English
Related papers

Related papers: Data-driven dimensionally decomposed generalized p…

200 papers

Generalized Polynomial Chaos (gPC) theory has been widely used for representing parametric uncertainty in a system, thanks to its ability to propagate uncertainty evolution. In an optimal control context, gPC can be combined with several…

Optimization and Control · Mathematics 2021-10-05 Yuichiro Aoyama , Augustinos D. Saravanos , Evangelos A. Theodorou

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

We present an enriched formulation of the Least Squares (LSQ) regression method for Uncertainty Quantification (UQ) using generalised polynomial chaos (gPC). More specifically, we enrich the linear system with additional equations for the…

Numerical Analysis · Mathematics 2023-08-09 Kyriakos D. Kantarakias , George Papadakis

This paper puts forward a new generalized polynomial dimensional decomposition (PDD), referred to as GPDD, comprising hierarchically ordered measure-consistent multivariate orthogonal polynomials in dependent random variables. Unlike the…

Numerical Analysis · Mathematics 2018-10-30 Sharif Rahman

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

Polynomial chaos expansion (PCE) is a versatile tool widely used in uncertainty quantification and machine learning, but its successful application depends strongly on the accuracy and reliability of the resulting PCE-based response…

Computation · Statistics 2023-06-14 Paul-Christian Bürkner , Ilja Kröker , Sergey Oladyshkin , Wolfgang Nowak

In this work we introduce a manifold learning-based surrogate modeling framework for uncertainty quantification in high-dimensional stochastic systems. Our first goal is to perform data mining on the available simulation data to identify a…

Machine Learning · Statistics 2024-11-11 Dimitris G. Giovanis , Dimitrios Loukrezis , Ioannis G. Kevrekidis , Michael D. Shields

Polynomial chaos based methods enable the efficient computation of output variability in the presence of input uncertainty in complex models. Consequently, they have been used extensively for propagating uncertainty through a wide variety…

Optimization and Control · Mathematics 2020-09-18 Tuhin Sahai

Polynomial chaos expansion (PCE) is a powerful surrogate model-based reliability analysis method. Generally, a PCE model with a higher expansion order is usually required to obtain an accurate surrogate model for some complex non-linear…

Machine Learning · Computer Science 2022-04-05 Xiaohu Zheng , Wen Yao , Yunyang Zhang , Xiaoya Zhang

Growing uncertainty from renewable energy integration and distributed energy resources motivate the need for advanced tools to quantify the effect of uncertainty and assess the risks it poses to secure system operation. Polynomial chaos…

Optimization and Control · Mathematics 2019-10-16 David Métivier , Marc Vuffray , Sidhant Misra

In this work, Uncertainty Quantification (UQ) based on non-intrusive Polynomial Chaos Expansion (PCE) is applied to the CFD problem of the flow past an airfoil with parameterized angle of attack and inflow velocity. To limit the…

Numerical Analysis · Mathematics 2024-12-20 Saddam Hijazi , Giovanni Stabile , Andrea Mola , Gianluigi Rozza

This letter proposes a data-driven sparse polynomial chaos expansion-based surrogate model for the stochastic economic dispatch problem considering uncertainty from wind power. The proposed method can provide accurate estimations for the…

Signal Processing · Electrical Eng. & Systems 2021-09-20 Xiaoting Wang , Rong-Peng Liu , Xiaozhe Wang , Yunhe Hou , François Bouffard

The surrogate model-based uncertainty quantification method has drawn much attention in many engineering fields. Polynomial chaos expansion (PCE) and deep learning (DL) are powerful methods for building a surrogate model. However, PCE needs…

Machine Learning · Computer Science 2022-03-02 Wen Yao , Xiaohu Zheng , Jun Zhang , Ning Wang , Guijian Tang

We consider the effect of multiple stochastic parameters on the time-average quantities of chaotic systems. We employ the recently proposed \cite{Kantarakias_Papadakis_2023} sensitivity-enhanced generalized polynomial chaos expansion,…

Chaotic Dynamics · Physics 2023-11-02 George Papadakis , Kyriakos D. Kantarakias

We present an approach to the simulation of quantum systems driven by classical stochastic processes that is based on the polynomial chaos expansion, a well-known technique in the field of uncertainty quantification. The polynomial chaos…

Quantum Physics · Physics 2013-12-17 Kevin C. Young , Matthew D. Grace

This paper addresses the Bayesian calibration of dynamic models with parametric and structural uncertainties, in particular where the uncertain parameters are unknown/poorly known spatio-temporally varying subsystem models. Independent…

Computation · Statistics 2012-11-02 Piyush Tagade , Han-Lim Choi

Uncertainty quantification based on generalized polynomial chaos has been used in many applications. It has also achieved great success in variation-aware design automation. However, almost all existing techniques assume that the parameters…

Numerical Analysis · Mathematics 2019-06-21 Chunfeng Cui , Zheng Zhang

This paper deals with some of the methodologies used to construct polynomial surrogate models based on generalized polynomial chaos (gPC) expansions for applications to uncertainty quantification (UQ) in aerodynamic computations. A core…

Fluid Dynamics · Physics 2018-03-14 Eric Savin , Andrea Resmini , Jacques Peter

The accessibility of spatially distributed data, enabled by affordable sensors, field, and numerical experiments, has facilitated the development of data-driven solutions for scientific problems, including climate change, weather…

Machine Learning · Computer Science 2023-11-09 Vardhan Dongre , Gurpreet Singh Hora

Polynomial chaos is a powerful technique for propagating uncertainty through ordinary and partial differential equations. Random variables are expanded in terms of orthogonal polynomials and differential equations are derived for the…

Computation · Statistics 2014-06-18 José Miguel Pasini , Tuhin Sahai