# Polynomial-Chaos-based Kriging

arXiv: https://arxiv.org/abs/1502.03939 · HTML: https://mlsanity.com/paper/1502.03939/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2015.

## Built on by (most cited first, 21 of 21)

- [Machine Learning in Aerodynamic Shape Optimization](https://mlsanity.com/paper/2202.07141/) (2022)
- [Uncertainty Quantification in Machine Learning for Engineering Design and Health Prognostics: A Tutorial](https://mlsanity.com/paper/2305.04933/) (2023)
- [State-of-the-Art Review of Design of Experiments for Physics-Informed Deep Learning](https://mlsanity.com/paper/2202.06416/) (2022)
- [Learning "best" kernels from data in Gaussian process regression. With application to aerodynamics](https://mlsanity.com/paper/2206.02563/) (2022)
- [PCENet: High Dimensional Surrogate Modeling for Learning Uncertainty](https://mlsanity.com/paper/2202.05063/) (2022)
- [Surrogate assisted active subspace and active subspace assisted surrogate -- A new paradigm for high dimensional structural reliability analysis](https://mlsanity.com/paper/2105.04979/) (2021)
- [Deep Polynomial Chaos Expansion](https://mlsanity.com/paper/2507.21273/) (2025)
- [All Emulators are Wrong, Many are Useful, and Some are More Useful Than Others: A Reproducible Comparison of Computer Model Surrogates](https://mlsanity.com/paper/2512.09060/) (2025)
- [A connection between probability, physics and neural networks](https://mlsanity.com/paper/2209.12737/) (2022)
- [Accelerating hypersonic reentry simulations using deep learning-based hybridization (with guarantees)](https://mlsanity.com/paper/2209.13434/) (2022)
- [Combining Gaussian processes and polynomial chaos expansions for stochastic nonlinear model predictive control](https://mlsanity.com/paper/2103.05441/) (2021)
- [Deep convolutional neural network for shape optimization using level-set approach](https://mlsanity.com/paper/2201.06210/) (2022)
- [Multielement polynomial chaos Kriging-based metamodelling for Bayesian inference of non-smooth systems](https://mlsanity.com/paper/2212.02250/) (2022)
- [Active learning for structural reliability analysis with multiple limit state functions through variance-enhanced PC-Kriging surrogate models](https://mlsanity.com/paper/2302.12074/) (2023)
- [Polynomial Chaos Expanded Gaussian Process](https://mlsanity.com/paper/2405.01052/) (2024)
- [Gradient-enhanced multifidelity neural networks for high-dimensional function approximation](https://mlsanity.com/paper/2103.12247/) (2021)
- [Spline Dimensional Decomposition with Interpolation-based Optimal Knot Selection for Stochastic Dynamic Analysis](https://mlsanity.com/paper/2505.12879/) (2025)
- [Multi-level informed optimization via decomposed Kriging for large design problems under uncertainty](https://mlsanity.com/paper/2510.07904/) (2025)
- [Conformalized Polynomial Chaos Expansion for Uncertainty-aware Surrogate Modeling](https://mlsanity.com/paper/2510.22375/) (2025)
- [Martingale Neural Operators: Learning Stochastic Marginals via Doob-Meyer Factorization](https://mlsanity.com/paper/2605.15806/) (2026)
- [Repulsive normalizing flow mixtures for adaptive importance sampling: reliability analysis of complex systems](https://mlsanity.com/paper/2609.21160/) (2026)

## Abstract (arXiv)

Computer simulation has become the standard tool in many engineering fields for designing and optimizing systems, as well as for assessing their reliability. To cope with demanding analysis such as optimization and reliability, surrogate models (a.k.a meta-models) have been increasingly investigated in the last decade. Polynomial Chaos Expansions (PCE) and Kriging are two popular non-intrusive meta-modelling techniques. PCE surrogates the computational model with a series of orthonormal polynomials in the input variables where polynomials are chosen in coherency with the probability distributions of those input variables. On the other hand, Kriging assumes that the computer model behaves as a realization of a Gaussian random process whose parameters are estimated from the available computer runs, i.e. input vectors and response values. These two techniques have been developed more or less in parallel so far with little interaction between the researchers in the two fields. In this paper, PC-Kriging is derived as a new non-intrusive meta-modeling approach combining PCE and Kriging. A sparse set of orthonormal polynomials (PCE) approximates the global behavior of the computational model whereas Kriging manages the local variability of the model output. An adaptive algorithm similar to the least angle regression algorithm determines the optimal sparse set of polynomials. PC-Kriging is validated on various benchmark analytical functions which are easy to sample for reference results. From the numerical investigations it is concluded that PC-Kriging performs better than or at least as good as the two distinct meta-modeling techniques. A larger gain in accuracy is obtained when the experimental design has a limited size, which is an asset when dealing with demanding computational models.