Dongbin Xiu

Publication Activity (10 Years)

Years Active: 2002-2024
Publications (10 Years): 49

Top Topics

Differential Equations

Dynamical Systems

High Dimensional

Top Venues

J. Comput. Phys.

SIAM J. Sci. Comput.

J. Sci. Comput.

Publications

Yuan Chen, Dongbin Xiu, Xiangxiong Zhang
On enforcing non-negativity in polynomial approximations in high dimensions. CoRR (2024)
Yuan Chen, Dongbin Xiu
Modeling Unknown Stochastic Dynamical System Subject to External Excitation. CoRR (2024)
Yuan Chen, Dongbin Xiu
Learning stochastic dynamical system via flow map operator. J. Comput. Phys. 508 (2024)
Zhongshu Xu, Yuan Chen, Qifan Chen, Dongbin Xiu
Modeling Unknown Stochastic Dynamical System via Autoencoder. CoRR (2023)
Victor Churchill, Dongbin Xiu
Flow Map Learning for Unknown Dynamical Systems: Overview, Implementation, and Benchmarks. CoRR (2023)
Victor Churchill, Steve Manns, Zhen Chen, Dongbin Xiu
Robust modeling of unknown dynamical systems via ensemble averaged learning. J. Comput. Phys. 474 (2023)
Victor Churchill, Yuan Chen, Zhongshu Xu, Dongbin Xiu
DNN modeling of partial differential equations with incomplete data. J. Comput. Phys. 493 (2023)
Yuan Chen, Dongbin Xiu
Learning Stochastic Dynamical System via Flow Map Operator. CoRR (2023)
Victor Churchill, Dongbin Xiu
Learning Fine Scale Dynamics from Coarse Observations via Inner Recurrence. CoRR (2022)
Xiaohan Fu, Weize Mao, Lo-Bin Chang, Dongbin Xiu
Modeling unknown dynamical systems with hidden parameters. CoRR (2022)
Victor Churchill, Dongbin Xiu
Deep Learning of Chaotic Systems from Partially-Observed Data. CoRR (2022)
Shuyi Wang, Zixu Zhou, Lo-Bin Chang, Dongbin Xiu
Construction of discontinuity detectors using convolutional neural networks. J. Sci. Comput. 91 (2) (2022)
Zhen Chen, Victor Churchill, Kailiang Wu, Dongbin Xiu
Deep neural network modeling of unknown partial differential equations in nodal space. J. Comput. Phys. 449 (2022)
Victor Churchill, Steve Manns, Zhen Chen, Dongbin Xiu
Robust Modeling of Unknown Dynamical Systems via Ensemble Averaged Learning. CoRR (2022)
Zhen Chen, Victor Churchill, Kailiang Wu, Dongbin Xiu
Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Space. CoRR (2021)
Tong Qin, Zhen Chen, John D. Jakeman, Dongbin Xiu
Data-Driven Learning of Nonautonomous Systems. SIAM J. Sci. Comput. 43 (3) (2021)
Zhen Chen, Dongbin Xiu
On generalized residual network for deep learning of unknown dynamical systems. J. Comput. Phys. 438 (2021)
Kailiang Wu, Dongbin Xiu
Data-driven deep learning of partial differential equations in modal space. J. Comput. Phys. 408 (2020)
Tong Qin, Zhen Chen, John D. Jakeman, Dongbin Xiu
Data-driven learning of non-autonomous systems. CoRR (2020)
Zhen Chen, Kailiang Wu, Dongbin Xiu
Methods to Recover Unknown Processes in Partial Differential Equations Using Data. J. Sci. Comput. 85 (2) (2020)
Zhen Chen, Kailiang Wu, Dongbin Xiu
Methods to Recover Unknown Processes in Partial Differential Equations Using Data. CoRR (2020)
Jun Hou, Tong Qin, Kailiang Wu, Dongbin Xiu
A Non-Intrusive Correction Algorithm for Classification Problems with Corrupted Data. CoRR (2020)
Zhen Chen, Dongbin Xiu
On generalized residue network for deep learning of unknown dynamical systems. CoRR (2020)
Kailiang Wu, Tong Qin, Dongbin Xiu
