<p>Radiative magnetohydrodynamic bioconvective transport of viscoelastic nanofluids in porous media is governed by strongly nonlinear and tightly coupled mechanisms that challenge conventional numerical solvers. Physics-informed neural networks (PINNs) offer a mesh-free alternative by embedding the governing conservation equations directly into the solution framework; however, their predictive capability is highly sensitive to hyperparameter selection, often leading to slow convergence and inconsistent accuracy. To address this limitation, a hybrid Reptile Search Algorithm (RSA)–optimized PINN is developed for the similarity equations describing upper-convected Maxwell nanofluid flow over an axially stretching cylinder in a Darcy–Forchheimer porous medium with thermal radiation and bioconvection effects. The RSA adaptively identifies optimal network hyperparameters, providing stable and consistent convergence and enabling reduction of the physics-based residuals to near machine-precision levels while avoiding premature convergence commonly observed in conventional training strategies. The optimized solutions are validated against a fourth-order collocation boundary-value solver, demonstrating excellent agreement for velocity, temperature, nanoparticle concentration, and motile microorganism distributions. Comparative studies with PSO, GA, and Bayesian-optimized PINNs show that the RSA-based framework yields improved robustness, reduced solution variability, and enhanced numerical stability in handling the highly nonlinear transport system. Statistical assessments using MAE, RMSE, TIC, and ENSE further confirm the accuracy of the approach. The proposed RSA–PINN formulation therefore provides an efficient and reliable computational tool for simulating complex multiphysics heat and mass transfer in non-Darcy porous boundary-layer configurations.</p>

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A hybrid RSA-optimized PINN framework for radiative MHD bioconvection of an upper-convected Maxwell nanofluid over a stretching cylinder in a Darcy-Forchheimer medium

  • K. P. Risana,
  • A. David Maxim Gururaj

摘要

Radiative magnetohydrodynamic bioconvective transport of viscoelastic nanofluids in porous media is governed by strongly nonlinear and tightly coupled mechanisms that challenge conventional numerical solvers. Physics-informed neural networks (PINNs) offer a mesh-free alternative by embedding the governing conservation equations directly into the solution framework; however, their predictive capability is highly sensitive to hyperparameter selection, often leading to slow convergence and inconsistent accuracy. To address this limitation, a hybrid Reptile Search Algorithm (RSA)–optimized PINN is developed for the similarity equations describing upper-convected Maxwell nanofluid flow over an axially stretching cylinder in a Darcy–Forchheimer porous medium with thermal radiation and bioconvection effects. The RSA adaptively identifies optimal network hyperparameters, providing stable and consistent convergence and enabling reduction of the physics-based residuals to near machine-precision levels while avoiding premature convergence commonly observed in conventional training strategies. The optimized solutions are validated against a fourth-order collocation boundary-value solver, demonstrating excellent agreement for velocity, temperature, nanoparticle concentration, and motile microorganism distributions. Comparative studies with PSO, GA, and Bayesian-optimized PINNs show that the RSA-based framework yields improved robustness, reduced solution variability, and enhanced numerical stability in handling the highly nonlinear transport system. Statistical assessments using MAE, RMSE, TIC, and ENSE further confirm the accuracy of the approach. The proposed RSA–PINN formulation therefore provides an efficient and reliable computational tool for simulating complex multiphysics heat and mass transfer in non-Darcy porous boundary-layer configurations.