Related papers: Conformally Mapped Polynomial Chaos Expansions for…
Generalized polynomial chaos expansions are a powerful tool to study differential equations with random coefficients, allowing in particular to efficiently approximate random invariant sets associated to such equations. In this work, we use…
Polynomial chaos expansion (PCE) is a classical and widely used surrogate modeling technique in physical simulation and uncertainty quantification. By taking a linear combination of a set of basis polynomials - orthonormal with respect to…
This paper introduces a new generalized polynomial chaos expansion (PCE) comprising measure-consistent multivariate orthonormal polynomials in dependent random variables. Unlike existing PCEs, whether classical or generalized, no…
Sampling orthogonal polynomial bases via Monte Carlo is of interest for uncertainty quantification of models with high-dimensional random inputs, using Polynomial Chaos (PC) expansions. It is known that bounding a probabilistic parameter,…
The non-intrusive generalized Polynomial Chaos (gPC) method is a popular computational approach for solving partial differential equations (PDEs) with random inputs. The main hurdle preventing its efficient direct application for…
In complex and unknown processes, global models are initially generated over the entire experimental space but often fail to provide accurate predictions in local areas. A common approach is to use local models, which requires partitioning…
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…
The post-Moore era casts a shadow of uncertainty on many aspects of computer system design. Managing that uncertainty requires new algorithmic tools to make quantitative assessments. While prior uncertainty quantification methods, such as…
For a large class of orthogonal basis functions, there has been a recent identification of expansion methods for computing accurate, stable approximations of a quantity of interest. This paper presents, within the context of uncertainty…
Polynomial chaos expansions (PCE) are well-suited to quantifying uncertainty in models parameterized by independent random variables. The assumption of independence leads to simple strategies for evaluating PCE coefficients. In contrast,…
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…
This paper reviews generalized Pareto copulas (GPC), which turn out to be a key to multivariate extreme value theory. Any GPC can be represented in an easy analytic way using a particular type of norm on $\mathbb{R}^d$, called $D$-norm. The…
Methods based on polynomial chaos expansion allow to approximate the behavior of systems with uncertain parameters by deterministic dynamics. These methods are used in a wide range of applications, spanning from simulation of uncertain…
This article is devoted to providing a review of mathematical formulations in which Polynomial Chaos Theory (PCT) has been incorporated into stochastic model predictive control (SMPC). In the past decade, PCT has been shown to provide a…
In this contribution, we discuss the construction of Polynomial Chaos surrogates for Monte Carlo radiation transport applications via non-intrusive spectral projection. This contribution focuses on improvements with respect to the approach…
It is known that standard stochastic Galerkin methods encounter challenges when solving partial differential equations with high-dimensional random inputs, which are typically caused by the large number of stochastic basis functions…
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…
This paper proposes a general framework to estimate coefficients of generalized polynomial chaos (gPC) used in uncertainty quantification via rotational sparse approximation. In particular, we aim to identify a rotation matrix such that the…
In this study, the applicability of generalized polynomial chaos (gPC) expansion for land surface model parameter estimation is evaluated. We compute the (posterior) distribution of the critical hydrological parameters that are subject to…
Dimensionally decomposed generalized polynomial chaos expansion (DD-GPCE) efficiently performs forward uncertainty quantification (UQ) in complex engineering systems with high-dimensional random inputs of arbitrary distributions. However,…