Bayesian regularization optimization technique for hybrid nanofluid with Cattaneo Christov flux model using wax and sand nanoparticles

Machine learning approaches, such as neural networks and data-driven regression frameworks, provide a viable alternative to classical computational fluid dynamics (CFD) by rapidly predicting velocity, pressure, and temperature fields in complex flow scenarios. These methods are very useful for the design and optimization of heat transfer devices, aerodynamic components, and energy-efficient flow systems since they drastically lower computational cost without sacrificing predictive dependability. Furthermore, ML-based models that are trained on high-resolution datasets—like those produced by Direct Numerical Simulation (DNS)—improve turbulence modeling skills and have the potential to outperform conventional turbulence closures in terms of prediction. ML advances fluid flow analysis in applications ranging from aerodynamic optimization to industrial cooling systems by identifying crucial factors that maximize efficiency and minimize energy losses. Ahmad et al. [ 1 ] deliberate the innovation modeling of penta HNF (hybrid nanofluid) flow for improving the transportation of heat in a spatially dependent magnetic field. Shah et al. [ 2 ] evaluated hydromagnetic bioconvective NF dynamics with gyrotactic microbes using a Bayesian neural network–based machine learning framework. Ul-Haq et al. [ 3 ] applied an ANN framework to analyze the flow of dissimilar MHD nanofluid via a bent surface. Mingliang et al. [ 4 ] inspect the non‐linear electromagnetic fields on mixed convection thermal flux in complex hybrid nanofluid with microorganism dynamics: Novel supervised machine learning exogenous neural network. Shah et al. [ 5 ] analyzed a solar-energy-based mono-hybrid nanofluid model using multilayer neural network–driven machine learning techniques. Shafiq et al. [ 6 ] applied artificial neural networks to simulate Buongiorno-based convective transfer of a mono-nanofluid via a Riga wedge in a Darcy–Forchheimer permeable medium.Hussain et al. [ 7 ] evaluated the mathematical and artificial intelligence perspectives on unsteady squeezing micropolar nanofluid flow between two discs with multiple physical processes. Employing a recurrent neural network optimized via the Levenberg–Marquardt process, Mahariq et al. [ 8 ] studied thermal transmission in ternary hybrid nanofluids with nonlinear source–sink impacts. Okasha et al. [ 9 ] used a BR (Bayesian-regularization) optimizer DNN (deep neural network) to investigate the properties of Stefan blowing and heat radiation on a Williamson NF (nanofluid) with a TNE (thermal non-Equilibrium) consequence. The properties of temperature prediction of a stable NF (nanofluid) with the involvement of an antibacterial agent in a magnetized environment was examined by Khan et al. [ 10 ] using artificial neurons. In order to solve the convective flow of a THNF (trihybrid nanofluid) with LTNECs and heat radiation, Abbas et al. [ 11 ] inspected an ANN (artificial neural network) optimized by the BRA (Bayesian-regularization approach). Darvesh et al. [ 12 ] scrutinize the influence of inter-particle spacing and particle size on the thermal presentation of MHD copper NF (nanofluid) flow across a rectangular frame. Using Cattaneo–Christov theory, Hussein et al. [ 13 ] investigated the creation of ANNs (artificial neural networks) for the Darcy–Forchheimer flow of Boger HNF (hybrid nanofluid). The Bayesian regularization algorithm-based machine learning study for the bioconvection flow of Boger NF in the occurrence of gyrotactic bacteria: Shaaban et al. [ 14 ] examine enzyme-based biosensor uses. Ayub et al. [ 15 ] investigated the neural intelligence strategy for trihybrid cross bio-nanofluid heat transmission uses across wedge geometry. In order to maximize the nanoscale heat transmission of ternary magnetized NF over a 3D wedge, Alqudah et al. [ 16 ] examine the neural network design. Using an ANN scheme, Shah et al. [ 17 ] inspected the characteristics of heat transmission and tilted MHD in a non-Newtonian THNF flow across a wedge-shaped artery. Using intelligent NNs, Ayub et al. [ 18 ] inspected thermal transportation in ternary radiative bio-nanofluids based on quadratic convection and magnetized.