The Sparse Grids Matlab kit--a Matlab implementation of sparse grids for high-dimensional function approximation and uncertainty quantification
C Piazzola, L Tamellini - arXiv preprint arXiv:2203.09314, 2022 - arxiv.org
The Sparse Grids Matlab Kit provides a Matlab implementation of sparse grids, and can be
used for approximating high-dimensional functions and, in particular, for surrogate-model …
used for approximating high-dimensional functions and, in particular, for surrogate-model …
Multilevel CNNs for Parametric PDEs
We combine concepts from multilevel solvers for partial differential equations (PDEs) with
neural network based deep learning and propose a new methodology for the efficient …
neural network based deep learning and propose a new methodology for the efficient …
Algorithm 1040: The Sparse Grids Matlab Kit-a Matlab implementation of sparse grids for high-dimensional function approximation and uncertainty quantification
C Piazzola, L Tamellini - ACM Transactions on Mathematical Software, 2024 - dl.acm.org
The Sparse Grids Matlab Kit provides a Matlab implementation of sparse grids, and can be
used for approximating high-dimensional functions and, in particular, for surrogate-model …
used for approximating high-dimensional functions and, in particular, for surrogate-model …
Investigations on the restrictions of stochastic collocation methods for high dimensional and nonlinear engineering applications
Sophisticated sampling techniques used for solving stochastic partial differential equations
efficiently and robustly are still in a state of development. It is known in the scientific …
efficiently and robustly are still in a state of development. It is known in the scientific …
Hessian-based adaptive sparse quadrature for infinite-dimensional Bayesian inverse problems
In this work we propose and analyze a Hessian-based adaptive sparse quadrature to
compute infinite-dimensional integrals with respect to the posterior distribution in the context …
compute infinite-dimensional integrals with respect to the posterior distribution in the context …
On the convergence of adaptive stochastic collocation for elliptic partial differential equations with affine diffusion
Convergence of an adaptive collocation method for the parametric stationary diffusion
equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on …
equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on …
Analyticity and sparsity in uncertainty quantification for PDEs with Gaussian random field inputs
We establish sparsity and summability results for coefficient sequences of Wiener-Hermite
polynomial chaos expansions of countably-parametric solutions of linear elliptic and …
polynomial chaos expansions of countably-parametric solutions of linear elliptic and …
Domain uncertainty quantification in computational electromagnetics
We study the numerical approximation of time-harmonic, electromagnetic fields inside a
lossy cavity of uncertain geometry. Key assumptions are a possibly high-dimensional …
lossy cavity of uncertain geometry. Key assumptions are a possibly high-dimensional …
[HTML][HTML] Novel results for the anisotropic sparse grid quadrature
AL Haji-Ali, H Harbrecht, MD Peters… - Journal of …, 2018 - Elsevier
This article is dedicated to the anisotropic sparse grid quadrature for functions which are
analytically extendable into an anisotropic tensor product domain. Taking into account this …
analytically extendable into an anisotropic tensor product domain. Taking into account this …
Sparse quadrature for high-dimensional integration with Gaussian measure
P Chen - ESAIM: Mathematical Modelling and Numerical …, 2018 - numdam.org
In this work we analyze the dimension-independent convergence property of an abstract
sparse quadrature scheme for numerical integration of functions of high-dimensional …
sparse quadrature scheme for numerical integration of functions of high-dimensional …