<p>This study investigates entropy optimization in a six-constant Jeffrey fluid through a divergent asymmetric channel in the inclusion of viscous dissipation and microorganisms. The governing nonlinear partial differential equations are systematically reduced to an equivalent system of ordinary differential equations for simplified analysis under the assumptions of lubrication approximations and Debye-Hückel linearization using suitable dimensionless variables. The resulting nonlinear ordinary differential equations (ODEs) are addressed via a well-known semi-analytic approach called the homotopy perturbation method, which converts them into linear perturbed subproblems. These subproblems are then solved using the DSolve command in Mathematica to obtain symbolic solutions for velocity, concentration, temperature, and bioconvection. The expressions for these quantities are Visualized across various physical parameters for comprehensive analysis. Furthermore, data extracted from these profiles are used to train an artificial neural network (ANN) model, which is implemented in a Python environment supported by TensorFlow 2.17. The ANN model consists of one input layer, two hidden layers with 100 neurons each, and an output layer. The Adam optimizer is used, with the tanh activation function applied in the hidden layers. The efficiency and precision of the ANN model are evaluated using performance metrics such as mean squared error (MSE), regression coefficient (R²), error histograms, validation, and relative error. The ANN demonstrates high accuracy in predicting non-linear patterns within the complex rheology of the six-constant Jeffrey fluid. The findings of this study indicate that the non-Newtonian rheology of the six-constant Jeffrey fluid is significantly influenced by electro-osmotic velocity and the magnetic field within the complex tapered channel. This work has significant applications in the development of microfluidic systems and targeted drug delivery in biomedical engineering.</p>