Conditional Flow Matching for Topology Optimization with Deterministic Manufacturing Constraint Projection

  • Sugai, Tomotaka (The University of Tokyo)
  • Yamada, Takayuki (The University of Tokyo)

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Topology optimization determines optimal material distributions under specified boundary conditions and has been widely studied [1]. Deep generative models have shown potential for accelerating this process [2,3]; however, existing diffusion-based approaches require fifty or more sampling steps, limiting interactive use, and frequently produce manufacturing infeasible features such as intermediate densities, thin members, and disconnected components. This paper presents a conditional flow matching (CFM) framework for topology optimization coupled with a deterministic projection pipeline for manufacturing constraint enforcement. The CFM backbone learns a velocity field that transports Gaussian noise to optimized density fields along near-linear ODE trajectories, enabling accurate generation in as few as five steps [4], substantially fewer than diffusion-based methods [2,3]. Design conditions are injected through spatial maps encoding boundary conditions and loads, together with feature-wise volume-fraction modulation, avoiding reliance on physics fields derived from the unknown target. The generated fields are then processed by a non-iterative pipeline of Helmholtz filtering, Heaviside projection, and connected-component enforcement, which guarantees binary design and single-component connectivity while promoting minimum-feature-size satisfaction. The framework is evaluated on benchmark problems with varying boundary conditions, loading scenarios, and volume fractions, demonstrating improvements in generation quality, sampling efficiency, and constraint satisfaction.