Design of a hybrid NAR-RBFs neural network for nonlinear dusty plasma system

Abstract

Robust modeling of a multimodal dynamic system is a challenging and fast-growing area of research. In this study, an integrated bi-modal computing paradigm based on Nonlinear Autoregressive Radial Basis Functions (NAR-RBFs) neural network model, a new family of deep learning with the strength of hybrid artificial neural network, is presented for the solution of nonlinear chaotic dusty system (NCDS) of tiny ionized gas particles arising in fusion devices, industry, astronomy, and space. In the proposed methodology, special transformations are introduced for a class of differential equations, which convert the local optimum to a global optimum. The proposed NAR-RBFs neural network model is implemented on bi-model NCDS represented with Van der Pol-Methiew Equation (VdP-ME) for different scenarios based on variation in dust gain production and loss for both small and large time domains. Excellent agreement for proposed bimodal computing paradigm by the result with the standard state of the arts numerical solvers is verified by attaining RMSE up to 1E−38 for the nonlinear VDP-ME. Accuracy of the proposed model in the critical time domain is also validated by convergence, stability and consistency analysis on statistics calculated from absolute error, root-mean-square error, and analysis of variance metrics.

Keywords

• Artificial neural network
• NAR model
• Radial basis functions: Levenberg-Marquardt Algorithm