Interacting particle systems are ubiquitous in nature and engineering. Revealing particle interaction laws is of fundamental importance but also particularly challenging due to underlying configurational complexities. Recently developed machine learning methods show great potential in discovering pairwise interactions from particle trajectories in homogeneous systems. However, they fail to reveal interactions in 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 uses a physics-induced graph neural network to learn physics-consistent pairwise interactions. We evaluate the proposed methodology across several benchmark datasets and demonstrate that it is consistent with the underlying physics. Furthermore, we showcase its ability to outperform existing methods in accurately inferring interaction types. In addition, the proposed model is data-efficient and generalizable to large systems when trained on smaller ones, which contrasts with previously proposed solutions. The developed methodology constitutes a key element for the discovery of the fundamental laws that determine macroscopic mechanical properties of particle systems.
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