Graph Switching Dynamical Systems

Abstract

Dynamical systems with complex behaviours, e.g. immune system cells interacting with a pathogen, are commonly modelled by splitting the behaviour in different regimes, or *modes*, each with simpler dynamics, and then learn the switching behaviour from one mode to another. To achieve this, 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 depend 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. For benchmarking, we create two new datasets, 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. We will release code and data after acceptance.