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.

翻译：拓扑优化旨在寻找满足一系列约束条件的同时最大化系统性能的最佳设计。传统的迭代优化方法（如SIMP）计算成本高昂且易于陷入局部最优，限制了其在复杂或大规模问题中的适用性。基于学习的方法已被开发用于加速拓扑优化过程，但这类方法在面临分布外约束配置时可能产生带有浮动材料且性能低下的设计。近年来，以约束和物理场为条件的深度生成模型（如生成对抗网络和扩散模型）展现出了潜力，但需要大量预处理和代理模型来提升性能。为解决这些问题，我们提出了一种生成式优化方法，将经典优化方法（如SIMP）作为深度生成模型所生成拓扑的细化机制。同时，我们借鉴经典常微分方程解法的思路，采用计算成本低廉的近似方法，消除了对物理场条件的依赖，并减少了生成可行且高性能拓扑所需的步骤数。我们的方法能够高效生成优质拓扑，并显式引导其走向高制造性与高性能区域，无需外部辅助模型或额外标注数据。我们相信，该方法可推动工程应用中结构设计与优化的显著进展，并适用于更广泛的性能感知工程优化问题。