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We investigate data-driven forward-inverse problems for Yajima-Oikawa (YO)system by employing two technologies which improve the performance of neuralnetwork in deep physics-informed neural network (PINN), namely neuron-wiselocally adaptive activation functions and $L^2$ norm parameter regularization.Indeed, we not only recover three different forms of vector rogue waves (RWs)by means of three distinct initial-boundary value conditions in the forwardproblem of YO system, including bright-bright RWs, intermediate-bright RWs anddark-bright RWs, but also study the inverse problem of YO system by usingtraining data with different noise intensity. In order to deal with the problemthat the capacity of learning unknown parameters is not ideal when the PINNwith only locally adaptive activation functions utilizes training data withnoise interference in the inverse problem of YO system, thus we introduce $L^2$norm regularization, which can drive the weights closer to origin, into PINNwith locally adaptive activation functions, then find that the PINN model withtwo strategies shows amazing training effect by using training data with noiseinterference to investigate the inverse problem of YO system.

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