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.

在当前的研究中，一种基于人工神经网络遗产的新型智能数值计算范式已经实施，涉及贝叶斯正则化 (ANN-BR) 方法，用于研究生物对流的非均匀热关注过程。涉及回旋微生物的纳米材料的流动动力学。通过探索适当的转换，最初由 PDE 系统表示的设计的生物对流分层纳米流体流 (BCSNF) 模型被转换为非线性 ODE。BCSNF 模型的参考数据集是通过亚当斯数值方法通过磁数、布朗运动参数、普朗特数、生物对流路易斯数、热泳参数和生物对流佩克莱特数的变化，通过亚当斯数值方法生成的。通过所设计的 ANN-BR 方案的测试、训练和验证过程，以 5-7 位小数精度确定近似解并解释为 BCSNF 模型。为了检查引入的 ANN-BR 方法的效率，绝对误差分析、直方图研究、回归指数和基于均方误差 (MSE) 的品质因数被详尽地用于解决涉及陀螺战术微生物的 BCSNF 模型的变体粘性耗散、分层和热浸，以研究突出参数对速度、温度、浓度和运动密度分布的影响。