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 …

PyApprox: A software package for sensitivity analysis, Bayesian inference, optimal experimental design, and multi-fidelity uncertainty quantification and surrogate …

JD Jakeman - Environmental Modelling & Software, 2023 - Elsevier
PyApprox is a Python-based one-stop-shop for probabilistic analysis of numerical models
such as those used in the earth, environmental and engineering sciences. Easy to use and …

Active learning and bayesian optimization: a unified perspective to learn with a goal

F Di Fiore, M Nardelli, L Mainini - Archives of Computational Methods in …, 2024 - Springer
Science and Engineering applications are typically associated with expensive optimization
problem to identify optimal design solutions and states of the system of interest. Bayesian …

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” …

A general framework for quantifying uncertainty at scale

IG Farcaş, G Merlo, F Jenko - Communications Engineering, 2022 - nature.com
In many fields of science, comprehensive and realistic computational models are available
nowadays. Often, the respective numerical calculations call for the use of powerful …

An adaptive sparse grid rational Arnoldi method for uncertainty quantification of dynamical systems in the frequency domain

U Römer, M Bollhöfer, H Sreekumar… - International Journal …, 2021 - Wiley Online Library
In this paper, we address discrete linear systems in the frequency domain, where both
frequency and random parameters are considered. Sampling such a system many times is …

Error estimation and adaptivity for stochastic collocation finite elements part I: single-level approximation

A Bespalov, DJ Silvester, F Xu - SIAM Journal on Scientific Computing, 2022 - SIAM
A general adaptive refinement strategy for solving linear elliptic partial differential equations
with random data is proposed and analysed herein. The adaptive strategy extends the a …

Error estimation and adaptivity for stochastic collocation finite elements Part II: multilevel approximation

A Bespalov, D Silvester - SIAM Journal on Scientific Computing, 2023 - SIAM
A multilevel adaptive refinement strategy for solving linear elliptic partial differential
equations with random data is recalled in this work. The strategy extends the a posteriori …

Fast solution of three‐dimensional elliptic equations with randomly generated jumping coefficients by using tensor‐structured preconditioners

BN Khoromskij, V Khoromskaia - Numerical Linear Algebra with …, 2023 - Wiley Online Library
In this paper, we propose and analyze the numerical algorithms for fast solution of periodic
elliptic problems in random media in ℝ d R^ d, d= 2, 3 d= 2, 3. Both the two‐dimensional …