# Path Signatures and Graph Neural Networks for Slow Earthquake Analysis: Better Together?

arXiv: https://arxiv.org/abs/2402.03558 · HTML: https://mlsanity.com/paper/2402.03558/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 49 references that are in the map.
- First posted on arXiv 5 Feb 2024.

## Builds on (most cited first, 27 of 27)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1708.00588/) (2017)
- [Self-Supervised Learning of Graph Neural Networks: A Unified Review](https://mlsanity.com/paper/2102.10757/) (2021)
- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Stability Properties of Graph Neural Networks](https://mlsanity.com/paper/1905.04497/) (2019)
- [A Primer on the Signature Method in Machine Learning](https://mlsanity.com/paper/1603.03788/) (2016)
- [Graph Neural Networks: Architectures, Stability and Transferability](https://mlsanity.com/paper/2008.01767/) (2020)
- [Deep Signature Transforms](https://mlsanity.com/paper/1905.08494/) (2019)
- [Gated Graph Recurrent Neural Networks](https://mlsanity.com/paper/2002.01038/) (2020)
- [Scalable Spatiotemporal Graph Neural Networks](https://mlsanity.com/paper/2209.06520/) (2022)
- [Signatory: differentiable computations of the signature and logsignature transforms, on both CPU and GPU](https://mlsanity.com/paper/2001.00706/) (2020)
- [VarNet: Variational Neural Networks for the Solution of Partial Differential Equations](https://mlsanity.com/paper/1912.07443/) (2019)
- [Signature Methods in Machine Learning](https://mlsanity.com/paper/2206.14674/) (2022)
- [A Survey on Deep Neural Network Compression: Challenges, Overview, and Solutions](https://mlsanity.com/paper/2010.03954/) (2020)
- [Embedding and learning with signatures](https://mlsanity.com/paper/1911.13211/) (2019)
- [Feature-based time-series analysis](https://mlsanity.com/paper/1709.08055/) (2017)
- [Developing the Path Signature Methodology and its Application to Landmark-based Human Action Recognition](https://mlsanity.com/paper/1707.03993/) (2017)
- [Backbones-Review: Feature Extraction Networks for Deep Learning and Deep Reinforcement Learning Approaches](https://mlsanity.com/paper/2206.08016/) (2022)
- [Space-Time Graph Neural Networks](https://mlsanity.com/paper/2110.02880/) (2021)
- [Path Signatures on Lie Groups](https://mlsanity.com/paper/2007.06633/) (2020)
- [The insertion method to invert the signature of a path](https://mlsanity.com/paper/2304.01862/) (2023)
- [Learning Paths from Signature Tensors](https://mlsanity.com/paper/1809.01588/) (2018)
- [Deep Learning for Robotic Mass Transport Cloaking](https://mlsanity.com/paper/1812.04157/) (2018)

## Abstract (arXiv)

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.