From pedestrians to Kuramoto oscillators, interactions between agents govern how dynamical systems evolve in space and time. Discovering how these agents relate to each other has the potential to 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 model relationship categories as outcomes of a categorical distribution which is limiting and contrary to real-world systems, where relationship categories often intermingle and interact. In this work, we introduce a level of abstraction between the observable behavior of agents and the latent categories that determine their behavior. To do this, we learn a mapping from agent observations to agent preferences for a set of latent categories. The learned preferences and inter-agent proximity are integrated in a nonlinear opinion dynamics model, which allows us to naturally identify mutually exclusive categories, predict an agent's evolution in time, and control an agent's behavior. Through extensive experiments, we demonstrate the utility of our model for learning interpretable categories, and the efficacy of our model for long-horizon trajectory prediction.

翻译：从行人到Kuramoto振子，智能体之间的相互作用支配着动力系统在时空中的演化方式。揭示这些智能体如何相互关联，有望增进我们对这些系统背后复杂动力学的理解。近期研究基于对智能体物理行为的观察，学习对其间关系进行分类。这些方法将关系类别建模为分类分布的结果，这具有局限性且与现实系统相悖，因为在现实系统中，关系类别常常相互交织并相互作用。在本工作中，我们在智能体的可观测行为与决定其行为的潜在类别之间引入了一个抽象层次。为此，我们学习从智能体观测到其对一组潜在类别偏好的映射。学习到的偏好与智能体间邻近性通过非线性意见动力学模型进行整合，这使我们能够自然地识别互斥的类别、预测智能体的时间演化，并控制智能体的行为。通过大量实验，我们证明了所提模型在学习可解释类别方面的有效性，以及其在长时程轨迹预测中的优异性能。