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Numerical Methods for Stochastic Computations: A Spectral Method Approach

Xiu, Dongbin

1, 2010

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Evaluation of failure probability via surrogate models

Journal of computational physics, 2010-11, Vol.229 (23), p.8966-8980

2010

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A generalized polynomial chaos based ensemble Kalman filter with high accuracy

Journal of computational physics, 2009-08, Vol.228 (15), p.5454-5469

2009

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Numerical approach for quantification of epistemic uncertainty

Journal of computational physics, 2010-06, Vol.229 (12), p.4648-4663

2010

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High-order collocation methods for differential equations with random inputs

SIAM journal on scientific computing, 2005-01, Vol.27 (3), p.1118-1139

2005

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Efficient stochastic Galerkin methods for random diffusion equations

Journal of computational physics, 2009-02, Vol.228 (2), p.266-281

2009

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The wiener-askey polynomial chaos for stochastic differential equations

SIAM journal on scientific computing, 2003, Vol.24 (2), p.619-644

2003

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An efficient surrogate-based method for computing rare failure probability

Journal of computational physics, 2011-10, Vol.230 (24), p.8683-8697

2011

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Data-driven deep learning of partial differential equations in modal space

Journal of computational physics, 2020-05, Vol.408, p.109307, Article 109307

2020

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Modeling uncertainty in flow simulations via generalized polynomial chaos

Journal of computational physics, 2003-05, Vol.187 (1), p.137-167

2003

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Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network

Journal of computational physics, 2007-10, Vol.226 (2), p.1385-1407

2007

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Numerical integration formulas of degree two

Applied numerical mathematics, 2008-10, Vol.58 (10), p.1515-1520

Xiu, Dongbin

2008

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Minimal multi-element stochastic collocation for uncertainty quantification of discontinuous functions

Journal of computational physics, 2013-06, Vol.242, p.790-808

2013

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Numerical aspects for approximating governing equations using data

Journal of computational physics, 2019-05, Vol.384, p.200-221

2019

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Stochastic analysis of transport in tubes with rough walls

Journal of computational physics, 2006-09, Vol.217 (1), p.248-259

2006

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Parameter uncertainty quantification using surrogate models applied to a spatial model of yeast mating polarization

PLoS computational biology, 2018-05, Vol.14 (5), p.e1006181-e1006181

2018

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On generalized residual network for deep learning of unknown dynamical systems

Journal of computational physics, 2021-08, Vol.438, p.110362, Article 110362

2021

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Deep Learning of Biological Models from Data: Applications to ODE Models

Bulletin of mathematical biology, 2021-03, Vol.83 (3), p.19-19, Article 19

2021

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Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos

Computer methods in applied mechanics and engineering, 2002-09, Vol.191 (43), p.4927-4948

2002

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Data driven governing equations approximation using deep neural networks

Journal of computational physics, 2019-10, Vol.395, p.620-635

2019

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Characterization of discontinuities in high-dimensional stochastic problems on adaptive sparse grids

Journal of computational physics, 2011, Vol.230 (10), p.3977-3997

2011

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A new stochastic approach to transient heat conduction modeling with uncertainty

International journal of heat and mass transfer, 2003-11, Vol.46 (24), p.4681-4693

2003

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Sequential data assimilation with multiple models

Journal of computational physics, 2012-08, Vol.231 (19), p.6401-6418

2012

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Learning stochastic dynamical system via flow map operator

Journal of computational physics, 2024-07, Vol.508, p.112984, Article 112984

2024

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Discontinuity detection in multivariate space for stochastic simulations

Journal of computational physics, 2009-04, Vol.228 (7), p.2676-2689

2009

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Numerical Methods for Stochastic Computations: A Spectral Method Approach

Evaluation of failure probability via surrogate models

A generalized polynomial chaos based ensemble Kalman filter with high accuracy

Numerical approach for quantification of epistemic uncertainty

High-order collocation methods for differential equations with random inputs

Efficient stochastic Galerkin methods for random diffusion equations

The wiener-askey polynomial chaos for stochastic differential equations

An efficient surrogate-based method for computing rare failure probability

Data-driven deep learning of partial differential equations in modal space

Modeling uncertainty in flow simulations via generalized polynomial chaos

Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network

Numerical integration formulas of degree two

Minimal multi-element stochastic collocation for uncertainty quantification of discontinuous functions

Numerical aspects for approximating governing equations using data

Stochastic analysis of transport in tubes with rough walls

Parameter uncertainty quantification using surrogate models applied to a spatial model of yeast mating polarization

On generalized residual network for deep learning of unknown dynamical systems

Deep Learning of Biological Models from Data: Applications to ODE Models

Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos

Data driven governing equations approximation using deep neural networks

Characterization of discontinuities in high-dimensional stochastic problems on adaptive sparse grids

A new stochastic approach to transient heat conduction modeling with uncertainty

Sequential data assimilation with multiple models

Learning stochastic dynamical system via flow map operator

Discontinuity detection in multivariate space for stochastic simulations

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