Path Signatures and Graph Neural Networks for Slow Earthquake Analysis:
  Better Together?
Hans Riess Manolis Veveakis Michael M. Zavlanos
The path signature, having enjoyed recent success in the machine learning
community, is a theoretically-driven method for engineering features from
irregular paths. On the other hand, graph neural networks (GNN), neural
architectures for processing data on graphs, excel on tasks with irregular
domains, such as sensor networks. In this paper, we introduce a novel approach,
Path Signature Graph Convolutional Neural Networks (PS-GCNN), integrating path
signatures into graph convolutional neural networks (GCNN), and leveraging the
strengths of both path signatures, for feature extraction, and GCNNs, for
handling spatial interactions. We apply our method to analyze slow earthquake
sequences, also called slow slip events (SSE), utilizing data from GPS
timeseries, with a case study on a GPS sensor network on the east coast of New
Zealand's north island. We also establish benchmarks for our method on
simulated stochastic differential equations, which model similar
reaction-diffusion phenomenon. Our methodology shows promise for future
advancement in earthquake prediction and sensor network analysis.