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Multivariate Polynomial Chaos Expansions with Dependent Variables
SIAM Journal on Scientific Computing, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Feinberg, Jonathan +2 more
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On the guaranteed accuracy of Polynomial Chaos Expansions
IEEE Conference on Decision and Control and European Control Conference, 2011This paper is concerned with the efficient simulation of stochastic nonlinear dynamical systems. A technique based on Polynomial Chaos Expansion (PCE) theory is used, in order to estimate the time evolution of the stochastic properties of the variables of interest.
FAGIANO, LORENZO +2 more
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Stochastic thermal modeling by polynomial chaos expansion
19th International Workshop on Thermal Investigations of ICs and Systems (THERMINIC), 2013In this paper an effective approach is proposed for generating stochastic compact thermal models of electronics components and packages. The approach exhibits high levels of accuracy for very small state space dimensions of the model. It is also efficient since it requires the solution of few deterministic thermal problems in the frequency domain.
CODECASA, LORENZO, DI RIENZO, LUCA
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Compressive polynomial chaos expansion for multidimensional model maps
2015Modern high-resolution numerical models used in engineering often produce multidimensional maps of outputs (e.g. nodal displacements on a FEM mesh) that may result in more than 105 highly correlated outputs for each set of model parameters. Most available metamodelling techniques, however, are not yet suitable for handling such large maps, including ...
Marelli, Stefano, Sudret, Bruno
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Adaptive sparse polynomial chaos expansions: A survey
2019ISBN:978-3-903024-84 ...
Lüthen, Nora, Sudret, Bruno
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Global sensitivity analysis using polynomial chaos expansions
Reliability Engineering & System Safety, 2008Abstract Global sensitivity analysis (SA) aims at quantifying the respective effects of input random variables (or combinations thereof) onto the variance of the response of a physical or mathematical model. Among the abundant literature on sensitivity measures, the Sobol’ indices have received much attention since they provide accurate information ...
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Generalized polynomial chaos expansions with weights.
2015Polynomial chaos is used as an alternative to Monte Carlo methods for the propagation of uncertainty through dynamical systems. By truncating the infinite series of the polynomial chaos expansion to a finite order, the positivity of the approximate solution may be lost.
Obermaier, J., Stavropoulou, F.
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Hermite Polynomials and Wiener Chaos Expansion
2022Francesco Russo, Pierre Vallois
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