Reduced dimensional Gaussian process emulators of parametrized partial differential equations based on Isomap

W Xing, AA Shah, PB Nair - Proceedings of the Royal …, 2015 - royalsocietypublishing.org
In this paper, Isomap and kernel Isomap are used to dramatically reduce the dimensionality
of the output space to efficiently construct a Gaussian process emulator of parametrized …

Deep coregionalization for the emulation of simulation-based spatial-temporal fields

WW Xing, RM Kirby, S Zhe - Journal of Computational Physics, 2021 - Elsevier
Data-driven surrogate models are widely used for applications such as design optimization
and uncertainty quantification, where repeated evaluations of an expensive simulator are …

Anchored analysis of variance Petrov–Galerkin projection schemes for linear stochastic structural dynamics

L Gao, C Audouze, PB Nair - Proceedings of the …, 2015 - royalsocietypublishing.org
In this paper, we propose anchored functional analysis of variance Petrov–Galerkin (AAPG)
projection schemes, originally developed in the context of parabolic stochastic partial …

Deep coregionalization for the emulation of spatial-temporal fields

W Xing, RM Kirby, S Zhe - arXiv preprint arXiv:1910.07577, 2019 - arxiv.org
Data-driven surrogate models are widely used for applications such as design optimization
and uncertainty quantification, where repeated evaluations of an expensive simulator are …

Anchored ANOVA Petrov–Galerkin projection schemes for parabolic stochastic partial differential equations

C Audouze, PB Nair - Computer Methods in Applied Mechanics and …, 2014 - Elsevier
We present a numerical scheme based on the combination of Hoeffding's functional analysis
of variance (ANOVA) decomposition with stochastic Galerkin projection for solving a class of …

Some a priori error estimates for finite element approximations of elliptic and parabolic linear stochastic partial differential equations

C Audouze, PB Nair - International Journal for Uncertainty …, 2014 - dl.begellhouse.com
We study some theoretical aspects of Legendre polynomial chaos based finite element
approximations of elliptic and parabolic linear stochastic partial differential equations …

Space and chaos‐expansion Galerkin proper orthogonal decomposition low‐order discretization of partial differential equations for uncertainty quantification

P Benner, J Heiland - International Journal for Numerical …, 2023 - Wiley Online Library
The quantification of multivariate uncertainties in partial differential equations can easily
exceed any computing capacity unless proper measures are taken to reduce the complexity …

Space and Chaos-Expansion Galerkin POD Low-order Discretization of PDEs for Uncertainty Quantification

P Benner, J Heiland - arXiv preprint arXiv:2009.01055, 2020 - arxiv.org
The quantification of multivariate uncertainties in partial differential equations can easily
exceed any computing capacity unless proper measures are taken to reduce the complexity …

A priori error estimates for finite element approximations of parabolic stochastic partial differential equations with generalized random variables

C Audouze, PB Nair - … An International Journal of Probability and …, 2015 - Taylor & Francis
We consider finite element approximations of parabolic stochastic partial differential
equations (SPDEs) in conjunction with the-weighted temporal discretization scheme. We …

[图书][B] Projection schemes for high-dimensional problems in stochastic structural dynamics

L Gao - 2018 - search.proquest.com
The focus of the present thesis is to formulate efficient schemes to solve high-dimensional
stochastic ordinary differential equations (SODEs) encountered in stochastic structural …