Study of Nonlinear Models of Oscillatory Systems by Applying an Intelligent Computational Technique.

In this paper, we have analyzed the mathematical model of various nonlinear oscillators arising in different fields of engineering. Further, approximate solutions for different variations in oscillators are studied by using feedforward neural networks (NNs) based on the backpropagated Levenberg-Marquardt algorithm (BLMA). A data set for different problem scenarios for the supervised learning of BLMA has been generated by the Runge-Kutta method of order 4 (RK-4) with the "NDSolve" package in Mathematica. The worth of the approximate solution by NN-BLMA is attained by employing the processing of testing, training, and validation of the reference data set. For each model, convergence analysis, error histograms, regression analysis, and curve fitting are considered to study the robustness and accuracy of the design scheme.

Mathematical Analysis of Reaction-Diffusion Equations Modeling the Michaelis-Menten Kinetics in a Micro-Disk Biosensor.

In 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.

VLSI Implementation of a High-Performance Nonlinear Image Scaling Algorithm.

This study implements the VLSI architecture for nonlinear-based picture scaling that is minimal in complexity and memory efficient. Image scaling is used to increase or decrease the size of an image in order to map the resolution of different devices, particularly cameras and printers. Larger memory and greater power are also necessary to produce high-resolution photographs. As a result, the goal of this project is to create a memory-efficient low-power image scaling methodology based on the effective weighted median interpolation methodology. Prefiltering is employed in linear interpolation scaling methods to improve the visual quality of the scaled image in noisy environments. By decreasing the blurring effect, the prefilter performs smoothing and sharpening processes to produce high-quality scaled images. Despite the fact that prefiltering requires more processing resources, the suggested solution scales via effective weighted median interpolation, which reduces noise intrinsically. As a result, a low-cost VLSI architecture can be created. The results of simulations reveal that the effective weighted median interpolation outperforms other existing approaches.

Application of Euler Neural Networks with Soft Computing Paradigm to Solve Nonlinear Problems Arising in Heat Transfer.

In this study, a novel application of neurocomputing technique is presented for solving nonlinear heat transfer and natural convection porous fin problems arising in almost all areas of engineering and technology, especially in mechanical engineering. The mathematical models of the problems are exploited by the intelligent strength of Euler polynomials based Euler neural networks (ENN's), optimized with a generalized normal distribution optimization (GNDO) algorithm and Interior point algorithm (IPA). In this scheme, ENN's based differential equation models are constructed in an unsupervised manner, in which the neurons are trained by GNDO as an effective global search technique and IPA, which enhances the local search convergence. Moreover, a temperature distribution of heat transfer and natural convection porous fin are investigated by using an ENN-GNDO-IPA algorithm under the influence of variations in specific heat, thermal conductivity, internal heat generation, and heat transfer rate, respectively. A large number of executions are performed on the proposed technique for different cases to determine the reliability and effectiveness through various performance indicators including Nash-Sutcliffe efficiency (NSE), error in Nash-Sutcliffe efficiency (ENSE), mean absolute error (MAE), and Thiel's inequality coefficient (TIC). Extensive graphical and statistical analysis shows the dominance of the proposed algorithm with state-of-the-art algorithms and numerical solver RK-4.