Artificial neural networks (ANNs) in an Electroosmosis-Controlled Darcy-Forchheimer flow for the Casson nanofluid model over stretching sheet

•To study the dynamics of Electroosmosis-Controlled Darcy-Forchheimer flow model, ANN-optimized with the Levenberg-Marquardt backpropagation (LMBP) algorithm is employed.•The bvp-4c numerical solver’s capability is utilized to generate data samples that are used to test, validate, and train LMBP-NNs.•For this model, the usefulness of the computing stochastic technique is verified by the exact and persistent overlapping of the numerical results in good agreement with standard solutions with slight absolute error (AE).•The consistency and reliability of the created LMBP-NNs to solve the Electroosmosis- Controlled Darcy-Forchheimer flow model are approved by the presentations of the regression, MSE, EHs, correlation, and STs. This study explores the intelligent computational capability of neural networks constructed on the Levenberg-Marquardt backpropagation (LMBP-NNs) neural networks methodology for the simulation of the Darcy-Forchheimer flow of the Casson nanofluid across a stretching sheet. Studying the effects of electroosmosis forces (EOF) regarding the Casson nanofluid boundary layer’s viscosity along with Joule dissipation is being done. With the appropriate degree of similarity, the approach converts partial differential equations from nanofluidic systems towards nonlinear differential equation systems. The non-linear nanofluid issue is solved by means of the (FDM) finite difference methodology (Lobatto IIIA) with a precision of order 4 to 5. The method transforms partial differential equations originating in nanofluidic systems into nonlinear differential equation systems with the proper degree of similarity. With a precision of order 4 to 5, the nonlinear nanofluid problem is solved using the (FDM) finite difference approach (Lobatto IIIA), which is accomplished using a number of collocation locations. The ability of Lobatto IIIA to handle coupled differential equations that are very nonlinear is one of its strengths. The boundary value dilemma (bvp4c) solver, which is a component of the MATLAB software programme, is used to reduce the higher order differential equations into a first order technique and computationally analyze the simplified mathematical model. The exact results of (FDM) are used to build the reference datasets for the LMBP-NNs technique for the different parts of the fluid issue. The design strategy covers a series of actions based on training, testing, and authentication using a reference dataset for various fluid problem compone