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Related papers: Polynomial-Chaos-based Kriging

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Kriging-based surrogate models have become very popular during the last decades to approximate a computer code output from few simulations. In practical applications, it is very common to sequentially add new simulations to obtain more…

Statistics Theory · Mathematics 2012-10-31 Loic Le Gratiet , Claire Cannamela

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…

Machine Learning · Statistics 2024-01-05 Kai Cheng , Ralf Zimmermann

In this paper, we investigate the capability of the universal Kriging (UK) model for single-objective global optimization applied within an efficient global optimization (EGO) framework. We implemented this combined UK-EGO framework and…

Machine Learning · Statistics 2018-03-26 Pramudita Satria Palar , Koji Shimoyama

Polynomial chaos expansion (PCE) is an increasingly popular technique for uncertainty propagation and quantification in systems and control. Based on the theory of Hilbert spaces and orthogonal polynomials, PCE allows for a unifying…

Systems and Control · Electrical Eng. & Systems 2020-04-09 Tillmann Mühlpfordt , Frederik Zahn , Veit Hagenmeyer , Timm Faulwasser

The large-scale integration of renewable energy sources introduces significant operational uncertainty into power systems. Although Polynomial Chaos Expansion (PCE) provides an efficient tool for uncertainty quantification (UQ) in power…

Systems and Control · Electrical Eng. & Systems 2026-03-24 Le Fang , Wangkun Xu , Fei Teng

The computational effort for the evaluation of numerical simulations based on e.g. the finite-element method is high. Metamodels can be utilized to create a low-cost alternative. However the number of required samples for the creation of a…

Machine Learning · Statistics 2019-05-15 Jan N. Fuhg

This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional…

Computation · Statistics 2017-04-05 Negin Alemazkoor , Hadi Meidani

In modern engineering, physical processes are modelled and analysed using advanced computer simulations, such as finite element models. Furthermore, concepts of reliability analysis and robust design are becoming popular, hence, making…

Methodology · Statistics 2017-03-20 Roland Schöbi , Bruno Sudret

We consider the numerical approximation of different ordinary differential equations (ODEs) and partial differential equations (PDEs) with periodic boundary conditions involving a one-dimensional random parameter, comparing the intrusive…

Numerical Analysis · Mathematics 2023-11-29 Julian Clausnitzer , Andreas Kleefeld

We propose a non-intrusive reduced-order modeling method based on proper orthogonal decomposition (POD) and polynomial chaos expansion (PCE) for stochastic representations in uncertainty quantification (UQ) analysis. Firstly, POD provides…

Computational Physics · Physics 2021-07-02 Xiang Sun , Xiaomin Pan , Jung-Il Choi

This paper proposes an adaptive sparse polynomial chaos expansion(PCE)-based method to quantify the impacts of uncertainties on critical clearing time (CCT) that is an important index in transient stability analysis. The proposed method can…

Systems and Control · Electrical Eng. & Systems 2022-06-10 Jingyu Liu , Xiaoting Wang , Xiaozhe Wang

As non-institutive polynomial chaos expansion (PCE) techniques have gained growing popularity among researchers, we here provide a comprehensive review of major sampling strategies for the least squares based PCE. Traditional sampling…

Computation · Statistics 2018-02-14 Mohammad Hadigol , Alireza Doostan

Kriging (or Gaussian process regression) is a popular machine learning method for its flexibility and closed-form prediction expressions. However, one of the key challenges in applying kriging to engineering systems is that the available…

Methodology · Statistics 2020-12-23 Jialei Chen , Zhehui Chen , Chuck Zhang , C. F. Jeff Wu

Computer experiments have become an indispensable alternative to complex physical and engineering experiments. The Kriging model is the most widely used surrogate model, with the core goal of minimizing the discrepancy between the surrogate…

Methodology · Statistics 2026-01-26 Ruonan Zheng , Min-Qian Liu , Yongdao Zhou , Xuan Chen

Recently, the use of Polynomial Chaos Expansion (PCE) has been increasing to study the uncertainty in mathematical models for a wide range of applications and several extensions of the original PCE technique have been developed to deal with…

Numerical Analysis · Mathematics 2014-06-23 Maria Navarro , Jeroen Witteveen , Joke Blom

Constructing approximations that can accurately mimic the behavior of complex models at reduced computational costs is an important aspect of uncertainty quantification. Despite their flexibility and efficiency, classical surrogate models…

Computation · Statistics 2020-06-29 S. Marelli , P. -R. Wagner , C. Lataniotis , B. Sudret

We study large-scale spatial systems that contain exogenous variables, e.g. environmental factors that are significant predictors in spatial processes. Building predictive models for such processes is challenging because the large numbers…

Machine Learning · Statistics 2019-12-20 Babak Farmanesh , Arash Pourhabib

As uncertainty and sensitivity analysis of complex models grows ever more important, the difficulty of their timely realizations highlights a need for more efficient numerical operations. Non-intrusive Polynomial Chaos methods are highly…

Numerical Analysis · Mathematics 2022-04-14 Konstantin Weise , Erik Müller , Lucas Poßner , Thomas R. Knösche

Frequency response functions (FRFs) are important for assessing the behavior of stochastic linear dynamic systems. For large systems, their evaluations are time-consuming even for a single simulation. In such cases, uncertainty…

Computation · Statistics 2017-03-23 V. Yaghoubi , S. Marelli , B. Sudret , T. Abrahamsson

The polynomial chaos (PC) expansion has been widely used as a surrogate model in the Bayesian inference to speed up the Markov chain Monte Carlo (MCMC) calculations. However, the use of a PC surrogate introduces the modeling error, that may…

Numerical Analysis · Mathematics 2019-02-20 Liang Yan , Tao Zhou