Gaussian Particle Flows for Unsupervised Topology Optimization

We propose an unsupervised, flow-based approach to topology optimization in which designs are produced by integrating a problem-conditioned velocity field on the configuration space of a Gaussian mixture. The density field is directly parameterised by this mixture distribution, and a transformer-parameterised velocity field evolves its configuration from a fixed initialisation to a high-quality design, conditioned on the physical boundary condition. The velocity field is trained via reinforcement learning (RL) with a structural objective as a black box reward, requiring no differentiable simulator and no dataset of pre-solved designs. On four canonical benchmark problems, a single RL-trained policy produces designs that closely approximate the performance of a classical per instance numerical method. Producing each design from a single forward pass without any simulator calls. A controlled gradient-based ablation confirms that our novel design representation is capable of learning shared structural priors, matching the numerical per instance method quality at matched number of solver calls when solving problem pools jointly.