# Sliced gradient-enhanced Kriging for high-dimensional function approximation

arXiv: https://arxiv.org/abs/2204.03562 · HTML: https://mlsanity.com/paper/2204.03562/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 50 references that are in the map.
- First posted on arXiv 5 Apr 2022.

## Builds on (most cited first, 3 of 3)

- [Physics-informed neural networks with hard constraints for inverse design](https://mlsanity.com/paper/2102.04626/) (2021)
- [Gradient-enhanced kriging for high-dimensional problems](https://mlsanity.com/paper/1708.02663/) (2017)
- [Global Sensitivity Analysis with Dependence Measures](https://mlsanity.com/paper/1311.2483/) (2013)

## Built on by (most cited first, 3 of 3)

- [GPLaSDI: Gaussian Process-based Interpretable Latent Space Dynamics Identification through Deep Autoencoder](https://mlsanity.com/paper/2308.05882/) (2023)
- [A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling](https://mlsanity.com/paper/2403.10748/) (2024)
- [A Tutorial Review of Bayesian Optimization with Gaussian Processes to Accelerate Stationary Point Searches](https://mlsanity.com/paper/2603.10992/) (2026)

## Abstract (arXiv)

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.