Many complex engineering systems can be represented in a topological form, such as graphs. This paper utilizes a machine learning technique called Geometric Deep Learning (GDL) to aid designers with challenging, graph-centric design problems. The strategy presented here is to take the graph data and apply GDL to seek the best realizable performing solution effectively and efficiently with lower computational costs. This case study used here is the synthesis of analog electrical circuits that attempt to match a specific frequency response within a particular frequency range. Previous studies utilized an enumeration technique to generate 43,249 unique undirected graphs presenting valid potential circuits. Unfortunately, determining the sizing and performance of many circuits can be too expensive. To reduce computational costs with a quantified trade-off in accuracy, the fraction of the circuit graphs and their performance are used as input data to a classification-focused GDL model. Then, the GDL model can be used to predict the remainder cheaply, thus, aiding decision-makers in the search for the best graph solutions. The results discussed in this paper show that additional graph-based features are useful, favorable total set classification accuracy of 80\% in using only 10\% of the graphs, and iteratively-built GDL models can further subdivide the graphs into targeted groups with medians significantly closer to the best and containing 88.2 of the top 100 best-performing graphs on average using 25\% of the graphs.

翻译：许多复杂工程系统可用拓扑形式（如图结构）表示。本文采用名为几何深度学习（Geometric Deep Learning, GDL）的机器学习技术，辅助设计人员解决具有挑战性的图中心设计问题。所提出的策略是将图数据应用于GDL，以较低的计算成本有效且高效地寻求最优可实现性能方案。本案例研究以模拟电路综合为例，旨在匹配特定频率范围内指定频率响应。先前研究采用枚举技术生成了43,249个表示有效潜在电路的无向图。然而，确定大量电路的尺寸参数与性能代价过高。为在量化精度权衡下降低计算成本，将部分电路图及其性能作为分类型GDL模型的输入数据，从而通过该模型廉价预测剩余数据，辅助决策者寻找最优图结构方案。研究结果表明：引入额外图特征具有实用性；仅使用10%的图即可实现总集分类准确率达80%的理想结果；基于迭代构建的GDL模型可进一步将图划分为目标分组，这些分组的性能中位数显著接近最优值，且在使用25%的图时，平均可包含前100个最优性能图中的88.2个。