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. Numerical experiments clearly demonstrate that the PIMNs can capture the nonlinear features of rogue waves solutions very well. This is of great significance for revealing the dynamical behavior of the rogue waves solutions and advancing the application of deep learning in the field of solving partial differential equations.

N-Acetylglucosamine Promotes Tomato Plant Growth by Shaping the Community Structure and Metabolism of the Rhizosphere Microbiome.

Communication between plants and microorganisms is vital because it influences their growth, development, defense, propagation, and metabolism in achieving maximal fitness. N-acetylglucosamine (N-GlcNAc), the building block of bacterial and fungal cell walls, was first reported to promote tomato plant growth via stimulation of microorganisms typically known to dominate the tomato root rhizosphere, such as members of Proteobacteria and Actinobacteria. Using KEGG pathway analysis of the rhizosphere microbial operational taxonomic units, the streptomycin biosynthesis pathway was enriched in the presence of N-GlcNAc. The biosynthesis of 3-hydroxy-2-butanone (acetoin) and 2,3-butanediol, two foremost types of plant growth promotion-related volatile organic compounds, were activated in both Bacillus subtilis and Streptomyces thermocarboxydus strains when they were cocultured with N-GlcNAc. In addition, the application of N-GlcNAc increased indole-3-acetic acid production in a dose-dependent manner in strains of Bacillus cereus, Proteus mirabilis, Pseudomonas putida, and S. thermocarboxydus that were isolated from an N-GlcNAc-treated tomato rhizosphere. Overall, this study found that N-GlcNAc could function as microbial signaling molecules to shape the community structure and metabolism of the rhizosphere microbiome, thereby regulating plant growth and development and preventing plant disease through complementary plant-microbe interactions. IMPORTANCE While the benefits of using plant growth-promoting rhizobacteria (PGPRs) to enhance crop production have been recognized and studied extensively under laboratory conditions, the success of their application in the field varies immensely. More fundamentally explicit processes of positive, plant-PGPRs interactions are needed. The utilization of organic amendments, such as chitin and its derivatives, is one of the most economical and practical options for improving soil and substrate quality as well as plant growth and resilience. In this study, we observed that the chitin monomer N-GlcNAc, a key microbial signaling molecule produced through interactions between chitin, soil microbes, and the plants, positively shaped the community structure and metabolism of the rhizosphere microbiome of tomatoes. Our findings also provide a new direction for enhancing the benefits and stability of PGPRs in the field.

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. At the same time, the different PINNs are applied to learn the same initial data by selecting the different numbers of initial points sampled, residual collocation points sampled, network layers, and neurons per hidden layer, respectively. The result shows that the PINNs well reconstruct the dynamical behaviors of the quasiperiodic wave, periodic wave, and soliton solutions for the KdV-mKdV equation, which gives a good way to simulate the solutions of nonlinear partial differential equations via one deep learning method.

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. For example, the load dropped significantly for a long period of time during the Chinese Lunar Spring Festival. Therefore, an artificial neural network model is constructed with six periodic and three nonperiodic factors. The load from January 2016 to August 2018 was divided into two parts in the ratio of 9 : 1 as the training set and the test set, respectively. The experimental results indicate that the daily prediction model with selected factors can achieve higher forecasting accuracy.