  Topology Optimization seeks to find the best design that satisfies a set of
constraints while maximizing system performance. Traditional iterative
optimization methods like SIMP can be computationally expensive and get stuck
in local minima, limiting their applicability to complex or large-scale
problems. Learning-based approaches have been developed to accelerate the
topology optimization process, but these methods can generate designs with
floating material and low performance when challenged with out-of-distribution
constraint configurations. Recently, deep generative models, such as Generative
Adversarial Networks and Diffusion Models, conditioned on constraints and
physics fields have shown promise, but they require extensive pre-processing
and surrogate models for improving performance. To address these issues, we
propose a Generative Optimization method that integrates classic optimization
like SIMP as a refining mechanism for the topology generated by a deep
generative model. We also remove the need for conditioning on physical fields
using a computationally inexpensive approximation inspired by classic ODE
solutions and reduce the number of steps needed to generate a feasible and
performant topology. Our method allows us to efficiently generate good
topologies and explicitly guide them to regions with high manufacturability and
high performance, without the need for external auxiliary models or additional
labeled data. We believe that our method can lead to significant advancements
in the design and optimization of structures in engineering applications, and
can be applied to a broader spectrum of performance-aware engineering design
problems.
