A Semi-Lagrangian Method for Turbulence Simulations Using Mixed Spectral Discretizations. - Jin Xu; Dongbin Xiu; George E. Karniadakis (J. Sci. Comput., 2002)

The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations. - Dongbin Xiu; George E. Karniadakis (SIAM J. Sci. Comput., 2002)

Performance Evaluation of Generalized Polynomial Chaos. - Dongbin Xiu; Didier Lucor; Chau-Hsing Su; George E. Karniadakis (International Conference on Computational Science, 2003)

A Two-Scale Nonperturbative Approach to Uncertainty Analysis of Diffusion in Random Composites. - Dongbin Xiu; Daniel M. Tartakovsky (Multiscale Model. Simul., 2004)

Stochastic Solutions for the Two-Dimensional Advection-Diffusion Equation. - Xiaoliang Wan; Dongbin Xiu; George E. Karniadakis (SIAM J. Sci. Comput., 2004)

An equation-free, multiscale approach to uncertainty quantification. - Dongbin Xiu; Ioannis G. Kevrekidis; Roger G. Ghanem (Comput. Sci. Eng., 2005)

Strong and Auxiliary Forms of the Semi-Lagrangian Method for Incompressible Flows. - Dongbin Xiu; Spencer J. Sherwin; Suchuan Dong; George E. Karniadakis (J. Sci. Comput., 2005)

Equation-Free, Multiscale Computation for Unsteady Random Diffusion. - Dongbin Xiu; Ioannis G. Kevrekidis (Multiscale Model. Simul., 2005)

High-Order Collocation Methods for Differential Equations with Random Inputs. - Dongbin Xiu; Jan S. Hesthaven (SIAM J. Sci. Comput., 2005)

Stochastic analysis of transport in tubes with rough walls. - Daniel M. Tartakovsky; Dongbin Xiu (J. Comput. Phys., 2006)

Numerical Methods for Differential Equations in Random Domains. - Dongbin Xiu; Daniel M. Tartakovsky (SIAM J. Sci. Comput., 2006)

Guest Editors' Introduction: Stochastic Modeling of Complex Systems. - Daniel M. Tartakovsky; Dongbin Xiu (Comput. Sci. Eng., 2007)

Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network. - Dongbin Xiu; Spencer J. Sherwin (J. Comput. Phys., 2007)

Discontinuity detection in multivariate space for stochastic simulations. - Rick Archibald; Anne Gelb; Rishu Saxena; Dongbin Xiu (J. Comput. Phys., 2009)

A generalized polynomial chaos based ensemble Kalman filter with high accuracy. - Jia Li 048; Dongbin Xiu (J. Comput. Phys., 2009)

Efficient stochastic Galerkin methods for random diffusion equations. - Dongbin Xiu; Jie Shen 001 (J. Comput. Phys., 2009)

Numerical approach for quantification of epistemic uncertainty. - John D. Jakeman; Michael S. Eldred; Dongbin Xiu (J. Comput. Phys., 2010)

Evaluation of failure probability via surrogate models. - Jing Li; Dongbin Xiu (J. Comput. Phys., 2010)

Characterization of discontinuities in high-dimensional stochastic problems on adaptive sparse grids. - John D. Jakeman; Richard Archibald; Dongbin Xiu (J. Comput. Phys., 2011)

An efficient surrogate-based method for computing rare failure probability. - Jing Li; Jinglai Li; Dongbin Xiu (J. Comput. Phys., 2011)

Sequential data assimilation with multiple models. - Akil Narayan 001; Youssef M. Marzouk; Dongbin Xiu (J. Comput. Phys., 2012)

Generalised Polynomial Chaos for a Class of Linear Conservation Laws. - Roland Pulch; Dongbin Xiu (J. Sci. Comput., 2012)

Stochastic Collocation for Optimal Control Problems with Stochastic PDE Constraints. - Hanne Tiesler; Robert M. Kirby; Dongbin Xiu; Tobias Preusser (SIAM J. Control. Optim., 2012)

Computation of Failure Probability Subject to Epistemic Uncertainty. - Jing Li; Dongbin Xiu (SIAM J. Sci. Comput., 2012)

Stochastic Collocation Methods on Unstructured Grids in High Dimensions via Interpolation. - Akil Narayan 001; Dongbin Xiu (SIAM J. Sci. Comput., 2012)

A flexible numerical approach for quantification of epistemic uncertainty. - Xiaoxiao Chen; Eun-Jae Park; Dongbin Xiu (J. Comput. Phys., 2013)

Minimal multi-element stochastic collocation for uncertainty quantification of discontinuous functions. - John D. Jakeman; Akil Narayan 001; Dongbin Xiu (J. Comput. Phys., 2013)

Constructing Nested Nodal Sets for Multivariate Polynomial Interpolation. - Akil Narayan 001; Dongbin Xiu (SIAM J. Sci. Comput., 2013)

Computational Aspects of Stochastic Collocation with Multifidelity Models. - Xueyu Zhu; Akil Narayan 001; Dongbin Xiu (SIAM/ASA J. Uncertain. Quantification, 2014)

