Interacting particle systems play a key role in science and engineering. Recently, machine learning methods have shown great potential in learning the behavior of interacting particle systems based on the observed particle trajectories. However, these purely data-driven models infer particle interactions that violate the Newtonian laws of motion, such as the action-reaction property. This discrepancy imposes a significant concern on applying these methods to learn particle interactions for real applications. To overcome this problem, we propose a new method, termed physics-induced graph network for particle interaction (PIG’N’PI). The proposed method combines graph neural networks with physics operators to guarantee physics consistency. We test the proposed methodology on multiple datasets and demonstrate that it achieves considerably better performance in inferring correctly the pairwise interactions while also being consistent with the underlying physics on all the datasets than existing purely data-driven models.

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