Analyzing the effects of various isotropic and anisotropic kernels on critical heat flux prediction using Gaussian process regression

The critical heat flux (CHF) is an important parameter determining the heat transfer capability of nuclear reactors. Therefore, prediction of CHF with accuracy and correct understanding is essential for the design and safety analysis of nuclear power plants (NPPs) and industrial boiling systems. This paper focuses on the CHF prediction using the Gaussian process regression (GPR), a machine learning (ML) technique for modeling nonlinear systems. The covariance kernel is a critical component of GPR modeling because it contains assumptions about the function we want to know and defines the dependence and similarity between the data. In this study, the prediction of CHF is investigated during training and prediction in two different approaches: isotropic and anisotropic covariance kernels. Besides, we evaluate the influence of various isotropic and anisotropic kernels on the accuracy of CHF prediction and quantification of uncertainty encoded in the posterior variances in each of the approaches. The use of anisotropic kernels, considering different shape parameters in line with different data dimensions, results in higher accuracy and better generalization. In addition, compared to other ML tools such as support vector regression (SVR) and artificial neural networks (ANNs), the GPR with anisotropic kernels has much better performance. The evaluation criteria involving root mean square error (RMSE) and mean absolute percentage error (MAPE) in anisotropic kernels are significantly improved compared to isotropic kernels. For example, in squared exponential and rational quadratic kernels, RMSE and MAPE values improved by {65.81%, 67.28%} and {61.97%, 60.12%} values, respectively. The results of the GPR method with the anisotropic kernels show the relative superiority of this method compared to SVR and ANN. The lowest RMSE and MAPE values of all three methods were compared, and these values have improved in GPR compared to SVR by 96.01% and 94.25% and compared to ANN by 84.40% and 85.51%, respectively. Finally, some valuable ideas and practical findings will be offered based on numerical simulations and comparisons between isotropic and anisotropic kernel assumptions. Since the approach of using anisotropic kernels has high computational time despite its high flexibility, we will address this issue in future studies and also use this approach for other nuclear engineering problems.