On Upper and Lower Bounds for Quantity of Interest in Problems Subject to Epistemic Uncertainty. - Jing Li; Xin Qi; Dongbin Xiu (SIAM J. Sci. Comput., 2014)

Surrogate Based Method for Evaluation of Failure Probability under Multiple Constraints. - Jing Li; Dongbin Xiu (SIAM J. Sci. Comput., 2014)

A Stochastic Collocation Algorithm with Multifidelity Models. - Akil Narayan 001; Claude Jeffrey Gittelson; Dongbin Xiu (SIAM J. Sci. Comput., 2014)

Asymptotic-preserving methods for hyperbolic and transport equations with random inputs and diffusive scalings. - Shi Jin 003; Dongbin Xiu; Xueyu Zhu (J. Comput. Phys., 2015)

Weighted discrete least-squares polynomial approximation using randomized quadratures. - Tao Zhou 010; Akil Narayan 001; Dongbin Xiu (J. Comput. Phys., 2015)

An Efficient Method for Uncertainty Propagation using Fuzzy Sets. - Xiaoxiao Chen; Yanyan He; Dongbin Xiu (SIAM J. Sci. Comput., 2015)

Local Polynomial Chaos Expansion for Linear Differential Equations with High Dimensional Random Inputs. - Yi Chen; John D. Jakeman; Claude Jeffrey Gittelson; Dongbin Xiu (SIAM J. Sci. Comput., 2015)

A Stochastic Galerkin Method for Hamilton-Jacobi Equations with Uncertainty. - Jingwei Hu; Shi Jin 003; Dongbin Xiu (SIAM J. Sci. Comput., 2015)

Numerical strategy for model correction using physical constraints. - Yanyan He; Dongbin Xiu (J. Comput. Phys., 2016)

On a near optimal sampling strategy for least squares polynomial regression. - Yeonjong Shin; Dongbin Xiu (J. Comput. Phys., 2016)

A Well-Balanced Stochastic Galerkin Method for Scalar Hyperbolic Balance Laws with Random Inputs. - Shi Jin 003; Dongbin Xiu; Xueyu Zhu (J. Sci. Comput., 2016)

Nonadaptive Quasi-Optimal Points Selection for Least Squares Linear Regression. - Yeonjong Shin; Dongbin Xiu (SIAM J. Sci. Comput., 2016)

Correcting Data Corruption Errors for Multivariate Function Approximation. - Yeonjong Shin; Dongbin Xiu (SIAM J. Sci. Comput., 2016)

A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty. - Kailiang Wu; Huazhong Tang; Dongbin Xiu (J. Comput. Phys., 2017)

Multi-fidelity stochastic collocation method for computation of statistical moments. - Xueyu Zhu; Erin M. Linebarger; Dongbin Xiu (J. Comput. Phys., 2017)

A Randomized Algorithm for Multivariate Function Approximation. - Yeonjong Shin; Dongbin Xiu (SIAM J. Sci. Comput., 2017)

A Randomized Tensor Quadrature Method for High Dimensional Polynomial Approximation. - Kailiang Wu; Yeonjong Shin; Dongbin Xiu (SIAM J. Sci. Comput., 2017)

Sparse Approximation using ℓ1-ℓ2 Minimization and Its Application to Stochastic Collocation. - Liang Yan 002; Yeonjong Shin; Dongbin Xiu (SIAM J. Sci. Comput., 2017)

Reducing Parameter Space for Neural Network Training. - Tong Qin 002; Ling Zhou 001; Dongbin Xiu (CoRR, 2018)

An Explicit Neural Network Construction for Piecewise Constant Function Approximation. - Kailiang Wu; Dongbin Xiu (CoRR, 2018)

Sequential function approximation with noisy data. - Yeonjong Shin; Kailiang Wu; Dongbin Xiu (J. Comput. Phys., 2018)

Sequential function approximation on arbitrarily distributed point sets. - Kailiang Wu; Dongbin Xiu (J. Comput. Phys., 2018)

Parameter uncertainty quantification using surrogate models applied to a spatial model of yeast mating polarization. - Marissa Renardy; Tau-Mu Yi; Dongbin Xiu; Ching-Shan Chou (PLoS Comput. Biol., 2018)

A neural network approach for uncertainty quantification for time-dependent problems with random parameters. - Tong Qin 002; Zhen Chen; John D. Jakeman; Dongbin Xiu (CoRR, 2019)

Uncertainty quantification of discontinuous outputs via a non-intrusive bifidelity strategy. - Claudio Canuto; Sandra Pieraccini; Dongbin Xiu (J. Comput. Phys., 2019)

Energy conserving Galerkin approximation of two dimensional wave equations with random coefficients. - Ching-Shan Chou; Yukun Li; Dongbin Xiu (J. Comput. Phys., 2019)

Data driven governing equations approximation using deep neural networks. - Tong Qin 002; Kailiang Wu; Dongbin Xiu (J. Comput. Phys., 2019)

Numerical aspects for approximating governing equations using data. - Kailiang Wu; Dongbin Xiu (J. Comput. Phys., 2019)

