🤖 AI Summary
本文提出了一种通过自动微分优化拓扑结构和超参数的方法，解决了拓扑优化中超参数调优的问题，且该方法可扩展至数千个超参数。
📝 Abstract
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.