Levenberg–Marquardt-optimized multilayer neural network for data-driven modeling of coupled transport in MHD nanofluid flow between porous disks

INTRODUCTION: Nanofluid transport through porous channels has significant applications in chemical processing, electronic cooling, thermal management systems, biomedical devices, aerospace engineering, and energy conversion technologies. In the present investigation, the cheological behavior of MHD laminar nanofluid flow flow bet between two infinite parallel porous disks is analyzed. The effects of Activation energy, chemical reaction, Darcy porous-medium resistance, and motile microorganism bioconvection are incorporated to examine the coupled momentum, thermal, concentration, and microorganism transport. METHODOLOGY: Suitable similarity transformations convert the governing equations into a coupled system of nonlinear ordinary differential equations, which is subsequently solved using the MATLAB bvp4c boundary-value solver. The numerical solutions are subsequently employed to develop a Levenberg--Marquardt backpropagation neural network (LM-BPNN) surrogate prediction model. RESULTS AND DISCUSSION: The developed LM-BPNN accurately reproduces the numerical solutions with excellent predictive capability, demonstrating its suitability as a surrogate model for rapid parametric analysis. The velocity field increases with increasing Hartmann number and porous-medium parameter, whereas higher Prandtl number and chemical reaction reduce the temperature field. The motile microorganism density increases with increasing bioconvective Lewis number and Peclet number, while the Sherwood number and skin-friction coefficient decrease with increasing M. Furthermore, the Nusselt number improves by approximately 25% with increasing Hartmann number, whereas the motile microorganism density number increases by nearly 35% with increasing Le and Pe. CONCLUSION: The proposed LM-BPNN serves as a reliable and computationally efficient surrogate framework for predicting complex nonlinear transport phenomena while significantly reducing the computational cost associated with repeated numerical simulations.