Novel Deep Learning Knowledge-Driven Supervised Backpropagated Recurrent Neural Networks for MHD Maxwell Hybrid Nanofluidic Model

Abstract

This study presents stochastic numerical computing paradigm of the Maxwell hybrid nanofluid (MHNF) with magnetohydrodynamic (MHD) effects using deep learning formation of artificial intelligence by exploiting layered recurrent neural networks backpropagated with Levenberg–Marquardt (LRNNs-LM) scheme. The intention of the present work is to offer better insight in to the dynamics of nanofluid by applying LRNNs-LM to produce numerical solution of the MHNF models, that is initially expressed with PDEs, and then transmuted into nonlinear ordinary ODEs using similarity transformations. The synthetic dataset for the MHNF model is numerically created for LRNNs-LM technique using Adams solver for varied physical quantities such as the magnetic parameter, radiation parameter, Prandtl number, and Eckert number. The designed deep neuro-structures of LRNNs-LM technique are implemented on the generated synthetic data to minimize the error and get the approximate solutions for several scenarios of MHNF system. The effectiveness of LRNNs-LM algorithm is verified through learning curves on mean square error, transition state index, fitness plots, error histogram, and regression analysis, intended for computational fluid dynamics of Maxwell hybrid nanofluid.