Browsing by Author "Laouini, Ghaylen"
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Item Mathematical analysis of reaction–diffusion equations modeling the michaelis–menten kinetics in a micro-disk biosensor(2021) Khan, Naveed Ahmad; Alshammari, Fahad Sameer; Tavera Romero, Carlos Andrés; Sulaiman, Muhammad; Laouini, GhaylenIn this study, we have investigated the mathematical model of an immobilized enzyme system that follows the Michaelis–Menten (MM) kinetics for a micro-disk biosensor. The film reaction model under steady state conditions is transformed into a couple differential equations which are based on dimensionless concentration of hydrogen peroxide with enzyme reaction (H) and substrate (S) within the biosensor. The model is based on a reaction–diffusion equation which contains highly non-linear terms related to MM kinetics of the enzymatic reaction. Further, to calculate the effect of variations in parameters on the dimensionless concentration of substrate and hydrogen peroxide, we have strengthened the computational ability of neural network (NN) architecture by using a backpropagated Levenberg–Marquardt training (LMT) algorithm. NNs–LMT algorithm is a supervised machine learning for which the initial data set is generated by using MATLAB built in function known as “pdex4”. Furthermore, the data set is validated by the processing of the NNs–LMT algorithm to find the approximate solutions for different scenarios and cases of mathematical model of micro-disk biosensors. Absolute errors, curve fitting, error histograms, regression and complexity analysis further validate the accuracy and robustness of the technique.Item Study of Rolling Motion of Ships in Random Beam Seas with Nonlinear Restoring Moment and Damping Effects Using Neuroevolutionary Technique(MDPI, 2022) Khan, Naveed Ahmad; Sulaiman, Muhammad; Tavera Romero, Carlos Andrés; Laouini, Ghaylen; Alshammari, Fahad SameerIn this paper, a mathematical model for the rolling motion of ships in random beam seas has been investigated. The ships’ steady-state rolling motion with a nonlinear restoring moment and damping effect is modeled by the nonlinear second-order differential equation. Furthermore, an artificial neural network (NN)-based, backpropagated Levenberg-Marquardt (LM) algorithm is utilized to interpret a numerical solution for the roll angle (x(t)), velocity (x′ (t)), and acceleration (x′′ (t)) of the ship in random beam seas. A reference data set based on numerical examples of the mathematical model for a rolling ship for the LM-NN algorithm is generated by the numerical solver Runge–Kutta method of order 4 (RK-4). The LM-NN algorithm further uses the created data set for the validation, testing, and training of approximate solutions. The outcomes of the design paradigm are compared with those of the homotopy perturbation method (HPM), optimal homotopy analysis method (OHAM), and RK-4. Statistical analyses of the mean square error (MSE), regression, error histograms, proportional performance, and computational complexity further validate the worth of the LM-NN algorithm.