Trajectory-Aware Flow Matching for Topology Optimisation

What the math gives to ML

The paper's main transferable contribution is to replace an endpoint-only probability path with a piecewise path built from intermediate states produced by a physics-guided optimisation trajectory. The learned vector field is trained to match the velocity of this multi-anchor path, so inference can follow a short deterministic flow while inheriting useful structure from the solver trajectory without running the solver at inference time. This suggests a general conditional generative-training method for distilling expensive iterative procedures such as optimisers, planners, simulators, or denoisers into few-step flow models.