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以表示为拓扑形式，例如图结构。本文利用名为几何深度学习（GDL）的机器学习技术，帮助设计人员应对以图为核心的复杂设计问题。所提出的策略是将图数据应用于GDL，以较低的计算成本高效地寻求可实现的最佳性能解决方案。本文的案例研究聚焦于模拟电路的综合设计，旨在匹配特定频率范围内的频率响应。此前的研究采用枚举方法生成了43,249个无向图，代表有效的潜在电路。然而，确定众多电路的尺寸与性能计算成本过高。为在量化精度权衡下降低计算成本，本文将部分电路图及其性能作为输入数据，训练面向分类的GDL模型。随后，该GDL模型可用于低成本预测剩余电路，从而辅助决策者寻找最优图结构方案。本文结果表明：引入额外图特征具有实用性，仅使用10%的图即可达到80%的总分类准确率；通过迭代构建的GDL模型可进一步将图细分为目标组，其性能中位数显著逼近最优值，并在仅使用25%的图时平均保留88.2个（共100个）最佳性能电路。