From Koopman operators to graph neural networks : a unified framework for structured timeseries modeling

The growing availability of multivariate waveform data from global monitoring networks, such as the International Monitoring System, has opened new plans for detecting and interpreting geophysical events. Despite advances, current processing systems remain limited by their reliance on rule-based methods and human expertise, particularly when waveforms propagate through changeful media such as atmosphere. This thesis introduces machine learning approaches grounded in physical principles, designed specifically for the structure and challenges of global sensor networks.Two complementary directions are explored. The first focuses on single-station infrasound data, where we use Koopman autoencoders to model and forecast low-frequency atmospheric dynamics, separating them from signals of interest. The second targets multi-station seismic data, leveraging Graph Neural Networks to exploit spatial relationships and waveform characteristics for improved event characterization, especially in estimating magnitudes. By combining dynamical systems theory with deep learning and graph-based models, this work aims to enhance the accuracy and the interpretability of global monitoring pipelines.