Purpose

Kriging surrogate model has demonstrated a powerful ability to be applied to a variety of engineering challenges by emulating time-consuming simulations. However, when it comes to problems with high-dimensional input variables, it may be difficult to obtain a model with high accuracy and efficiency due to the curse of dimensionality. To meet this challenge, an improved high-dimensional Kriging modeling method based on maximal information coefficient (MIC) is developed in this work.

Design/methodology/approach

The hyperparameter domain is first derived and the dataset of hyperparameter and likelihood function is collected by Latin Hypercube Sampling. MIC values are innovatively calculated from the dataset and used as prior knowledge for optimizing hyperparameters. Then, an auxiliary parameter is introduced to establish the relationship between MIC values and hyperparameters. Next, the hyperparameters are obtained by transforming the optimized auxiliary parameter. Finally, to further improve the modeling accuracy, a novel local optimization step is performed to discover more suitable hyperparameters.

Findings

The proposed method is then applied to five representative mathematical functions with dimensions ranging from 20 to 100 and an engineering case with 30 design variables.

Originality/value

The results show that the proposed high-dimensional Kriging modeling method can obtain more accurate results than the other three methods, and it has an acceptable modeling efficiency. Moreover, the proposed method is also suitable for high-dimensional problems with limited sample points.

中文翻译：

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一种改进的利用最大信息系数的高维克里格建模方法

目的

克里金代理模型通过模拟耗时的模拟，展示了应用于各种工程挑战的强大能力。然而，当涉及高维输入变量的问题时，由于维数灾难，可能很难获得高精度和高效的模型。为了应对这一挑战，本文开发了一种基于最大信息系数（MIC）的改进高维克里格建模方法。

设计/方法论/途径

首先导出超参数域，并通过拉丁超立方采样收集超参数和似然函数的数据集。MIC 值是根据数据集创新地计算出来的，并用作优化超参数的先验知识。然后，引入辅助参数来建立MIC值和超参数之间的关系。接下来，通过对优化后的辅助参数进行变换得到超参数。最后，为了进一步提高建模精度，执行了一种新颖的局部优化步骤来发现更合适的超参数。

发现

然后将所提出的方法应用于维度范围从 20 到 100 的五个代表性数学函数以及具有 30 个设计变量的工程案例。

原创性/价值

结果表明，所提出的高维Kriging建模方法比其他三种方法可以获得更准确的结果，并且具有可接受的建模效率。此外，该方法还适用于样本点有限的高维问题。