$\alpha$-SGHN: A Robust Model for Learning Particle Interactions in Lattice Systems

TL;DR

The paper introduces $eta$-SGHN, a novel graph neural network model that learns complex particle interactions in lattice systems from trajectory data, preserving physical laws and outperforming traditional models.

Contribution

It presents $eta$-SGHN, a new model that infers particle interactions without prior knowledge and maintains conservation laws, advancing lattice system modeling.

Findings

Outperforms baseline neural networks in predicting lattice dynamics.

Successfully infers interaction patterns without predefined links.

Applicable to various lattice models like Frenkel-Kontorova and Toda.

Abstract

We propose an $\alpha$-separable graph Hamiltonian network ($\alpha$-SGHN) that reveals complex interaction patterns between particles in lattice systems. Utilizing trajectory data, $\alpha$-SGHN infers potential interactions without prior knowledge about particle coupling, overcoming the limitations of traditional graph neural networks that require predefined links. Furthermore, $\alpha$-SGHN preserves all conservation laws during trajectory prediction. Experimental results demonstrate that our model, incorporating structural information, outperforms baseline models based on conventional neural networks in predicting lattice systems. We anticipate that the results presented will be applicable beyond the specific onsite and inter-site interaction lattices studied, including the Frenkel-Kontorova model, the rotator lattice, and the Toda lattice.