Multi-index Monte Carlo: when sparsity meets sampling

AL Haji-Ali, F Nobile, R Tempone - Numerische Mathematik, 2016 - Springer
We propose and analyze a novel multi-index Monte Carlo (MIMC) method for weak
approximation of stochastic models that are described in terms of differential equations …

Multi-index stochastic collocation for random PDEs

AL Haji-Ali, F Nobile, L Tamellini, R Tempone - Computer Methods in …, 2016 - Elsevier
In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for
computing statistics of the solution of a PDE with random data. MISC is a combination …

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 …

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 …

Adaptive experimental design for multi‐fidelity surrogate modeling of multi‐disciplinary systems

JD Jakeman, S Friedman, MS Eldred… - International Journal …, 2022 - Wiley Online Library
We present an adaptive algorithm for constructing surrogate models of multi‐disciplinary
systems composed of a set of coupled components. With this goal we introduce “coupling” …

Convergence of sparse collocation for functions of countably many Gaussian random variables (with application to elliptic PDEs)

OG Ernst, B Sprungk, L Tamellini - SIAM Journal on Numerical Analysis, 2018 - SIAM
We give a convergence proof for the approximation by sparse collocation of Hilbert-space-
valued functions depending on countably many Gaussian random variables. Such functions …

A dynamically adaptive sparse grids method for quasi-optimal interpolation of multidimensional functions

MK Stoyanov, CG Webster - Computers & Mathematics with Applications, 2016 - Elsevier
In this work we develop a dynamically adaptive sparse grids (SG) method for quasi-optimal
interpolation of multidimensional analytic functions defined over a product of one …

Sparse-grid discontinuous Galerkin methods for the Vlasov–Poisson–Lenard–Bernstein model

S Schnake, C Kendrick, E Endeve, M Stoyanov… - Journal of …, 2024 - Elsevier
Sparse-grid methods have recently gained interest in reducing the computational cost of
solving high-dimensional kinetic equations. In this paper, we construct adaptive and hybrid …

Multilevel approximation of parametric and stochastic PDEs

J Zech, D Dũng, C Schwab - Mathematical Models and Methods in …, 2019 - World Scientific
We analyze the complexity of the sparse-grid interpolation and sparse-grid quadrature of
countably-parametric functions which take values in separable Banach spaces with …

An adaptive sparse grid algorithm for elliptic PDEs with lognormal diffusion coefficient

F Nobile, L Tamellini, F Tesei, R Tempone - Sparse Grids and Applications …, 2016 - Springer
In this work we build on the classical adaptive sparse grid algorithm (T. Gerstner and M.
Griebel, Dimension-adaptive tensor-product quadrature), obtaining an enhanced version …