The technique of Levenberg–Marquardt back propagation with neural networks (TLMB-NN) was used in this research article to investigate the heat transfer of Maxwell base fluid flow of nanomaterials (HTM-BFN) with MHD over vertical moving surfaces. In this study, the effects of thermal energy, concentration, and Brownian motion are also employed. Moreover, the impacts of a heat-absorbing fluid with viscous dissipation and radiation have been explored. To simplify the governing equations from a stiff to a simple system of non-linear ODEs, we exploited the efficacy of suitable similarity transformation mechanism. Through applicability of state-of-the-art Adams numerical technique, a set of data for suggested (TLMB-NN) is generated for several situations (scenarios) by changing parameters, such as the Thermophoresis factor N_t, Hartmann number M, Eckert number E_c, concentration Grashoff parameter G_c, Prandtl number P_r, Lewis number Le, thermal Grashof number G_T, and Brownian motion factor N_b. The estimate solution of different instances has validated using the (TLMB-NN) training, testing, and validation method, and the recommended model was compared for excellence. Following that, regression analysis, mean square error, and histogram explorations are used to validate the suggested (TLMB-NN). The proposed technique is distinguished based on the proximity of the proposed and reference findings, with an accuracy level ranging from 10⁻⁹ to 10⁻¹⁰.

The present study aims to design stochastic intelligent computational heuristics for the numerical treatment of a nonlinear SITR system representing the dynamics of novel coronavirus disease 2019 (COVID-19). The mathematical SITR system using fractal parameters for COVID-19 dynamics is divided into four classes; that is, susceptible (S), infected (I), treatment (T), and recovered (R). The comprehensive details of each class along with the explanation of every parameter are provided, and the dynamics of novel COVID-19 are represented by calculating the solution of the mathematical SITR system using feed-forward artificial neural networks (FF-ANNs) trained with global search genetic algorithms (GAs) and speedy fine tuning by sequential quadratic programming (SQP)—that is, an FF-ANN-GASQP scheme. In the proposed FF-ANN-GASQP method, the objective function is formulated in the mean squared error sense using the approximate differential mapping of FF-ANNs for the SITR model, and learning of the networks is proficiently conducted with the integrated capabilities of GA and SQP. The correctness, stability, and potential of the proposed FF-ANN-GASQP scheme for the four different cases are established through comparative assessment study from the results of numerical computing with Adams solver for single as well as multiple autonomous trials. The results of statistical evaluations further authenticate the convergence and prospective accuracy of the FF-ANN-GASQP method.