Structure-Preserving Method for Reconstructing Unknown Hamiltonian Systems From Trajectory Data. SIAM J. Sci. Comput. 42 (6) (2020)
Xiaohan Fu, Lo-Bin Chang, Dongbin Xiu
Learning reduced systems via deep neural networks with memory. CoRR (2020)
Tong Qin, Kailiang Wu, Dongbin Xiu
Data driven governing equations approximation using deep neural networks. J. Comput. Phys. 395 (2019)
Ching-Shan Chou, Yukun Li, Dongbin Xiu
Energy conserving Galerkin approximation of two dimensional wave equations with random coefficients. J. Comput. Phys. 381 (2019)
Claudio Canuto, Sandra Pieraccini, Dongbin Xiu
Uncertainty quantification of discontinuous outputs via a non-intrusive bifidelity strategy. J. Comput. Phys. 398 (2019)
Kailiang Wu, Dongbin Xiu
Data-Driven Deep Learning of Partial Differential Equations in Modal Space. CoRR (2019)
Kailiang Wu, Tong Qin, Dongbin Xiu
Structure-preserving Method for Reconstructing Unknown Hamiltonian Systems from Trajectory Data. CoRR (2019)
Kailiang Wu, Dongbin Xiu
Numerical aspects for approximating governing equations using data. J. Comput. Phys. 384 (2019)
Tong Qin, Zhen Chen, John D. Jakeman, Dongbin Xiu
A neural network approach for uncertainty quantification for time-dependent problems with random parameters. CoRR (2019)
Kailiang Wu, Dongbin Xiu
An Explicit Neural Network Construction for Piecewise Constant Function Approximation. CoRR (2018)
Marissa Renardy, Tau-Mu Yi, Dongbin Xiu, Ching-Shan Chou
Parameter uncertainty quantification using surrogate models applied to a spatial model of yeast mating polarization. PLoS Comput. Biol. 14 (5) (2018)
Yeonjong Shin, Kailiang Wu, Dongbin Xiu
Sequential function approximation with noisy data. J. Comput. Phys. 371 (2018)
Tong Qin, Ling Zhou, Dongbin Xiu
Reducing Parameter Space for Neural Network Training. CoRR (2018)
Kailiang Wu, Dongbin Xiu
Numerical Aspects for Approximating Governing Equations Using Data. CoRR (2018)
Kailiang Wu, Dongbin Xiu
Sequential function approximation on arbitrarily distributed point sets. J. Comput. Phys. 354 (2018)
Tong Qin, Kailiang Wu, Dongbin Xiu
Data Driven Governing Equations Approximation Using Deep Neural Networks. CoRR (2018)
Kailiang Wu, Yeonjong Shin, Dongbin Xiu
A Randomized Tensor Quadrature Method for High Dimensional Polynomial Approximation. SIAM J. Sci. Comput. 39 (5) (2017)
Yeonjong Shin, Dongbin Xiu
A Randomized Algorithm for Multivariate Function Approximation. SIAM J. Sci. Comput. 39 (3) (2017)
Liang Yan, Yeonjong Shin, Dongbin Xiu
Minimization and Its Application to Stochastic Collocation. SIAM J. Sci. Comput. 39 (1) (2017)
Kailiang Wu, Huazhong Tang, Dongbin Xiu
A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty. J. Comput. Phys. 345 (2017)
Xueyu Zhu, Erin M. Linebarger, Dongbin Xiu
Multi-fidelity stochastic collocation method for computation of statistical moments. J. Comput. Phys. 341 (2017)
Yeonjong Shin, Dongbin Xiu
Nonadaptive Quasi-Optimal Points Selection for Least Squares Linear Regression. SIAM J. Sci. Comput. 38 (1) (2016)
Yanyan He, Dongbin Xiu
Numerical strategy for model correction using physical constraints. J. Comput. Phys. 313 (2016)
Yeonjong Shin, Dongbin Xiu
Correcting Data Corruption Errors for Multivariate Function Approximation. SIAM J. Sci. Comput. 38 (4) (2016)
Yeonjong Shin, Dongbin Xiu
On a near optimal sampling strategy for least squares polynomial regression. J. Comput. Phys. 326 (2016)
