## 1 Introduction
There are usually three ways to deal with such high-dimensional problems: one is to simplify the calculation of the inverse of the correlation matrix by dividing the high-dimensional space into several subspaces, and then build a high-dimensional model through integration; one is to improve the efficiency of Kriging modeling by reducing the calculation time of hyper-parameters under the condition that the dimensionality does not change; the other way is to establish a Kriging approximation model after dimensionality reduction. Applying gradient enhancement Kriging (GEK) [23; 24; 25; 26] using cheap gradient information to solve high-dimensional problems can effectively enhance the accuracy of the Kriging model. To this end, solving the large correlation matrices problem that affects the GEK models applied to high-dimensional problems enables GEK to be efficient and accurate. For example, the weighted gradient enhancement Kriging method [27] reduces the time spent decomposing large correlation matrices in high-dimensional gradient enhancement Kriging by establishing a series of sub-models with smaller correlation matrices and integrating into these sub-models appropriate weight coefficients. [PERSON] et al. proposed a screening-based gradient-enhanced Kriging modeling method [28], which uses feature selection technology to evaluate and rank the impact of each input variable on the output, and proposes empirical screening criteria to select the gradient, and finally uses the selected partial gradient to construct the Kriging model, thereby improving the modeling efficiency of high-dimensional problems. By combining recursive decomposition and sequential sampling for the establishment of accurate Kriging problems in high-dimensional spaces, [PERSON] et al. [29] perform variable decomposition using an interactive estimation of the full-dimensional Kriging meta-model, and divide the whole space into several subspaces according to the result of variable decomposition. The conversion from high-dimensional space sampling to low-dimensional space sampling is realized in each subspace. [PERSON] et al. [30; 31] proposed a method (KPLS) whereby the partial least squares (PLS) technique is combined with the Kriging model. This method uses the least squares dimensionality reduction method in the process of establishing the Kriging model, which reduces the number of hyper-parameter calculations of the model to be consistent with the number of principal components retained by the PLS, thereby accelerating the construction of the Kriging model. [PERSON] et al. [32] combined KPLS and GEK to propose a new GE-KPLS method. It adds gradient information to the correlation matrix. Although the size of the correlation matrix is slightly increased, it greatly reduces the number of hyper-parameter calculations. [PERSON] et al. [33] proposed a new Kriging modeling method (KMIC)that combines Kriging and the maximum information coefficient (MIC). This method uses the MIC to estimate the relative size of hyper-parameters according to the characteristics of the hyper-parameters after optimization. Then, the maximum likelihood estimation is reconstructed to reduce the calculation amount of hyper-parameter estimation. A distance correlation-based Kriging modeling method (KDIC) [34], which is somewhat similar to the KMIC method, uses distance correlation (DIC) to estimate the relative size of the hyper-parameters in the new correlation function, and transforms the hyper-parameter tuning process into a one-dimensional optimization problem. For the dimensionality reduction methods used to improve modeling efficiency, [PERSON] et al. [35] used Sammon mapping [36] to transform the training data from the original space to the lower dimensional space by minimizing the distance error between the sample points in the two data sets before and after dimensionality reduction to achieve the purpose of dimensionality reduction. However, this mapping method does not consider the relationship between input and response when reducing dimensionality. [PERSON] et al.