The current research aims to study the heat transfer rate in mixed convection flow of viscous fluid along a vertical cylinder containing swimming microorganisms and velocity slip effects. The thermal and solutal processes are examined using gyrotactic microorganisms, chemical reaction and slip conditions. The non-linear (PDEs) of the governing flow are transformed into set of highly nonlinear (ODEs) by employing appropriate similarity transformations, which are then resolved computationally by Runge-Kutta-Fehlberg 4th order toward with shooting approach. The predicted solution is derived using the Levenberg-Marquardt scheme combined with a backpropagation neural network (LMS-BPNN). The labelled data sheet is divided into three parts: 80% data is used for training, 10% for validation and 10% for testing. The performance of the proposed AI-based LMS-BPNN is examined in term of MSE for considered scenarios. An optimal solution is achieved at 675, 397, 727, 647, and 711, epochs, while performance in terms of MSE for these epochs is to be 1.06×E−9, 8.47×E−10, 9.20×10−9, 9.94×E−10,and 9.09×10−10. The assigned computational valuations and ANN valuations are in excellent alignment than those existing studies on numerous special cases. The predicted solution with AI-based technique LMS-BPNN is reliable, well-organized, and easy to handle the thermal and solutal transport analysis of flow across a stretchable cylinder. The validity of proposed LMS-BPNN algorithm is examined with absolute error analysis and error is found to be approximately 10−4.