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 …
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 …
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 …
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 …
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” …
systems composed of a set of coupled components. With this goal we introduce “coupling” …
A general framework for quantifying uncertainty at scale
In many fields of science, comprehensive and realistic computational models are available
nowadays. Often, the respective numerical calculations call for the use of powerful …
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
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 …
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 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 …
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 …
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 …
elliptic problems in random media in ℝ d R^ d, d= 2, 3 d= 2, 3. Both the two‐dimensional …