Related papers: Computation of the Response Surface in the Tensor …
We apply the Tensor Train (TT) decomposition to construct the tensor product Polynomial Chaos Expansion (PCE) of a random field, to solve the stochastic elliptic diffusion PDE with the stochastic Galerkin discretization, and to compute some…
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…
We consider the approximate solution of parametric PDEs using the low-rank Tensor Train (TT) decomposition. Such parametric PDEs arise for example in uncertainty quantification problems in engineering applications. We propose an algorithm…
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 expansions (PCE) allow us to propagate uncertainties in the coefficients of differential equations to the statistics of their solutions. Their main advantage is that they replace stochastic equations by systems of…
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…
We propose an algorithm for solution of high-dimensional evolutionary equations (ODEs and discretized time-dependent PDEs) in the Tensor Train (TT) decomposition, assuming that the solution and the right-hand side of the ODE admit such a…
Sparse polynomial chaos expansions (PCE) are a popular surrogate modelling method that takes advantage of the properties of PCE, the sparsity-of-effects principle, and powerful sparse regression solvers to approximate computer models with…
The growing need for uncertainty analysis of complex computational models has led to an expanding use of meta-models across engineering and sciences. The efficiency of meta-modeling techniques relies on their ability to provide…
Uncertainty quantification (UQ) has received much attention in the literature in the past decade. In this context, Sparse Polynomial chaos expansions (PCE) have been shown to be among the most promising methods because of their ability to…
In the field of uncertainty quantification, sparse polynomial chaos (PC) expansions are commonly used by researchers for a variety of purposes, such as surrogate modeling. Ideas from compressed sensing may be employed to exploit this…
The Tensor-Train (TT) format is a highly compact low-rank representation for high-dimensional tensors. TT is particularly useful when representing approximations to the solutions of certain types of parametrized partial differential…
A new Wasserstein multi-element polynomial chaos expansion (WPCE) is proposed, which is inspired by recent advances in computational optimal transport for estimating Wasserstein distances. The developed method combines unsupervised learning…
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…
In the field of surrogate modeling, polynomial chaos expansion (PCE) allows practitioners to construct inexpensive yet accurate surrogates to be used in place of the expensive forward model simulations. For black-box simulations,…
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…
Surrogate modelling techniques have opened up new possibilities to overcome the limitations of computationally intensive numerical models in various areas of engineering and science. However, while fundamental in many engineering…
In this paper the efficiency of multilevel sparse tensor approximation methods for high-dimensional affine parametric diffusion equations is investigated. Methodologically, the recently presented Sparse Alternating Least Squares (SALS)…
The increasing uncertainty level caused by growing renewable energy sources (RES) and aging transmission networks poses a great challenge in the assessment of total transfer capability (TTC) and available transfer capability (ATC). In this…
In surrogate modeling, polynomial chaos expansion (PCE) is popularly utilized to represent the random model responses, which are computationally expensive and usually obtained by deterministic numerical modeling approaches including finite…