Intelligent Bayesian regularization networks for bio-convective nanofluid flow model involving gyro-tactic organisms with viscous dissipation, stratification and heat immersion

In the current study, a novel intelligent numerical computing paradigm based upon the foundation of the artificial neural networks legacy involving the Bayesian regularization (ANN-BR) approach has been implemented for the investigation of the non-uniform heat preoccupation process with the bio-convective flow dynamics of nanomaterial involving gyro-tactic microorganisms. The designed bio-convective stratified nanofluid flow (BCSNF) model initially represented by a system of PDEs is transformed into nonlinear ODEs by exploring appropriate transformations. The reference dataset for the BCSNF model was generated by the Adams numerical method for six scenarios by variation of the magnetic number, Brownian motion parameter, Prandtl number, bio-convection Lewis number, thermophoretic parameter, and bio-convection Peclet number. The approximate solutions were determined with 5-7 decimal places of accuracy and interpreted for the BCSNF model by the testing, training, and validation processes of the designed ANN-BR scheme. To check the efficiency of the introduced ANN-BR method, absolute error analysis, histogram studies, regression indices, and mean squared error (MSE) based figures of merit were used exhaustively to solve the variants of the BCSNF model involving gyro-tactic microorganisms with viscous dissipation, stratification, and heat immersion to study the influence of prominent parameters on the velocity, temperature, concentration, and motile density profiles.

Automated summary

A novel intelligent numerical computing paradigm based on the artificial neural networks with Bayesian regularization approach was implemented to study the non-uniform heat preoccupation process with bio-convective flow dynamics of nanomaterial involving gyro-tactic microorganisms. Extensive analysis of prominent parameters in the model was conducted using methods such as absolute error analysis, histogram studies, regression indices, and mean squared error (MSE) based figures of merit to investigate the impact on velocity, temperature, concentration, and motile density profiles.