Sparse polynomial chaos expansions: Literature survey and benchmark
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 …
takes advantage of the properties of PCE, the sparsity-of-effects principle, and powerful …
[图书][B] Introduction to uncertainty quantification
TJ Sullivan - 2015 - books.google.com
This text provides a framework in which the main objectives of the field of uncertainty
quantification (UQ) are defined and an overview of the range of mathematical methods by …
quantification (UQ) are defined and an overview of the range of mathematical methods by …
nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications
Physics-informed neural networks (PINNs) are effective in solving inverse problems based
on differential and integro-differential equations with sparse, noisy, unstructured, and multi …
on differential and integro-differential equations with sparse, noisy, unstructured, and multi …
Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies
Sampling orthogonal polynomial bases via Monte Carlo is of interest for uncertainty
quantification of models with random inputs, using Polynomial Chaos (PC) expansions. It is …
quantification of models with random inputs, using Polynomial Chaos (PC) expansions. It is …
Learning smooth functions in high dimensions: from sparse polynomials to deep neural networks
Learning approximations to smooth target functions of many variables from finite sets of
pointwise samples is an important task in scientific computing and its many applications in …
pointwise samples is an important task in scientific computing and its many applications in …
Enhancing ℓ1-minimization estimates of polynomial chaos expansions using basis selection
JD Jakeman, MS Eldred, K Sargsyan - Journal of Computational Physics, 2015 - Elsevier
In this paper we present a basis selection method that can be used with ℓ 1-minimization to
adaptively determine the large coefficients of polynomial chaos expansions (PCE). The …
adaptively determine the large coefficients of polynomial chaos expansions (PCE). The …
A weighted ℓ1-minimization approach for sparse polynomial chaos expansions
This work proposes a method for sparse polynomial chaos (PC) approximation of high-
dimensional stochastic functions based on non-adapted random sampling. We modify the …
dimensional stochastic functions based on non-adapted random sampling. We modify the …
Coherence motivated sampling and convergence analysis of least squares polynomial chaos regression
Independent sampling of orthogonal polynomial bases via Monte Carlo is of interest for
uncertainty quantification of models using Polynomial Chaos (PC) expansions. It is known …
uncertainty quantification of models using Polynomial Chaos (PC) expansions. It is known …
Polynomial chaos expansions for dependent random variables
JD Jakeman, F Franzelin, A Narayan, M Eldred… - Computer Methods in …, 2019 - Elsevier
Polynomial chaos expansions (PCE) are well-suited to quantifying uncertainty in models
parameterized by independent random variables. The assumption of independence leads to …
parameterized by independent random variables. The assumption of independence leads to …
Sparse polynomial chaos expansions via compressed sensing and D-optimal design
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 …
commonly used by researchers for a variety of purposes, such as surrogate modeling. Ideas …