Data-driven forward-inverse problems and modulational instability for Yajima-Oikawa system using deep learning with parameter regularization

We investigate data-driven forward-inverse problems for Yajima-Oikawa system by employing two technologies which improve the performance of PINN in deep physics-informed neural network (PINN), namely neuron-wise locally adaptive activation functions and L2 norm parameter regularization. In particular, we not only recover three different forms of vector rogue waves (RWs) in the forward problem of Yajima-Oikawa (YO) system, including bright-bright RWs, intermediatebright RWs and dark-bright RWs, but also study the inverse problem of YO system by data-driven with noise of different intensity. Compared with PINN method using only locally adaptive activation function, the PINN method with two strategies shows amazing robustness when studying the inverse problem of YO system with noisy training data, that is, the improved PINN model proposed by us has excellent noise immunity. The asymptotic analysis of wavenumber k and the MI analysis for YO system with unknown parameters are derived systematically by applying the linearized instability analysis on plane wave.