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

摘要

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 appro-priately 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 inter-action 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 set-ting 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.

关键词