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.

翻译：具有复杂行为的动力系统（例如免疫系统细胞与病原体相互作用）通常通过将行为拆分为不同状态或模式来建模，每种模式具有较简单的动力学特性，并学习模式间的切换行为。切换动力系统（SDS）是一种强大工具，可自动从时间序列数据中发现这些模式及模式切换行为。尽管有效，但现有方法聚焦于独立对象，其中每个对象的模式独立于其他对象的模式。本文关注切换动力系统中更具普适性的交互对象场景，其中各对象的动力学还依赖于未知且动态变化的其他对象子集及其模式。为此，我们提出一种新颖的基于图的切换动力系统方法——图切换动力系统（GRASS），通过动态图刻画对象间的交互，并同时学习对象内部与对象间的模式切换行为。我们针对该场景引入两个新数据集：基于常微分方程驱动的合成粒子数据集和真实世界的萨尔萨双人舞数据集。实验表明，GRASS能够持续优于先前的最优方法。