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.

该研究提出了一个新的概率方法进行关系推断，使用基于物理的图神经网络来学习物理一致的两两粒子之间的相互作用，具有数据效率和泛化到大系统的能力，并能够比现有方法准确地推断相互作用类型，是发现宏观粒子系统机械性质的基本规律的关键元素。