Flow-Matching Framework for Two-Dimensional Airfoil Multipoint Inverse Design

Intelligent generative models have demonstrated remarkable potential in aircraft inverse design. However, current mainstream intelligent generative design approaches still face critical limitations that impede their transition to practical implementation. The first is the single-point constraint. Most prevailing approaches are confined to single-condition scenarios. However, practical aircraft design necessitates a holistic evaluation of performance under diverse flight regimes. The second is inflexible input. Directly applying existing methods to multipoint design lacks adaptability; specifically, the predefined set of design points cannot be dynamically adjusted. To bridge these gaps, this paper introduces a Transformer-based flow-matching model. By leveraging a rigorous mathematical framework and a multipoint sampling strategy, the proposed method effectively decomposes the complex multipoint design task into a series of well-defined single-point problems, which can then be efficiently addressed. Key features include i) multipoint flexibility and ii) data flexibility. Regarding multipoint flexibility, once trained, the model can take arbitrary combinations of target aerodynamic performance values across multiple working conditions as its input; regarding data flexibility, its training requires only single-point performance data, a minimal requirement that significantly lowers the barrier for practical application. Extensive quantitative results on multipoint airfoil design demonstrate a close alignment between the target aerodynamic performances and those achieved by the generated shapes across a range of test cases.