. Figure 1 shows four representative physical guidance strategies of generative design. Figure 1a combined with the flow matching loss during model training. This strategy has been adopted in previous studies [9,10].
The remaining strategies apply physical guidance during inference: the energy-based approach is shown in Figures 1b and1c (to be discussed in Section 3.2.1) and the proposed Dflow-SUR approach is illustrated in Figure 1d (to be detailed in Section 3.2.2).
In conditional training, the physical loss L phys is typically combined with the flow-matching loss into a single composite objective, serving as a conditional signal alongside the design x under which the neural network jointly learns the velocity field parameterization. In the context of aerodynamic inverse design, conditional training has been applied to solve multipoint [11] and multifidelity problems [10]. Lin et al. [11] implemented a classifier-free conditioning by randomly dropping and concatenating performance targets as inputs during diffusion training so the model learns to generate airfoil shapes both with and without explicit condition guidance, eliminating the need for separate classifier networks. Yang et al. [10] trained a conditional diffusion model by optimizing a score network on noisy shapes given performance targets and a value function network via contrastive learning of predicted target values to guide sampling toward the desired aerodynamic performance. However, this approach is fundamentally constrained by its training paradigm. First, it lacks flexibility, as any modification to design objectives or constraints necessitates retraining the model. Second, accurately modeling both the design space and the underlying physics jointly demands substantially more data, increasing the burden on data collection and model complexity. Third, the conditioning mechanism is limited to low-dimensional settings, where only a few scalar values can be used as auxiliary inputs to the network.
Currently, the prevailing consensus is to introduce physical guidance during the inference phase of flow model. In this framework, a pre-trained, unconditional flow model handles solely geometry sampling, whereas the physical constraint is incorporated at certain inference time. The physics loss is typically cast as an energy model [12], giving rise to the energy-based approach (Figures 1b and1c). In this approach, physical losses are formulated as an energy equation and its gradients are used to guide the flow model during inference. In the engineering design domain, energy-based generative models constitute a new trend, gaining attention for their ability to incorporate physical constraints into the generation process. Wu et al. [13] developed the Compositional Inverse Design with Diffusion Models (CinDM) method, which reframes inverse design as energy minimization via diffusion, compositing multiple diffusion-based energy functions over overlapping subsets of variables. The composite strategy ensures that designs remain in-distribution locally while generalizing to multi-body designs. In the context of topology optimization, TopoDiff [14] injects physical information during intermediate inference stages, leveraging low-uncertainty data for physical generation to help control sample qua
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