Interacting systems are ubiquitous in nature and engineering, ranging from particle dynamics in physics to functionally connected brain regions. These interacting systems can be modeled by graphs where edges correspond to the interactions between interactive entities. Revealing interaction laws is of fundamental importance but also particularly challenging due to underlying configurational complexities. The associated challenges become exacerbated for heterogeneous systems that are prevalent in reality, where multiple interaction types coexist simultaneously and relational inference is required. Here, we propose a novel probabilistic method for relational inference, which possesses two distinctive characteristics compared to existing methods. First, it infers the interaction types of different edges collectively, and second, it allows handling systems with variable topological structure over time. We evaluate the proposed methodology across several benchmark datasets and demonstrate that it outperforms existing methods in accurately inferring interaction types. We further show that when combined with known constraints, it allows us, for example, to discover physics-consistent interaction laws of particle systems. Overall the proposed model is data-efficient and generalizable to large systems when trained on smaller ones. The developed methodology constitutes a key element for understanding interacting systems and may find application in graph structure learning.

翻译：相互作用系统在自然界与工程中普遍存在，涵盖从物理学中的粒子动力学到功能连接的大脑区域。此类系统可用图模型表示，其中边对应交互实体间的相互作用。揭示相互作用规律具有根本重要性，但由于潜在构型复杂性而极具挑战性。对于现实中普遍存在的异构系统（其中多种交互类型同时并存且需要进行关系推断），相关挑战更为严峻。本文提出一种新型概率关系推断方法，与现有方法相比具有两个显著特征：第一，它能集体推断不同边的交互类型；第二，它允许处理随时间变化的拓扑结构系统。我们通过多个基准数据集评估所提方法，证明其在精准推断交互类型方面优于现有方法。进一步研究表明，当该方法与已知约束条件结合时，可发现粒子系统中符合物理规律的相互作用。总体而言，所提模型具有数据高效性，且可通过较小系统训练后泛化至大型系统。本方法为理解相互作用系统提供了关键要素，并可应用于图结构学习。