论文标题
切片梯度增强的kriging用于高维函数近似
Sliced gradient-enhanced Kriging for high-dimensional function approximation
论文作者
论文摘要
梯度增强的Kriging（GE-KRIGING）是一种公认的替代建模技术，用于近似昂贵的计算模型。但是，由于固有相关矩阵的大小和相关的高维高参数调音问题，因此对于高维问题而言，它往往会变得不切实际。为了解决这些问题，在本文中开发了一种称为切片的GE-Kriging（SGE-KRIGING）的新方法，用于减少相关矩阵的大小和超参数的数量。我们首先将设置的训练样本分为多个切片，并通过切片的似然函数调用贝叶斯定理，以近似完全的可能性函数，其中使用多个小相关矩阵来描述样品集的相关性而不是一个大型。然后，我们通过学习超参数与基于衍生的全球灵敏度指数之间的关系，将原始的高维高参数调音问题替换为低维的对应物。最终通过具有多个基准和高维空气动力学建模问题的数值实验来验证SGE-Kriging的性能。结果表明，SGE-Kriging模型具有准确性和鲁棒性，可与标准型相媲美，但培训成本却少得多。对于具有数十个变量的高维问题，最明显的好处是最明显的。
Gradient-enhanced Kriging (GE-Kriging) is a well-established surrogate modelling technique for approximating expensive computational models. However, it tends to get impractical for high-dimensional problems due to the size of the inherent correlation matrix and the associated high-dimensional hyper-parameter tuning problem. To address these issues, a new method, called sliced GE-Kriging (SGE-Kriging), is developed in this paper for reducing both the size of the correlation matrix and the number of hyper-parameters. We first split the training sample set into multiple slices, and invoke Bayes' theorem to approximate the full likelihood function via a sliced likelihood function, in which multiple small correlation matrices are utilized to describe the correlation of the sample set rather than one large one. Then, we replace the original high-dimensional hyper-parameter tuning problem with a low-dimensional counterpart by learning the relationship between the hyper-parameters and the derivative-based global sensitivity indices. The performance of SGE-Kriging is finally validated by means of numerical experiments with several benchmarks and a high-dimensional aerodynamic modeling problem. The results show that the SGE-Kriging model features an accuracy and robustness that is comparable to the standard one but comes at much less training costs. The benefits are most evident for high-dimensional problems with tens of variables.
