Related papers: A Near-Optimal Sampling Strategy for Sparse Recove…

Compressive sampling has been widely used for sparse polynomial chaos (PC) approximation of stochastic functions. The recovery accuracy of compressive sampling highly depends on the incoherence properties of the measurement matrix. In this…

This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional…

As non-institutive polynomial chaos expansion (PCE) techniques have gained growing popularity among researchers, we here provide a comprehensive review of major sampling strategies for the least squares based PCE. Traditional sampling…

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…

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,…

In this chapter, we discuss recent work on learning sparse approximations to high-dimensional functions on data, where the target functions may be scalar-, vector- or even Hilbert space-valued. Our main objective is to study how the…

As uncertainty and sensitivity analysis of complex models grows ever more important, the difficulty of their timely realizations highlights a need for more efficient numerical operations. Non-intrusive Polynomial Chaos methods are highly…

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…

In this paper we propose an algorithm for recovering sparse orthogonal polynomials using stochastic collocation. Our approach is motivated by the desire to use generalized polynomial chaos expansions (PCE) to quantify uncertainty in models…

We present an algorithm for computing sparse, least squares-based polynomial chaos expansions, incorporating both adaptive polynomial bases and sequential experimental designs. The algorithm is employed to approximate stochastic…

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…

Polynomial chaos expansion is a popular way to develop surrogate models for stochastic systems with arbitrary random variables. Standard techniques such as Galerkin projection, stochastic collocation, and least squares approximation, are…

For optimization on large-scale data, exactly calculating its solution may be computationally difficulty because of the large size of the data. In this paper we consider subsampled optimization for fast approximating the exact solution. In…

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 that bounding the spectral radius of a random matrix consisting…

With appropriately chosen sampling probabilities, sampling-based random projection can be used to implement large-scale statistical methods, substantially reducing computational cost while maintaining low statistical error. However,…

Surrogate models are used to alleviate the computational burden in engineering tasks, which require the repeated evaluation of computationally demanding models of physical systems, such as the efficient propagation of uncertainties. For…

Compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quantification analysis of expensive and high-dimensional physical models. We perform…

We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological…

We present a hybrid sampling-surrogate approach for reducing the computational expense of uncertainty quantification in nonlinear dynamical systems. Our motivation is to enable rapid uncertainty quantification in complex mechanical systems…

The recovery of approximately sparse or compressible coefficients in a Polynomial Chaos Expansion is a common goal in modern parametric uncertainty quantification (UQ). However, relatively little effort in UQ has been directed toward…