Dongbin Xiu

,

J. Comput. Phys., 2024

A Training-Free Conditional Diffusion Model for Learning Stochastic Dynamical Systems.

[BibT_eX]

[DOI]

,

,

,

CoRR, 2024

Chebyshev Feature Neural Network for Accurate Function Approximation.

[BibT_eX]

[DOI]

Zhongshu Xu

,

,

CoRR, 2024

Data-driven Effective Modeling of Multiscale Stochastic Dynamical Systems.

[BibT_eX]

[DOI]

,

CoRR, 2024

Modeling Unknown Stochastic Dynamical System Subject to External Excitation.

[BibT_eX]

[DOI]

,

CoRR, 2024

On enforcing non-negativity in polynomial approximations in high dimensions.

[BibT_eX]

[DOI]

,

,

Xiangxiong Zhang

CoRR, 2024

DNN modeling of partial differential equations with incomplete data.

[BibT_eX]

[DOI]

,

,

,

J. Comput. Phys., November, 2023

Robust modeling of unknown dynamical systems via ensemble averaged learning.

[BibT_eX]

[DOI]

,

,

,

J. Comput. Phys., February, 2023

Modeling Unknown Stochastic Dynamical System via Autoencoder.

[BibT_eX]

[DOI]

,

,

,

CoRR, 2023

Flow Map Learning for Unknown Dynamical Systems: Overview, Implementation, and Benchmarks.

[BibT_eX]

[DOI]

Victor Churchill

,

CoRR, 2023

Construction of discontinuity detectors using convolutional neural networks.

[BibT_eX]

[DOI]

,

,

,

J. Sci. Comput., 2022

Deep neural network modeling of unknown partial differential equations in nodal space.

[BibT_eX]

[DOI]

,

,

,

J. Comput. Phys., 2022

Learning Fine Scale Dynamics from Coarse Observations via Inner Recurrence.

[BibT_eX]

[DOI]

Victor Churchill

,

CoRR, 2022

Deep Learning of Chaotic Systems from Partially-Observed Data.

[BibT_eX]

[DOI]

Victor Churchill

,

CoRR, 2022

Modeling unknown dynamical systems with hidden parameters.

[BibT_eX]

[DOI]

,

,

,

CoRR, 2022

Data-Driven Learning of Nonautonomous Systems.

[BibT_eX]

[DOI]

,

,

,

SIAM J. Sci. Comput., 2021

On generalized residual network for deep learning of unknown dynamical systems.

[BibT_eX]

[DOI]

Zhen Chen

,

J. Comput. Phys., 2021

Structure-Preserving Method for Reconstructing Unknown Hamiltonian Systems From Trajectory Data.

[BibT_eX]

[DOI]

,

Tong Qin

,

SIAM J. Sci. Comput., 2020

Methods to Recover Unknown Processes in Partial Differential Equations Using Data.

[BibT_eX]

[DOI]

Zhen Chen

,

,

J. Sci. Comput., 2020

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

[BibT_eX]

[DOI]

,

J. Comput. Phys., 2020

Data-driven learning of non-autonomous systems.

[BibT_eX]

[DOI]

,

,

,

CoRR, 2020

Learning reduced systems via deep neural networks with memory.

[BibT_eX]

[DOI]

Xiaohan Fu

,

Lo-Bin Chang

,

CoRR, 2020

A Non-Intrusive Correction Algorithm for Classification Problems with Corrupted Data.

[BibT_eX]

[DOI]

,

,

,

CoRR, 2020

On generalized residue network for deep learning of unknown dynamical systems.

[BibT_eX]

[DOI]

Zhen Chen

,

CoRR, 2020

Numerical aspects for approximating governing equations using data.

[BibT_eX]

[DOI]

,

J. Comput. Phys., 2019

Data driven governing equations approximation using deep neural networks.

[BibT_eX]

[DOI]

Tong Qin

,

,

J. Comput. Phys., 2019

Energy conserving Galerkin approximation of two dimensional wave equations with random coefficients.

[BibT_eX]

[DOI]

Ching-Shan Chou

,

Yukun Li

,

J. Comput. Phys., 2019

Uncertainty quantification of discontinuous outputs via a non-intrusive bifidelity strategy.

[BibT_eX]

[DOI]

Claudio Canuto

,

Sandra Pieraccini

,

J. Comput. Phys., 2019

A neural network approach for uncertainty quantification for time-dependent problems with random parameters.

