Data-driven vector localized waves and parameters discovery for Manakov system using deep learning approach - Pu, Jun-Cai; Chen, Yong (Chaos, solitons and fractals, 2022)
An improved physics-informed neural network (IPINN) algorithm with four output functions and four physics constraints, which possesses neuron-wise locally adaptive activation function and slope recovery term, is appropriately proposed to obtain the data-driven vector localized waves, including vector solitons, breathers and rogue waves (RWs) for the Manakov system with initial and boundary conditions, as well as data-driven parameters discovery for Manakov system with unknown parameters. The data-driven vector RWs which also contain interaction waves of RWs and bright-dark solitons, interaction waves of RWs and breathers, as well as RWs evolved from bright-dark solitons are learned to verify the capability of the IPINN algorithm in training complex localized wave. In the process of parameter discovery, routine IPINN can not accurately train unknown parameters whether using clean data or noisy data. Thus we introduce parameter regularization strategy with adjustable weight coefficients into IPINN to effectively and accurately train prediction parameters, then find that once setting the appropriate weight coefficients, the training effect is better as using noisy data. Numerical results show that IPINN with parameter regularization shows superior noise immunity in parameters discovery problem. •The improved PINN method with four outputs and four nonlinear equation constraints is firstly proposed.•The data-driven vector localized waves and parameters discovery for the Manakov system are considered.•The data-driven vector interaction solutions and parameters discovery are obtained.•We introduce L2 norm parameter regularization strategy with adjustable weight coefficients into improved PINN.•The training effect is better as using noisy data in improved PINN with parameter regularization.