A novel machine learning approach to analysis of electroosmotic effects and heat transfer on Multi-phase wavy flow

Abstract

Abstract In this contribution, a novel hybrid approach involving artificial neural networks (ANNs) and heuristic algorithms is employed for Hall currents and electromagnetic effects analysis for a multi-phase wavy flow. The governing partial differential equations (PDEs) for flow dynamics are reduced into a corresponding system of ordinary differential equations (ODEs) with a pertinent transformation technique. The novelty of this work is combination of Morlet wavelet and hyperbolic tangent (Tanh) functions is employed as an activation function in artificial neural networks (ANNs) to effectively capture nonlinear behavior for flow dynamics. The novel effective Morlet wavele Tanh neural networks (MTNNs) based fitness function is formulated for solution estimation of the model. The weights and biases of MTNNs are optimized with a global searching technique by particle swarm optimization (PSO). Numerical solution of ODEs is also obtained through Python physics informed neural networks (PINNs) with Adam optimizer for validation of the proposed solutions. Statistical analysis involving histogram visualizations, probability plots, and boxplots is performed for accuracy, robustness, convergence, and stability evaluation of the proposed solution with respect to crucial error measures such as cost function, absolute error, and mean squared error (MSE). The MSE values for velocity and temperature range from $$\:{10}^{-07}$$ to $$\:{10}^{-09}$$ and $$\:{10}^{-06}$$ to $$\:{10}^{-09}$$ , respectively. Graphical analysis reveals that flow velocity and thermal distributions are influenced directly by electroosmotic factor but are affected inversely with the applied magnetic field. The proposed MTNNs yield results that closely align with those obtained using PINNs.