Graph Switching Dynamical Systems
Yongtuo Liu Sara Magliacane Miltiadis Kofinas Efstratios Gavves
Dynamical systems with complex behaviours, e.g. immune system cells
interacting with a pathogen, are commonly modelled by splitting the behaviour
into different regimes, or modes, each with simpler dynamics, and then learning
the switching behaviour from one mode to another. Switching Dynamical Systems
(SDS) are a powerful tool that automatically discovers these modes and
mode-switching behaviour from time series data. While effective, these methods
focus on independent objects, where the modes of one object are independent of
the modes of the other objects. In this paper, we focus on the more general
interacting object setting for switching dynamical systems, where the
per-object dynamics also depends on an unknown and dynamically changing subset
of other objects and their modes. To this end, we propose a novel graph-based
approach for switching dynamical systems, GRAph Switching dynamical Systems
(GRASS), in which we use a dynamic graph to characterize interactions between
objects and learn both intra-object and inter-object mode-switching behaviour.
We introduce two new datasets for this setting, a synthesized ODE-driven
particles dataset and a real-world Salsa Couple Dancing dataset. Experiments
show that GRASS can consistently outperforms previous state-of-the-art methods.