Spectral Analysis of Heterogeneous Graph Representation for GNN Tasks on Electric Circuits

Machine learning (ML) holds significant potential for transforming electronic design automation (EDA), but it currently lacks scalable and robust representations of electric circuits. Existing methodologies in the literature fail to represent circuits in a scalable and general-purpose representation, limiting their methodology to specific circuit orders and fixed topologies. This paper presents a spectral analysis of the heterogeneous graph representation of electric circuits, as introduced in [1], which offers a scalable and circuit-topology-independent heterogeneous graph representation. By examining the circuit graphs in the spectral domain, the frequency components distribution is shown to affect the performance of Graph Neural Networks (GNNs). The analysis highlights the limitations of traditional GNNs with homogeneous representation and demonstrates that GNNs designed for heterogeneous graphs are better suited for capturing system dynamics and variations. Finally, several case studies that apply heterogeneous graph neural networks (Hetero-GNN) to various ML tasks are implemented, such as converter dynamics prediction and converter topology classification.