Artificial neural network algorithm for time dependent radiative Casson fluid flow with couple stresses through a microchannel

Abstract

Artificial neural network due to its versatile applications is used in various domains. It helps in analysing large datasets which might be difficult to accomplish by conventional models. They help in modelling and analysing complex fluid flow problems and when properly trained they help in predicting the flow structures. Thus, this study focuses on constructing an artificial neural network design to solve mathematical problem of Casson fluid flow in the presence of non-linear radiation and a magnetic field. The study focuses on the flow that changes with time in a microchannel, resulting in partial differential equations that are computed with the help of finite difference approach. The occurrence of irreversibility in the medium is analysed in relation to the flow, and a neural network model is developed. The numerical results indicate that the irreversibility produced in the medium increases as the radiation parameter and temperature difference parameter increase. The mean squared error values achieved for all the scenarios fall within the range of $e^{-12}$ to $e^{-8}$, indicating the successful interpretation of the neural network model constructed in tight correlation with the target data. Gradient descent was performed within the range of $e^{-8}$, and the error histograms have the lowest values within the range of $e^{-8}$ to $e^{-6}$. The regression analysis and plotfit demonstrate a high degree of concordance between the data points for training, testing, and validation, with an approximate correlation coefficient $\approx 1$. An investigation of absolute error conducted for various parameters reveals that the errors fall within the range of ${10}^{-4}$ to ${10}^{-5}$.