Deep learning applications in radiative magnetohydrodynamic bioconvection within a vertical wavy porous structure

This study provides an in-depth analysis of the combined effects of spatially stationary surface waves, fluid inertia, and thermal radiation on natural convection along a heated vertical wavy surface. The surface is embedded within a porous medium saturated with an electrically conducting fluid while also examining the intricate dynamics of magnetohydrodynamic (MHD) bioconvection. Conducted within the boundary layer regime at a high Darcy–Rayleigh number, the research employs a coordinate transformation to reformulate the governing boundary layer equations into a nonsimilar form. The nonlinear and coupled differential equations are solved using the advanced framework of deep learning, specifically through physics-informed neural networks (PINNs). The study investigates the impact of critical factors such as learning rates, neuron configurations, boundary conditions, activation functions, and the number of collocation and training data points on the convergence rate and accuracy of PINNs. Additionally, it analyzes the behavior of the loss function and residuals at various data points. Comprehensive histograms are generated to illustrate the dimensionless velocity, temperature, concentration, and motile micro-organism density. Furthermore, the study evaluates the influence of key physical parameters on the local Nusselt and Sherwood numbers, as well as the motile micro-organism density number. By leveraging deep learning techniques, this work provides valuable insights into the dynamics of natural convection and MHD bioconvection, demonstrating the efficacy of PINNs in modeling complex heat, mass, and micro-organism transfer phenomena in porous media under the influence of thermal radiation.