Simon Heilig

In this project, we will provide fundamental properties of spatiotemporal models to build a rigorous understanding of deep learning methods in terms of domain generalization and anomaly detection. Within the class of (stochastic-) graph-coupled neural ODEs, the PhD project will apply and enhance state-of-the-art methods on challenging spatiotemporal data given, e.g., by power-grid data and satellite images. By bridging the fields of dynamical systems, physics and statistics, this work will provide mathematical guarantees for safe application of deep learning models. In particular, by developing stochastic graph neural networks inspired by stochastic partial differential equations, this PhD project offers a way to learn distributions over graph features through time. The time axis increases the complexity in terms of data management of large-scale networks, hence, this project strives to develop resource efficient approaches by means of event-driven online learning approaches.