Data-driven rogue waves solutions for the focusing and variable coefficient nonlinear Schrödinger equations via deep learning.

In this paper, we investigate the data-driven rogue waves solutions of the focusing and the variable coefficient nonlinear Schrödinger (NLS) equations by the deep learning method from initial and boundary conditions. Specifically, first- and second-order rogue wave solutions for the focusing NLS equation and three deformed rogue wave solutions for the variable coefficient NLS equation are solved using physics-informed memory networks (PIMNs). The effects of optimization algorithm, network structure, and mesh size on the solution accuracy are discussed.

Derivation and rogue waves of the fractional nonlinear Schrödinger equation for the Rossby waves.

The Cartesian coordinate system is not sufficient to study wave propagation on the coastline or in the sea where the terrain is extremely complicated, so it is necessary to study it in an unconventional coordinate system, fractals. In this paper, from the governing equations of fluid, the fractional nonlinear Schrödinger equation is derived to describe the evolution of Rossby waves in fractal by using multi-scale analysis and perturbation method. Based on the equation, the rogue-wave solution is obtained by the integral preserving transformation to explain some serious threats at sea.

On soliton solutions, periodic wave solutions and asymptotic analysis to the nonlinear evolution equations in (2+1) and (3+1) dimensions.

In this paper, the (2+1)-dimensional generalized fifth-order KdV equation and the extended (3+1)-dimensional Jimbo-Miwa equation were transformed into the Hirota bilinear forms with Hirota direct method. In this process, the Hirota bilinear operator played a significant role. Based on the Hirota bilinear forms, the single soliton solutions and the single periodic wave solutions of these two types of equations were obtained respectively.

The New Simulation of Quasiperiodic Wave, Periodic Wave, and Soliton Solutions of the KdV-mKdV Equation via a Deep Learning Method.

How to solve the numerical solution of nonlinear partial differential equations efficiently and conveniently has always been a difficult and meaningful problem. In this paper, the data-driven quasiperiodic wave, periodic wave, and soliton solutions of the KdV-mKdV equation are simulated by the multilayer physics-informed neural networks (PINNs) and compared with the exact solution obtained by the generalized Jacobi elliptic function method. Firstly, the different types of solitary wave solutions are used as initial data to train the PINNs.

The Short-Term Load Forecasting Using an Artificial Neural Network Approach with Periodic and Nonperiodic Factors: A Case Study of Tai'an, Shandong Province, China.

Accurate electricity load forecasting is an important prerequisite for stable electricity system operation. In this paper, it is found that daily and weekly variations are prominent by the power spectrum analysis of the historical loads collected hourly in Tai'an, Shandong Province, China. In addition, the influence of the extraneous variables is also very obvious.

The Short-Term Load Forecasting for Special Days Based on Bagged Regression Trees in Qingdao, China.

There are many factors that affect short-term load forecasting performance, such as weather and holidays. However, most of the existing load forecasting models lack more detailed considerations for some special days. In this paper, the applicability of the bagged regression trees (BRT) model combined with eight variables is investigated to forecast short-term load in Qingdao.