Time and solution error analysis of neural network model of (2+1)documentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$(2+1)$$end{document} dimensional wave equation

摘要

Series solution (SS) of (2+1)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$(2+1)$$end{document} dimensional wave equation has been represented by Neural Network (NN) model. Experiments have been performed to find a combination of NN structure and size of sample data such that error and time cost are the minimum. Error and time cost of NN models have been studied w.r.t structure, size of sample, random choice of initial weights and selection of data. Peak signal to noise ratio (PSNR) between series solution and solution by NN model is approximately 30 dB. This ensures that solution obtained by NN model is acceptable at human visual system. The average training time of constructed NN models is better than state-of-the-art related to solution of differential equation by NN. NN models are 18 times faster than series solution for solution prediction.