# Gradient-enhanced kriging for high-dimensional problems

arXiv: https://arxiv.org/abs/1708.02663 · HTML: https://mlsanity.com/paper/1708.02663/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Aug 2017.

## Built on by (most cited first, 15 of 15)

- [Machine Learning in Aerodynamic Shape Optimization](https://mlsanity.com/paper/2202.07141/) (2022)
- [SMT 2.0: A Surrogate Modeling Toolbox with a focus on Hierarchical and Mixed Variables Gaussian Processes](https://mlsanity.com/paper/2305.13998/) (2023)
- [High-dimensional mixed-categorical Gaussian processes with application to multidisciplinary design optimization for a green aircraft](https://mlsanity.com/paper/2311.06130/) (2023)
- [Model-data-driven constitutive responses: application to a multiscale computational framework](https://mlsanity.com/paper/2104.02650/) (2021)
- [Sliced gradient-enhanced Kriging for high-dimensional function approximation](https://mlsanity.com/paper/2204.03562/) (2022)
- [Bayesian Optimization of a Lightweight and Accurate Neural Network for Aerodynamic Performance Prediction](https://mlsanity.com/paper/2503.19479/) (2025)
- [Incorporating Prior Knowledge into Neural Networks through an Implicit Composite Kernel](https://mlsanity.com/paper/2205.07384/) (2022)
- [Digital Twin and Artificial Intelligence Incorporated With Surrogate Modeling for Hybrid and Sustainable Energy Systems](https://mlsanity.com/paper/2210.00073/) (2022)
- [Gradient-enhanced multifidelity neural networks for high-dimensional function approximation](https://mlsanity.com/paper/2103.12247/) (2021)
- [A Markov Reward Process-Based Approach to Spatial Interpolation](https://mlsanity.com/paper/2106.00538/) (2021)
- [Density reconstruction from schlieren images through Bayesian nonparametric models](https://mlsanity.com/paper/2201.05233/) (2022)
- [Gradient-enhanced deep Gaussian processes for multifidelity modelling](https://mlsanity.com/paper/2402.16059/) (2024)
- [Open-Source High-Speed Flight Surrogate Modeling Framework](https://mlsanity.com/paper/2411.03598/) (2024)
- [Optimization-Embedded Active Multi-Fidelity Surrogate Learning for Multi-Condition Airfoil Shape Optimization](https://mlsanity.com/paper/2603.17057/) (2026)
- [KT-EGO: A Knowledge Transfer Assisted Efficient Global Optimization Algorithm for Solving High-Dimensional Expensive Black-Box Problems](https://mlsanity.com/paper/2609.37473/) (2026)

## Abstract (arXiv)

Surrogate models provide a low computational cost alternative to evaluating expensive functions. The construction of accurate surrogate models with large numbers of independent variables is currently prohibitive because it requires a large number of function evaluations. Gradient-enhanced kriging has the potential to reduce the number of function evaluations for the desired accuracy when efficient gradient computation, such as an adjoint method, is available. However, current gradient-enhanced kriging methods do not scale well with the number of sampling points due to the rapid growth in the size of the correlation matrix where new information is added for each sampling point in each direction of the design space. They do not scale well with the number of independent variables either due to the increase in the number of hyperparameters that needs to be estimated. To address this issue, we develop a new gradient-enhanced surrogate model approach that drastically reduced the number of hyperparameters through the use of the partial-least squares method that maintains accuracy. In addition, this method is able to control the size of the correlation matrix by adding only relevant points defined through the information provided by the partial-least squares method. To validate our method, we compare the global accuracy of the proposed method with conventional kriging surrogate models on two analytic functions with up to 100 dimensions, as well as engineering problems of varied complexity with up to 15 dimensions. We show that the proposed method requires fewer sampling points than conventional methods to obtain the desired accuracy, or provides more accuracy for a fixed budget of sampling points. In some cases, we get over 3 times more accurate models than a bench of surrogate models from the literature, and also over 3200 times faster than standard gradient-enhanced kriging models.