Graph Switching Dynamical Systems
This addresses the limitation of independent object modeling in dynamical systems for applications like immune system interactions or dancing, though it is incremental by extending existing switching dynamical systems to include graph-based interactions.
The paper tackles the problem of modeling interacting objects in switching dynamical systems, where per-object dynamics depend on other objects and their modes, by proposing GRASS, a graph-based approach that learns intra- and inter-object mode-switching behavior, and it outperforms previous state-of-the-art methods on new datasets.
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.