On generalized residue network for deep learning of unknown dynamical systems. - Zhen Chen; Dongbin Xiu (CoRR, 2020)

A Non-Intrusive Correction Algorithm for Classification Problems with Corrupted Data. - Jun Hou; Tong Qin 002; Kailiang Wu; Dongbin Xiu (CoRR, 2020)

Learning reduced systems via deep neural networks with memory. - Xiaohan Fu; Lo-Bin Chang; Dongbin Xiu (CoRR, 2020)

Data-driven learning of non-autonomous systems. - Tong Qin 002; Zhen Chen; John D. Jakeman; Dongbin Xiu (CoRR, 2020)

Data-driven deep learning of partial differential equations in modal space. - Kailiang Wu; Dongbin Xiu (J. Comput. Phys., 2020)

Methods to Recover Unknown Processes in Partial Differential Equations Using Data. - Zhen Chen; Kailiang Wu; Dongbin Xiu (J. Sci. Comput., 2020)

Structure-Preserving Method for Reconstructing Unknown Hamiltonian Systems From Trajectory Data. - Kailiang Wu; Tong Qin 002; Dongbin Xiu (SIAM J. Sci. Comput., 2020)

On generalized residual network for deep learning of unknown dynamical systems. - Zhen Chen; Dongbin Xiu (J. Comput. Phys., 2021)

Data-Driven Learning of Nonautonomous Systems. - Tong Qin 002; Zhen Chen; John D. Jakeman; Dongbin Xiu (SIAM J. Sci. Comput., 2021)

Modeling unknown dynamical systems with hidden parameters. - Xiaohan Fu; Weize Mao; Lo-Bin Chang; Dongbin Xiu (CoRR, 2022)

Deep Learning of Chaotic Systems from Partially-Observed Data. - Victor Churchill; Dongbin Xiu (CoRR, 2022)

Learning Fine Scale Dynamics from Coarse Observations via Inner Recurrence. - Victor Churchill; Dongbin Xiu (CoRR, 2022)

Deep neural network modeling of unknown partial differential equations in nodal space. - Zhen Chen; Victor Churchill; Kailiang Wu; Dongbin Xiu (J. Comput. Phys., 2022)

Construction of discontinuity detectors using convolutional neural networks. - Shuyi Wang; Zixu Zhou; Lo-Bin Chang; Dongbin Xiu (J. Sci. Comput., 2022)

Flow Map Learning for Unknown Dynamical Systems: Overview, Implementation, and Benchmarks. - Victor Churchill; Dongbin Xiu (CoRR, 2023)

Modeling Unknown Stochastic Dynamical System via Autoencoder. - Zhongshu Xu; Yuan Chen; Qifan Chen; Dongbin Xiu (CoRR, 2023)

Robust modeling of unknown dynamical systems via ensemble averaged learning. - Victor Churchill; Steve Manns; Zhen Chen; Dongbin Xiu (J. Comput. Phys., 2023)

DNN modeling of partial differential equations with incomplete data. - Victor Churchill; Yuan Chen; Zhongshu Xu; Dongbin Xiu (J. Comput. Phys., 2023)

On enforcing non-negativity in polynomial approximations in high dimensions. - Yuan Chen; Dongbin Xiu; Xiangxiong Zhang (CoRR, 2024)

Modeling Unknown Stochastic Dynamical System Subject to External Excitation. - Yuan Chen; Dongbin Xiu (CoRR, 2024)

Data-driven Effective Modeling of Multiscale Stochastic Dynamical Systems. - Yuan Chen; Dongbin Xiu (CoRR, 2024)

Chebyshev Feature Neural Network for Accurate Function Approximation. - Zhongshu Xu; Yuan Chen; Dongbin Xiu (CoRR, 2024)

A Training-Free Conditional Diffusion Model for Learning Stochastic Dynamical Systems. - Yanfang Liu; Yuan Chen; Dongbin Xiu; Guannan Zhang (CoRR, 2024)

Learning stochastic dynamical system via flow map operator. - Yuan Chen; Dongbin Xiu (J. Comput. Phys., 2024)

Deep Learning for Model Correction of Dynamical Systems with Data Scarcity. - Caroline Tatsuoka; Dongbin Xiu (SIAM/ASA J. Uncertain. Quantification, 2025)

On Enforcing Nonnegativity in Polynomial Approximations in High Dimensions. - Yuan Chen; Dongbin Xiu; Xiangxiong Zhang (SIAM J. Sci. Comput., 2025)

Multi-fidelity Parameter Estimation Using Conditional Diffusion Models. - Caroline Tatsuoka; Minglei Yang 005; Dongbin Xiu; Guannan Zhang (CoRR, 2025)

DUE: A Deep Learning Framework and Library for Modeling Unknown Equations. - Junfeng Chen; Kailiang Wu; Dongbin Xiu (CoRR, 2025)

Exact Conditional Score-Guided Generative Modeling for Amortized Inference in Uncertainty Quantification. - Zezhong Zhang; Caroline Tatsuoka; Dongbin Xiu; Guannan Zhang (CoRR, 2025)