G-KdVNet: ANN-ADM Surrogate for Geophysical KdV Equation

Abstract

This research examines the influence of the Coriolis parameter on the behaviour of the geophysical Korteweg-de Vries (KdV) equation. To efficiently approximate its solution, a novel surrogate framework, termed G-KdVNet, is proposed by integrating artificial neural networks with the Adomian decomposition method (ADM). In the proposed approach, ADM is first employed to generate reliable semi-analytical solution data, which are subsequently used to train the neural network model. The developed model demonstrates strong predictive capability in capturing the nonlinear dynamics of the KdV system. Numerical results indicate that the proposed model achieves improved accuracy compared with conventional baseline methods, with absolute errors of the order of e-3 for unseen data. The results suggest that the proposed ANN-ADM surrogate offers an efficient and accurate alternative for solving nonlinear geophysical models, with potential applicability to a broader class of dispersive wave equations.