Towards optimal sampling for learning sparse approximations in high dimensions
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 …
dimensional functions on data, where the target functions may be scalar-,'vector-or even …
On efficient algorithms for computing near-best polynomial approximations to high-dimensional, Hilbert-valued functions from limited samples
Sparse polynomial approximation has become indispensable for approximating smooth,
high-or infinite-dimensional functions from limited samples. This is a key task in …
high-or infinite-dimensional functions from limited samples. This is a key task in …
[LIVRE][B] On Efficient Algorithms for Computing Near-Best Polynomial Approximations to High-Dimensional, Hilbert-Valued Functions from Limited Samples
Sparse polynomial approximation has become an indispensable technique for
approximating smooth, high-or infinite-dimensional functions from limited samples. This is a …
approximating smooth, high-or infinite-dimensional functions from limited samples. This is a …
A data-driven framework for sparsity-enhanced surrogates with arbitrary mutually dependent randomness
The challenge of quantifying uncertainty propagation in real-world systems is rooted in the
high-dimensionality of the stochastic input and the frequent lack of explicit knowledge of its …
high-dimensionality of the stochastic input and the frequent lack of explicit knowledge of its …
Stochastic collocation methods via minimization of Transformed penalty
We study the properties of sparse reconstruction of transformed $\ell_1 $(TL1) minimization
and present improved theoretical results about the recoverability and the accuracy of this …
and present improved theoretical results about the recoverability and the accuracy of this …
Sparse recovery via ℓq-minimization for polynomial chaos expansions
In this paper we consider the algorithm for recovering sparse orthogonal polynomials using
stochastic collocation via ℓq minimization. The main results include: 1) By using the norm …
stochastic collocation via ℓq minimization. The main results include: 1) By using the norm …
[PDF][PDF] Methods in Computational Science
B Adcock, S Brugiapaglia, CG Webster - 2022 - SIAM
Over seventy years ago, Richard Bellman coined the term the curse of dimensionality to
describe phenomena and computational challenges that arise in high dimensions. These …
describe phenomena and computational challenges that arise in high dimensions. These …
Optimal and efficient algorithms for learning high-dimensional, Banach-valued functions from limited samples
SA Moraga Scheuermann - 2024 - summit.sfu.ca
Learning high-or infinite-dimensional functions from limited samples is a key task in
Computational Science and Engineering (CSE). For example, in Uncertainty Quantification …
Computational Science and Engineering (CSE). For example, in Uncertainty Quantification …