Data-driven high-order rogue waves and parameters discovery for Gardner equation using deep learning approach

In this paper, an adaptive mix training physics-informed neural networks (A-MTPINNs) model is proposed to study the high-order rogue waves of the famous Gardner equation (GE). Through a series of numerical experiments, we can conclude that this A-MTPINNs model can not only recover the dynamic behavior of the high-order rogue waves of the GE well, but also can guarantee higher learning ability and prediction accuracy than the original PINNs model, and the prediction accuracy is improved by two orders of magnitude. By testing that the A-MTPINNs model can maintain high robustness under different noises for the data-driven solutions of the GE. Furthermore, this model also has good performance for the inverse problem of the Gardner equation by a data-driven discovery approach and also remains robust in noise experiments. •An adaptive mix training physics-informed neural networks model is proposed.•New algorithm can learn and predict the dynamics of higher-order rogue waves well.•Numerical experiments show that the algorithm can maintain good robustness.•The algorithm can also maintain excellent learning ability in inverse problems.