  Interacting particle systems play a key role in science and engineering.
Access to the governing particle interaction law is fundamental for a complete
understanding of such systems. However, the inherent system complexity keeps
the particle interaction hidden in many cases. Machine learning methods have
the potential to learn the behavior of interacting particle systems by
combining experiments with data analysis methods. However, most existing
algorithms focus on learning the kinetics at the particle level. Learning
pairwise interaction, e.g., pairwise force or pairwise potential energy,
remains an open challenge. Here, we propose an algorithm that adapts the Graph
Networks framework, which contains an edge part to learn the pairwise
interaction and a node part to model the dynamics at particle level. Different
from existing approaches that use neural networks in both parts, we design a
deterministic operator in the node part that allows to precisely infer the
pairwise interactions that are consistent with underlying physical laws by only
being trained to predict the particle acceleration. We test the proposed
methodology on multiple datasets and demonstrate that it achieves superior
performance in inferring correctly the pairwise interactions while also being
consistent with the underlying physics on all the datasets. The proposed
framework is scalable to larger systems and transferable to any type of
particle interactions, contrary to the previously proposed purely data-driven
solutions. The developed methodology can support a better understanding and
discovery of the underlying particle interaction laws, and hence guide the
design of materials with targeted properties.
