发表机构
Delft University of Technology; Brown University（代尔夫特理工大学; 布朗大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出BOTH方法，通过自动微分对拓扑优化过程本身求超梯度，实现超参数与主优化同步调整，可扩展到数千超参数，开销仅相当于几次标准TO运行，并在应力约束和柔度问题上验证有效性。
AI 中文摘要
拓扑优化（TO）是迈向设计过程自动化的重要一步：给定一个可行的仿真，通过按一下按钮对仿真进行微分并迭代改进设计，TO即可生成可行的原型。然而，在实践中，TO充满了“魔法数字”——这些超参数的调整会显著影响结果。找到合适的值通常不仅需要深入的问题特定知识，还需要大量的试错。虽然从业者可以使用代理辅助的超参数优化作为替代方案，但这种方法要求通过仔细的问题表述来严格限制超参数的数量。在此，我们提出使用自动微分对TO本身进行微分。这产生了“超梯度”，使我们能够与主优化同步调整这些超参数。我们表明，仅评估TO的一两步就足以提供信息，并且该方法可扩展到数千个超参数，其开销仅相当于几次标准TO运行。我们在应力约束和柔度问题上展示了这种方法，后者利用了密度场的神经参数化。
英文摘要
Topology optimization (TO) represents a significant step towards automating the design process: given a working simulation, TO can produce a viable prototype at the press of a button by differentiating the simulation and iteratively improving the design. In practice, however, TO is riddled with ``magic numbers''---hyperparameters whose tuning significantly affects the outcome. Finding the right values typically requires not only deep problem-specific knowledge but also extensive trial-and-error. While practitioners can use surrogate-assisted hyperparameter optimization as an alternative, this approach requires strictly limiting the number of hyperparameters through careful problem formulation. Here, we propose differentiating TO itself using automatic differentiation. This yields ``hypergradients'' that allow us to tune these hyperparameters in tandem with the primary optimization. We show that evaluating just one or two steps of TO is sufficiently informative and that the method scales favorably to thousands of hyperparameters at an expense comparable to only a few standard TO runs. We demonstrate this approach on stress-constrained and compliance problems, with the latter utilizing a neural parameterization of the density field.
CommentsCurrently under submission to SMO journal
