Integrating geometric deep learning with a set-based design approach for the exploration of graph-based engineering systems - Sirico, Anthony, Jr., author; Herber, Daniel R., advisor; Chen, Haonan, committee member; Simske, Steven, committee member; Conrad, Steven A., committee member (Colorado State University. Libraries, 2024)
Many complex engineering systems can be represented in a topological form, such as graphs. This dissertation introduces a framework of Graph-Set-Based Design (GSBD) that integrates graph-based techniques with Geometric Deep Learning (GDL) within a Set-Based Design (SBD) approach to address graph-centric design problems. We also introduce Iterative Classification (IC), a method for narrowing down large datasets to a subset of more promising and feasible solutions. When we combine the two, we have IC-GSBD, a methodological framework where the primary goal is to effectively and efficiently seek the best-performing solutions with lower computational costs. IC-GSBD is a method that employs an iterative approach to efficiently narrow down a graph-based dataset containing diverse design solutions to identify the most useful options. This approach is particularly valuable as the dataset would be computationally expensive to process using other conventional methods. The implementation involves analyzing a small subset of the dataset to train a machine-learning model. This model is then utilized to predict the remaining dataset iteratively, progressively refining the top solutions with each iteration. In this work, we present two case studies demonstrating this method. In the first case study utilizing IC-GSBD, the goal is the analysis of analog electrical circuits, aiming to match a specific frequency response within a particular range. Previous studies generated 43,249 unique undirected graphs representing valid potential circuits through enumeration techniques. However, determining the sizing and performance of these circuits proved computationally expensive. By using a fraction of the circuit graphs and their performance as input data for a classification-focused GDL model, we can predict the performance of the remaining graphs with favorable accuracy. The results show that incorporating additional graph-based features enhances model performance, achieving a classification accuracy of 80% using only 10% of the graphs and further subdividing 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.
Keywords: geometric deep learning; machine learning; graph theory; engineering design