Finite-element-based machine-learning algorithm for studying gyrotactic-nanofluid flow via stretching surface

The Levenberg-Marquardt algorithm with back-propagated neural network (BLM-NN) based on machine learning is used in a dynamic fashion in this study to examine the 2D boundary layer flow of a nanofluid comprising gyrotactic microorganisms flowing across a stretchable vertically inclined surface (NGM-ISSFM), immersed in a porous medium. An extensively verified finite-element method (FEM) is used to produce the reference data set for BLM-NN by altering five crucial parameters of the flow model in MATLAB. The main objective of this innovative approach is to minimize longer execution times (for larger number of elements) and more expensive digital computer requirements that are the key barriers to opting the FEM, and in order to obtain the entire function instead of the discrete solution that other numerical methods typically produce. To estimate the NGM-ISSFM model's result for diverse scenario, BLM-NN is trained, tested, and validated. Several BLM-NN implementations using MSE-based indices have shown the performance's veracity and validity through descriptive statistics. The results show that when the Prandtl number increases, the temperature profile and density profile of microorganisms fall dramatically, implying that a fluid with a low Prandtl number is required to enhance the rate of heat transmission.