Flow Matching Improves Generative Topology Optimization

Topology optimization (TO) is crucial for engineering design but often involves costly iterative simulations. Generative TO offers a faster alternative, yet existing models can struggle with structural feasibility, physical consistency, or require lengthy sampling processes. This research proposes a new flow matching-based topology optimization (FMTO) framework to address these limitations. The core innovation is a trajectory-aware FMTO formulation that integrates mechanically meaningful intermediate states into the generative process. Instead of simple interpolation, it uses volume-fraction-indexed BESO (Bi-directional Evolutionary Structural Optimization) states to construct the probability path and target velocity field. This effectively embeds physics-guided optimization history directly into the generative flow learning, eliminating the need for additional inference-time optimization. Numerical examples demonstrate that FMTO generates diverse and high-quality topology candidates, showing improved compliance, volume-fraction satisfaction, and fidelity. Crucially, it achieves these results with substantially fewer sampling steps compared to diffusion-based methods. The study also highlights how moderate trajectory weighting enhances generation stability, making the framework applicable to both 2D and 3D problems, even with limited training data.