Separable graph Hamiltonian network: A graph deep learning model for lattice systems

Abstract

Addressing the challenges posed by nonlinear lattice models, which are vital across diverse scientific disciplines, we present a new deep learning approach that harnesses the power of graph neural networks. By representing the lattice system as a graph and leveraging the graph structures to identify complex nonlinear relationships, we have developed a flexible solution that outperforms traditional techniques. Our model not only offers precise trajectory predictions and energy conservation properties by incorporating separable Hamiltonians but also proves superior to existing top-tier models when tested on classic nonlinear oscillator lattice problems: a mixed Fermi-Pasta-Ulam Klein-Gordon, a Klein-Gordon system with long-range interactions, and a two-dimensional Frenkel-Kontorova, highlighting its potential for wide-reaching applications.