Machine-learning model for nanofluid hemodynamics in stenotic arteries using Bayesian regularization

• Computational process of the blood nanofluid model (BNM) in stenotic arteries is studied. • It is proposed to resolve the model utilizing a deep neural network (DNN) with fifteen and thirty neurons. • The optimization of the Levenberg-Marquardt backpropagation (LMB) is carried out to solve the BNM. • Thes level of discretization of the statistical performances is decided to decrease the nonlinear BNM mean square error. The study presents a computational framework based on machine learning for the study of blood nanofluid flow and heat transmission via stenotic arteries. Calculation of the velocity and temperature fields that couple together for the system of blood nanofluid is done using a new form of a hyperbolic tangent sigmoid transfer function (HTSTF). This new HTSTF is applied in combination with the Navier–Stokes equations to solve the nonlinear model using a deep neural network (DNN) made up of two hidden layers with 30 and 30 neuron count for those layers, respectively. DNN is trained using Bayesian regularization and the Levenberg–Marquardt back propagation method. A valid set of data is created using bvp4c (two-point boundary value problem), which is broken down into a training (15%), testing (13%) and validation (72%) data set. The new approach has both very good convergence and very good accuracy; the sample's generated mean square error (MSE) values are 10 -12 to 10 -9 and absolute error values are as small as 10 -7 . The sample also shows that there is good correspondence between predicted and reference solutions (for both velocity and temperature) based on statistical regression results. Nanoparticles' volume fraction greatly affects blood's rheological behaviour as well as heat transfer through the stenosed portion of a vessel. This new method is far more efficient and accurate than standard numerical methods and has potential applications within cardiovascular (CV) diagnostics, targeted drug delivery (TDL), and thermal therapies using nanoparticles.