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

TL;DR

This paper introduces an improved physics-informed neural network (IPINN) with adaptive activation functions and regularization for data-driven discovery of vector localized waves and unknown parameters in the Manakov system, demonstrating high accuracy and noise robustness.

Contribution

The paper develops an enhanced IPINN algorithm with neuron-wise adaptive activation and parameter regularization for accurate data-driven wave and parameter discovery in complex Manakov system scenarios.

Findings

IPINN accurately models vector solitons, breathers, and rogue waves.

Parameter regularization improves training accuracy with noisy data.

IPINN outperforms routine methods in parameter estimation robustness.

Abstract

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.