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.

翻译：相互作用粒子系统在自然界和工程中普遍存在。揭示粒子相互作用规律具有根本重要性，但由于潜在的构型复杂性而极具挑战性。近期发展的机器学习方法在从均匀系统中粒子轨迹发现成对相互作用方面展现出巨大潜力。然而，这些方法无法揭示现实中普遍存在的非均匀系统中的相互作用——此类系统同时存在多种相互作用类型，需要关系推理。本文提出一种新颖的概率关系推理方法，与现有方法相比具有两个显著特征：其一，它能集体推断不同边界的相互作用类型；其二，它利用物理诱导图神经网络学习物理一致的成对相互作用。我们在多个基准数据集上评估了所提方法，证明其与底层物理规律一致。此外，我们展示了该方法在准确推断相互作用类型方面优于现有方法的能力。同时，所提模型具有数据高效性，且在小系统上训练后能泛化至大型系统，这与先前提出的方案形成对比。所发展的方法论为揭示决定粒子系统宏观力学特性的基本规律提供了关键要素。