α -separable graph Hamiltonian network: A robust model for learning particle interactions in lattice systems

We propose an $\ensuremath{\alpha}$-separable graph Hamiltonian network ($\ensuremath{\alpha}$-SGHN) that reveals complex interaction patterns between particles in lattice systems. Utilizing trajectory data, $\ensuremath{\alpha}$-SGHN infers potential interactions without prior knowledge about particle coupling, overcoming the limitations of traditional graph neural networks that require predefined links. Furthermore, $\ensuremath{\alpha}$-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 on-site and intersite interaction lattices studied, including the Frenkel-Kontorova model, the rotator lattice, and the Toda lattice.