From pedestrians to Kuramoto oscillators, interactions between agents govern how a multitude of dynamical systems evolve in space and time. Discovering how these agents relate to each other can improve our understanding of the often complex dynamics that underlie these systems. Recent works learn to categorize relationships between agents based on observations of their physical behavior. These approaches are limited in that the relationship categories are modelled as independent and mutually exclusive, when in real world systems categories are often interacting. In this work, we introduce a level of abstraction between the physical behavior of agents and the categories that define their behavior. To do this, we learn a mapping from the agents' states to their affinities for each category in a graph neural network. We integrate the physical proximity of agents and their affinities in a nonlinear opinion dynamics model which provides a mechanism to identify mutually exclusive categories, predict an agent's evolution in time, and control an agent's behavior. We demonstrate the utility of our model for learning interpretable categories for mechanical systems, and demonstrate its efficacy on several long-horizon trajectory prediction benchmarks where we consistently out perform existing methods.

翻译：从行人到Kuramoto振子，智能体间的相互作用决定了众多动力系统在时空中的演化方式。揭示这些智能体间的关联机制，能深化我们对这些系统背后复杂动力学原理的理解。近期研究尝试通过观测智能体的物理行为来学习其关系分类。这些方法的局限在于将关系类别建模为独立且互斥的，而现实系统中各类别往往存在交互作用。本研究在智能体物理行为与定义其行为的类别之间引入了抽象层级。为实现这一目标，我们在图神经网络中学习从智能体状态到其对各类别亲和度的映射。通过非线性观点动力学模型整合智能体的物理邻近性及其亲和度，该机制能够：识别互斥类别、预测智能体时序演化、控制智能体行为。我们通过机械系统可解释类别学习验证了模型的有效性，并在多个长时程轨迹预测基准测试中持续超越现有方法，证明了其优越性能。