Design of neuro-swarming computational solver for the fractional Bagley-Torvik mathematical model

A mathematical model of coronavirus transmission by using the heuristic computing neural networks

In this study, the nonlinear mathematical model of COVID-19 is investigated by stochastic solver using the scaled conjugate gradient neural networks (SCGNNs). The nonlinear mathematical model of COVID-19 is represented by coupled system of ordinary differential equations and is studied for three different cases of initial conditions with suitable parametric values. This model is studied subject to seven class of human population N(t) and individuals are categorized as: susceptible S(t), exposed E(t), quarantined Q(t), asymptotically diseased I_A (t), symptomatic diseased I_S (t) and finally the persons removed from COVID-19 and are denoted by R(t). The stochastic numerical computing SCGNNs approach will be used to examine the numerical performance of nonlinear mathematical model of COVID-19. The stochastic SCGNNs approach is based on three factors by using procedure of verification, sample statistics, testing and training. For this purpose, large portion of data is considered, i.e., 70%, 16%, 14% for training, testing and validation, respectively. The efficiency, reliability and authenticity of stochastic numerical SCGNNs approach are analysed graphically in terms of error histograms, mean square error, correlation, regression and finally further endorsed by graphical illustrations for absolute errors in the range of 10^-05 to 10^-07 for each scenario of the system model.

Neuro-swarm computational heuristic for solving a nonlinear second-order coupled Emden–Fowler model

The aim of the current study is to present the numerical solutions of a nonlinear second-order coupled Emden–Fowler equation by developing a neuro-swarming-based computing intelligent solver. The feedforward artificial neural networks (ANNs) are used for modelling, and optimization is carried out by the local/global search competences of particle swarm optimization (PSO) aided with capability of interior-point method (IPM), i.e., ANNs-PSO-IPM. In ANNs-PSO-IPM, a mean square error-based objective function is designed for nonlinear second-order coupled Emden–Fowler (EF) equations and then optimized using the combination of PSO-IPM. The inspiration to present the ANNs-PSO-IPM comes with a motive to depict a viable, detailed and consistent framework to tackle with such stiff/nonlinear second-order coupled EF system. The ANNs-PSO-IP scheme is verified for different examples of the second-order nonlinear-coupled EF equations. The achieved numerical outcomes for single as well as multiple trials of ANNs-PSO-IPM are incorporated to validate the reliability, viability and accuracy.