Data-driven vector localized waves and parameters discovery for Manakov system using deep learning approach

An improved physics-informed neural network (IPINN) algorithm with four output functions and physics constraints, which possesses neuron-wise locally adaptive activation function slope recovery term, is appropriately proposed to obtain the data-driven vector localized waves, including solitons, breathers rogue waves (RWs) for Manakov system initial boundary conditions, as well parameters discovery unknown parameters. The RWs also contain interaction of bright-dark breathers, evolved from solitons are learned verify capability IPINN in training complex wave. In process parameter discovery, routine can not accurately train whether using clean data or noisy data. Thus we introduce regularization strategy adjustable weight coefficients into effectively prediction parameters, then find that once setting appropriate coefficients, effect better Numerical results show shows superior noise immunity problem.