In this study, three machine learning techniques and RBF interpolation are compared on a heat transfer and fluid flow problem in a cavity having rounded corner through the left bottom corner. The two dimensional, time dependent dimensionless governing equations of the problem are numerically solved by the radial basis function (RBF) method for space derivatives and by the backward Euler method for time derivatives. The differentially heated cavity has straight hot left wall and cold right wall, the top wall is the adiabatic wall and the bottom wall involving the rounded corner is the insulated wall. The numerical results show that the presence of the rounded corner causes convective heat transfer to increase. A dataset involving inputs as Rayleigh number and the radius of the circular corner and output as the average Nusselt number along the hot left wall is collected from the numerical results. The machine learning techniques, neural networks, gaussian process regression and ensemble learning as well as RBF interpolation are deployed for modeling. Each modeling results in small mean squared error metric results, but the best modeling is found by RBF interpolation.

In this study, neural network modeling on a bioconvection flow problem is utilized. The data is collected from the numerical computations. The dimensionless governing equations of Cu-water nanofluid flow in a square cavity involving oxytactic bacteria under the effect of a magnetic source are numerically solved by radial basis function collocation method. In various values of Rayleigh, bioconvection Rayleigh, Peclet, Hartmann, magnetic numbers and coordinates of location of magnetic source, an iterative system is executed, and the outputs, average Nusselt and Sherwood numbers, density and the mean of bacteria are stored with the associated computed parameter values. The dataset of size 3645 × 11 created by this way is used for neural network modeling. The different train-test set sizes as well as the number of hidden layers, the layer sizes are controlled. In the light of mean squared error metric results, the obtained models show that the one layer neural network using small number of neurons also give good results. These models allow one to get prompt results instead of many times repeated numerical calculations.

Abstract In this study, neural network (NN) and curve fitting modeling of fluid flow characteristics of the magnetohydrodynamic (MHD) Stokes flow in a lid-driven cavity are utilized. Firstly, the MHD Stokes flow equations are numerically solved by the method of approximate particular solution for the variations of Hartmann number $$M\in [1,120]$$ M ∈ [ 1 , 120 ] and the inclination angle $$a \in [0, \pi ]$$ a ∈ [ 0 , π ] . The essential data for modeling are extracted from the numerical results. The inputs are M and a, and the outputs are the infinity norm of stream function $$\psi$$ ψ , v velocity component, vorticity $$\omega$$ ω and the minimum value of u velocity. In modeling of these outputs, the distinct curve fitting functions are examined. NN is employed for different layer numbers and data partitions. It is obtained that the increase in the number of the hidden layers gives less error and locally weighted quadratic regression fit captures the best behavior in curve fitting. The usage of modeling allows us to be independent from the repeated numerical calculations. The capability of trilayer NN for modeling $$\psi ,u,v,\omega$$ ψ , u , v , ω in the entire region is also shown.

In this study, the trilayer neural network (TNN) is generated for the prediction of some chosen problem variables of Stokes flow in a lid-driven cavity subjected to the uniform magnetic field with an inclination angle for the first time. The data set to develop TNN model of magnetohydrodynamics (MHD) Stokes flow is gathered from the numerical results. The method of approximate particular solution (MAPS) is employed to the nondimensional governing equations which are comprised of the Navier-Stokes equations and Maxwell equations neglecting the convective terms. The numerical outcomes are obtained for several values of Hartmann number in [0,100] and the inclination angle in [0,π]. In TNN model, the input variables are Hartmann number and inclination angle of magnetic field, and the output variables are the norm of stream function and v velocity component, the minimum value of u velocity and the norm of vorticity. It is shown that TNN model gives the efficient predictions of velocity indicators of Stokes flow.