  Traditional discrete learning methods involve discretizing continuous
equations using difference schemes, necessitating considerations of stability
and convergence. Integrable nonlinear lattice equations possess a profound
mathematical structure that enables them to revert to continuous integrable
equations in the continuous limit, particularly retaining integrable properties
such as conservation laws, Hamiltonian structure, and multiple soliton
solutions. The pseudo grid-based physics-informed convolutional-recurrent
network (PG-PhyCRNet) is proposed to investigate the localized wave solutions
of integrable lattice equations, which significantly enhances the model's
extrapolation capability to lattice points beyond the temporal domain. We
conduct a comparative analysis of PG-PhyCRNet with and without pseudo grid by
investigating the multi-soliton solutions and rational solitons of the Toda
lattice and self-dual network equation. The results indicate that the
PG-PhyCRNet excels in capturing long-term evolution and enhances the model's
extrapolation capability for solitons, particularly those with steep waveforms
and high wave speeds. Finally, the robustness of the PG-PhyCRNet method and its
effect on the prediction of solutions in different scenarios are confirmed
through repeated experiments involving pseudo grid partitioning.
