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.

翻译：许多复杂的工程系统可以用拓扑形式表示，例如图。本文利用一种称为几何深度学习（GDL）的机器学习技术，帮助设计人员解决具有挑战性的以图为中心的设计问题。所提出的策略是获取图数据并应用GDL，以较低的计算成本高效地寻求最佳可实现性能的解决方案。本文采用的案例研究是模拟电路的综合，旨在匹配特定频率范围内的频率响应。以往的研究采用枚举技术生成43,249个唯一的无向图，表示有效的潜在电路。不幸的是，确定许多电路的尺寸和性能可能过于昂贵。为了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导向型GDL模型的输入数据。然后，GDL模型可用于廉价地预测剩余部分，从而辅助决策者寻找最佳图解决方案。本文讨论的结果表明，额外的基于图的特征是有用的，仅使用10%的图即可达到80%的总体集合分类准确率，并且迭代构建的GDL模型可以进一步将图细分为目标组，其中位数显著更接近最优值，平均包含前100个最佳性能图中的88.2个。