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

We investigate data-driven forward-inverse problems for Yajima–Oikawa (YO) system by employing two technologies to improve the performance of deep physics-informed neural network (PINN), namely neuron-wise locally adaptive activation functions and L2 norm parameter regularization. Indeed, we not only recover three different forms of vector rogue waves (RWs) under three distinct initial–boundary value conditions in the forward problem of YO system, including bright–bright RWs, intermediate–bright RWs and dark–bright RWs, but also study the inverse problem of YO system by using training data with different noise intensity. In order to deal with the problem that the capacity of learning unknown parameters is not ideal as utilizing training data with noise interference in the PINN with only locally adaptive activation functions, thus we introduce L2 norm regularization, which can drive the weights closer to origin, into PINN with locally adaptive activation functions. Then we find that the PINN model with two strategies shows amazing training effect by using training data with noise interference to investigate the inverse problem of YO system.