[BibT_eX]

[DOI]

,

,

,

CoRR, 2019

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

[BibT_eX]

[DOI]

,

,

,

PLoS Comput. Biol., 2018

Sequential function approximation on arbitrarily distributed point sets.

[BibT_eX]

[DOI]

,

J. Comput. Phys., 2018

Sequential function approximation with noisy data.

[BibT_eX]

[DOI]

,

,

J. Comput. Phys., 2018

An Explicit Neural Network Construction for Piecewise Constant Function Approximation.

[BibT_eX]

[DOI]

,

CoRR, 2018

Reducing Parameter Space for Neural Network Training.

[BibT_eX]

[DOI]

Tong Qin

,

Ling Zhou

,

CoRR, 2018

Sparse Approximation using ℓ<sub>1-ℓ<sub>2</sub></sub> Minimization and Its Application to Stochastic Collocation.

[BibT_eX]

[DOI]

Liang Yan

,

,

SIAM J. Sci. Comput., 2017

A Randomized Tensor Quadrature Method for High Dimensional Polynomial Approximation.

[BibT_eX]

[DOI]

,

,

SIAM J. Sci. Comput., 2017

A Randomized Algorithm for Multivariate Function Approximation.

[BibT_eX]

[DOI]

,

SIAM J. Sci. Comput., 2017

Multi-fidelity stochastic collocation method for computation of statistical moments.

[BibT_eX]

[DOI]

,

Erin M. Linebarger

,

J. Comput. Phys., 2017

A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty.

[BibT_eX]

[DOI]

,

Huazhong Tang

,

J. Comput. Phys., 2017

Correcting Data Corruption Errors for Multivariate Function Approximation.

[BibT_eX]

[DOI]

,

SIAM J. Sci. Comput., 2016

Nonadaptive Quasi-Optimal Points Selection for Least Squares Linear Regression.

[BibT_eX]

[DOI]

,

SIAM J. Sci. Comput., 2016

A Well-Balanced Stochastic Galerkin Method for Scalar Hyperbolic Balance Laws with Random Inputs.

[BibT_eX]

[DOI]

Shi Jin

,

,

J. Sci. Comput., 2016

On a near optimal sampling strategy for least squares polynomial regression.

[BibT_eX]

[DOI]

,

J. Comput. Phys., 2016

Numerical strategy for model correction using physical constraints.

[BibT_eX]

[DOI]

Yanyan He

,

J. Comput. Phys., 2016

A Stochastic Galerkin Method for Hamilton-Jacobi Equations with Uncertainty.

[BibT_eX]

[DOI]

Jingwei Hu

,

Shi Jin

,

SIAM J. Sci. Comput., 2015

Local Polynomial Chaos Expansion for Linear Differential Equations with High Dimensional Random Inputs.

[BibT_eX]

[DOI]

Yi Chen

,

,

Claude Jeffrey Gittelson

,

SIAM J. Sci. Comput., 2015

An Efficient Method for Uncertainty Propagation using Fuzzy Sets.

[BibT_eX]

[DOI]

Xiaoxiao Chen

,

Yanyan He

,

SIAM J. Sci. Comput., 2015

Weighted discrete least-squares polynomial approximation using randomized quadratures.

[BibT_eX]

[DOI]

Tao Zhou

,

,

J. Comput. Phys., 2015

Asymptotic-preserving methods for hyperbolic and transport equations with random inputs and diffusive scalings.

[BibT_eX]

[DOI]

Shi Jin

,

,

J. Comput. Phys., 2015

A Stochastic Collocation Algorithm with Multifidelity Models.

[BibT_eX]

[DOI]

,

Claude Jeffrey Gittelson

,

SIAM J. Sci. Comput., 2014

Surrogate Based Method for Evaluation of Failure Probability under Multiple Constraints.

[BibT_eX]

[DOI]

,

SIAM J. Sci. Comput., 2014

On Upper and Lower Bounds for Quantity of Interest in Problems Subject to Epistemic Uncertainty.

[BibT_eX]

[DOI]

,

Xin Qi

,

SIAM J. Sci. Comput., 2014

Computational Aspects of Stochastic Collocation with Multifidelity Models.

[BibT_eX]

[DOI]

,

,

SIAM/ASA J. Uncertain. Quantification, 2014

Constructing Nested Nodal Sets for Multivariate Polynomial Interpolation.

