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.Comment: Draft, 14 pages, 8 figures, Submitted to ASME Journal of Mechanical
Design Special Issue IDETC202