[论文解读] Data files for "Neural reparameterization improves structural optimization"

Stephan Hoyer|arXiv (Cornell University)|Sep 10, 2019

Topology Optimization in Engineering参考文献 28被引用 51

一句话总结

本文通过优化一个输出材料密度的神经网络来重新参数化结构优化，在116个任务中产生更优的设计，且比基线更常获得最佳设计，达到50%更高的频率。

ABSTRACT

Structural optimization is a popular method for designing objects such as bridge trusses, airplane wings, and optical devices. Unfortunately, the quality of solutions depends heavily on how the problem is parameterized. In this paper, we propose using the implicit bias over functions induced by neural networks to improve the parameterization of structural optimization. Rather than directly optimizing densities on a grid, we instead optimize the parameters of a neural network which outputs those densities. This reparameterization leads to different and often better solutions. On a selection of 116 structural optimization tasks, our approach produces the best design 50% more often than the best baseline method.

研究动机与目标

• 动机：参数化如何影响结构优化中的解的质量。
• 提出一种基于CNN的重新参数化，用于输出拓扑优化中的单元密度。
• 在116个多样化的结构优化任务上演示该方法。
• 在梯度基优化框架下，将基于CNN的重参数化与基于像素的参数化以及传统基线进行比较。
• 分析随问题规模变化的定性与定量收益以及可扩展性。

提出的方法

• 通过用输出密度的CNN替代直接的像素密度来重新参数化优化问题。
• 通过带有约束的sigmoid映射的可微前向模型来强制体积和密度约束。
• 使用隐式微分对约束变换进行反向传播。
• 使用梯度基优化器（L-BFGS）对每个任务训练CNN参数，以最小化柔顺性。
• 将前向传播实现为可微的TensorFlow图，配合伴随式物理求解器。
• 在116个任务上将CNN-LBFGS和Pixel-LBFGS与MMA和OC基线进行比较。

实验结果

研究问题

• RQ1 基于CNN的重参数化是否比像素参数化和传统优化基线产生更好的结构设计？
• RQ2 神经重参数化在问题规模（小网格与大网格）上性能如何扩展？
• RQ3 与传统方法相比，在CNN参数化下得到的结构中出现了哪些定性差异？
• RQ4 在提高设计质量的同时，该方法是否能够满足物理约束（体积、密度）？

主要发现

• CNN-based reparameterization matches MMA on small problems and outperforms it on large problems.
• Across 116 tasks, CNN-LBFGS produced better designs than OC and Pixel-LBFGS in most cases.
• CNN-parameterized solutions tended to be simpler and showed fewer spiderweb artifacts than baselines.
• Large problems benefited more from CNN reparameterization due to multi-scale optimization effects and mesh-dependency considerations.
• Best-of-ensemble CNN designs were best or near-best in 99 of 116 tasks, outperforming MMA in qualitative examples.
• Reparameterization with neural networks often yielded qualitatively different design patterns, such as treelike pillars and fewer supports, compared to baseline structures.