[BibT_eX]

[DOI]

,

SIAM J. Sci. Comput., 2013

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

[BibT_eX]

[DOI]

,

,

J. Comput. Phys., 2013

A flexible numerical approach for quantification of epistemic uncertainty.

[BibT_eX]

[DOI]

Xiaoxiao Chen

,

Eun-Jae Park

,

J. Comput. Phys., 2013

Stochastic Collocation Methods on Unstructured Grids in High Dimensions via Interpolation.

[BibT_eX]

[DOI]

,

SIAM J. Sci. Comput., 2012

Computation of Failure Probability Subject to Epistemic Uncertainty.

[BibT_eX]

[DOI]

,

SIAM J. Sci. Comput., 2012

Stochastic Collocation for Optimal Control Problems with Stochastic PDE Constraints.

[BibT_eX]

[DOI]

,

,

,

SIAM J. Control. Optim., 2012

Generalised Polynomial Chaos for a Class of Linear Conservation Laws.

[BibT_eX]

[DOI]

Roland Pulch

,

J. Sci. Comput., 2012

Sequential data assimilation with multiple models.

[BibT_eX]

[DOI]

,

Youssef M. Marzouk

,

J. Comput. Phys., 2012

An efficient surrogate-based method for computing rare failure probability.

[BibT_eX]

[DOI]

,

Jinglai Li

,

J. Comput. Phys., 2011

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

[BibT_eX]

[DOI]

,

Richard Archibald

,

J. Comput. Phys., 2011

Evaluation of failure probability via surrogate models.

[BibT_eX]

[DOI]

,

J. Comput. Phys., 2010

Numerical approach for quantification of epistemic uncertainty.

[BibT_eX]

[DOI]

,

Michael S. Eldred

,

J. Comput. Phys., 2010

Efficient stochastic Galerkin methods for random diffusion equations.

[BibT_eX]

[DOI]

,

Jie Shen

J. Comput. Phys., 2009

A generalized polynomial chaos based ensemble Kalman filter with high accuracy.

[BibT_eX]

[DOI]

Jia Li

,

J. Comput. Phys., 2009

Discontinuity detection in multivariate space for stochastic simulations.

[BibT_eX]

[DOI]

,

,

,

J. Comput. Phys., 2009

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

[BibT_eX]

[DOI]

,

Spencer J. Sherwin

J. Comput. Phys., 2007

Guest Editors' Introduction: Stochastic Modeling of Complex Systems.

[BibT_eX]

[DOI]

,

Comput. Sci. Eng., 2007

Numerical Methods for Differential Equations in Random Domains.

[BibT_eX]

[DOI]

,

SIAM J. Sci. Comput., 2006

Stochastic analysis of transport in tubes with rough walls.

[BibT_eX]

[DOI]

,

J. Comput. Phys., 2006

High-Order Collocation Methods for Differential Equations with Random Inputs.

[BibT_eX]

[DOI]

,

Jan S. Hesthaven

SIAM J. Sci. Comput., 2005

Equation-Free, Multiscale Computation for Unsteady Random Diffusion.

[BibT_eX]

[DOI]

,

Ioannis G. Kevrekidis

Multiscale Model. Simul., 2005

Strong and Auxiliary Forms of the Semi-Lagrangian Method for Incompressible Flows.

[BibT_eX]

[DOI]

,

Spencer J. Sherwin

,

Suchuan Dong

,

J. Sci. Comput., 2005

An equation-free, multiscale approach to uncertainty quantification.

[BibT_eX]

[DOI]

,

Ioannis G. Kevrekidis

,

Roger G. Ghanem

Comput. Sci. Eng., 2005

Stochastic Solutions for the Two-Dimensional Advection-Diffusion Equation.

[BibT_eX]

[DOI]

Xiaoliang Wan

,

,

SIAM J. Sci. Comput., 2004

A Two-Scale Nonperturbative Approach to Uncertainty Analysis of Diffusion in Random Composites.

[BibT_eX]

[DOI]

,

Multiscale Model. Simul., 2004

The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations.

[BibT_eX]

[DOI]

,

SIAM J. Sci. Comput., 2002

A Semi-Lagrangian Method for Turbulence Simulations Using Mixed Spectral Discretizations.

[BibT_eX]

[DOI]

Jin Xu

,

,