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A surrogate model approximates a computationally expensive solver. Polynomial Chaos is a method to construct surrogate models by summing combinations of carefully chosen polynomials. The polynomials are chosen to respect the probability…

Numerical Analysis · Mathematics 2017-06-29 Thomas A. McCourt , Brodie Lawson , Fengde Zhou , Bevan Thompson , Stephen Tyson , Diane Donovan

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

In this paper we address the problem of uncertainty management for robust design, and verification of large dynamic networks whose performance is affected by an equally large number of uncertain parameters. Many such networks (e.g. power,…

Computation · Statistics 2011-10-12 Amit Surana , Tuhin Sahai , Andrzej Banaszuk

Since the invention of generalized polynomial chaos in 2002, uncertainty quantification has impacted many engineering fields, including variation-aware design automation of integrated circuits and integrated photonics. Due to the fast…

Numerical Analysis · Computer Science 2018-07-06 Chunfeng Cui , Zheng Zhang

In this paper we present a basis selection method that can be used with $\ell_1$-minimization to adaptively determine the large coefficients of polynomial chaos expansions (PCE). The adaptive construction produces anisotropic basis sets…

Numerical Analysis · Computer Science 2015-06-22 John D. Jakeman , Michael S. Eldred , Khachik Sargsyan

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

Continuous-time random disturbances (also called stochastic excitations) due to increasing renewable generation have an increasing impact on power system dynamics; However, except from the Monte Carlo simulation, most existing methods for…

Optimization and Control · Mathematics 2020-07-07 Yiwei Qiu , Jin Lin , Xiaoshuang Chen , Feng Liu , Yonghua Song

We introduce PoCET: a free and open-scource Polynomial Chaos Expansion Toolbox for Matlab, featuring the automatic generation of polynomial chaos expansion (PCE) for linear and nonlinear dynamic systems with time-invariant stochastic…

Systems and Control · Electrical Eng. & Systems 2020-07-13 Felix Petzke , Ali Mesbah , Stefan Streif

Parameter identification is crucial in virtual engineering processes, yet determining appropriate system excitations for identifying specific parameters remains challenging. In practice, extensive experimental programs often fail to…

Optimization and Control · Mathematics 2026-05-07 Kevin Schmidt , Nicola Henkelmann , Christoph Mark , Johannes von Keler

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

Polynomial Chaos Expansions represent a powerful tool to simulate stochastic models of dynamical systems. Yet, deriving the expansion's coefficients for complex systems might require a significant and non-trivial manipulation of the model,…

Computation · Statistics 2012-11-13 Lorenzo Fagiano , Mustafa Khammash

Sparse polynomial chaos expansions (PCE) are an efficient and widely used surrogate modeling method in uncertainty quantification for engineering problems with computationally expensive models. To make use of the available information in…

Computation · Statistics 2021-07-26 Nora Lüthen , Stefano Marelli , Bruno Sudret

Gradient-enhanced Uncertainty Quantification (UQ) has received recent attention, in which the derivatives of a Quantity of Interest (QoI) with respect to the uncertain parameters are utilized to improve the surrogate approximation.…

Computation · Statistics 2016-03-23 Ji Peng , Jerrad Hampton , Alireza Doostan

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

In this paper, we develop a numerical approach based on Chaos expansions to analyze the sensitivity and the propagation of epistemic uncertainty through a queueing systems with breakdowns. Here, the quantity of interest is the stationary…

Probability · Mathematics 2017-05-17 Katia Bachi , Cédric Chauvière , Hacène Djellout , Karim Abbas

Compressive sensing has become a powerful addition to uncertainty quantification when only limited data is available. In this paper we provide a general framework to enhance the sparsity of the representation of uncertainty in the form of…

Numerical Analysis · Mathematics 2018-11-28 Xiu Yang , Xiaoliang Wan , Lin Lin , Huan Lei

The work presented here investigates the application of polynomial chaos expansion toward input shaper design in order to maintain robustness in dynamical systems subject to uncertainty. Furthermore, this work intends to specifically…

Systems and Control · Electrical Eng. & Systems 2026-02-05 Johannes Güttler , Karan Baker , Premjit Saha , James Warner , Adrian Stein

Polynomial chaos expansions (PCE) have proven efficiency in a number of fields for propagating parametric uncertainties through computational models of complex systems, namely structural and fluid mechanics, chemical reactions and…

Computation · Statistics 2017-04-13 Chu V. Mai , Bruno Sudret

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

Robustness analysis is very important in biology and neuroscience, to unravel behavioural patterns of systems that are conserved despite large parametric uncertainties. To make studies of probabilistic robustness more efficient and scalable…

Quantitative Methods · Quantitative Biology 2026-01-08 Uros Sutulovic , Daniele Proverbio , Rami Katz , Giulia Giordano