In this study, the unsteady squeezing flow between infinite parallel plates (USF-IPP) is investigated through the intelligent computing paradigm of Levenberg-Marquard backpropagation neural networks (LMBNN). Similarity transformation introduces the fluidic system of the governing partial differential equations (PDEs) into nonlinear ordinary differential equations (ODEs). A dataset is generated based on squeezing fluid flow system USF-IPP for the LMBNN through the Runge-Kutta method by the suitable variations of Reynolds number and volume flow rate. TO attain approximation solutions for USF-IPP to different scenarios and cases of LMBNN, the operations of training, testing, and validation are prepared and then the outcomes are compared with the reference data set to ensure the suggested model's accuracy. The output of LMBNN is discussed by the mean square error, dynamics of state transition, analysis of error histograms, and regression illustrations.