Shi Jin, Dongbin Xiu, Xueyu Zhu
A Well-Balanced Stochastic Galerkin Method for Scalar Hyperbolic Balance Laws with Random Inputs. J. Sci. Comput. 67 (3) (2016)
Yi Chen, John D. Jakeman, Claude Jeffrey Gittelson, Dongbin Xiu
Local Polynomial Chaos Expansion for Linear Differential Equations with High Dimensional Random Inputs. SIAM J. Sci. Comput. 37 (1) (2015)
Xiaoxiao Chen, Yanyan He, Dongbin Xiu
An Efficient Method for Uncertainty Propagation using Fuzzy Sets. SIAM J. Sci. Comput. 37 (6) (2015)
Tao Zhou, Akil Narayan, Dongbin Xiu
Weighted discrete least-squares polynomial approximation using randomized quadratures. J. Comput. Phys. 298 (2015)
Jingwei Hu, Shi Jin, Dongbin Xiu
A Stochastic Galerkin Method for Hamilton-Jacobi Equations with Uncertainty. SIAM J. Sci. Comput. 37 (5) (2015)
Shi Jin, Dongbin Xiu, Xueyu Zhu
Asymptotic-preserving methods for hyperbolic and transport equations with random inputs and diffusive scalings. J. Comput. Phys. 289 (2015)
Akil Narayan, Claude Jeffrey Gittelson, Dongbin Xiu
A Stochastic Collocation Algorithm with Multifidelity Models. SIAM J. Sci. Comput. 36 (2) (2014)
Xueyu Zhu, Akil Narayan, Dongbin Xiu
Computational Aspects of Stochastic Collocation with Multifidelity Models. SIAM/ASA J. Uncertain. Quantification 2 (1) (2014)
Jing Li, Xin Qi, Dongbin Xiu
On Upper and Lower Bounds for Quantity of Interest in Problems Subject to Epistemic Uncertainty. SIAM J. Sci. Comput. 36 (2) (2014)
Jing Li, Dongbin Xiu
Surrogate Based Method for Evaluation of Failure Probability under Multiple Constraints. SIAM J. Sci. Comput. 36 (2) (2014)
Akil Narayan, Dongbin Xiu
Constructing Nested Nodal Sets for Multivariate Polynomial Interpolation. SIAM J. Sci. Comput. 35 (5) (2013)
Xiaoxiao Chen, Eun-Jae Park, Dongbin Xiu
A flexible numerical approach for quantification of epistemic uncertainty. J. Comput. Phys. 240 (2013)
John D. Jakeman, Akil Narayan, Dongbin Xiu
Minimal multi-element stochastic collocation for uncertainty quantification of discontinuous functions. J. Comput. Phys. 242 (2013)
Akil Narayan, Dongbin Xiu
Stochastic Collocation Methods on Unstructured Grids in High Dimensions via Interpolation. SIAM J. Sci. Comput. 34 (3) (2012)
Akil Narayan, Youssef M. Marzouk, Dongbin Xiu
Sequential data assimilation with multiple models. J. Comput. Phys. 231 (19) (2012)
Jing Li, Dongbin Xiu
Computation of Failure Probability Subject to Epistemic Uncertainty. SIAM J. Sci. Comput. 34 (6) (2012)
Roland Pulch, Dongbin Xiu
Generalised Polynomial Chaos for a Class of Linear Conservation Laws. J. Sci. Comput. 51 (2) (2012)
Hanne Tiesler, Robert M. Kirby, Dongbin Xiu, Tobias Preusser
Stochastic Collocation for Optimal Control Problems with Stochastic PDE Constraints. SIAM J. Control. Optim. 50 (5) (2012)
John D. Jakeman, Richard Archibald, Dongbin Xiu
Characterization of discontinuities in high-dimensional stochastic problems on adaptive sparse grids. J. Comput. Phys. 230 (10) (2011)
Jing Li, Jinglai Li, Dongbin Xiu
An efficient surrogate-based method for computing rare failure probability. J. Comput. Phys. 230 (24) (2011)
Jing Li, Dongbin Xiu
Evaluation of failure probability via surrogate models. J. Comput. Phys. 229 (23) (2010)
John D. Jakeman, Michael S. Eldred, Dongbin Xiu
Numerical approach for quantification of epistemic uncertainty. J. Comput. Phys. 229 (12) (2010)
Dongbin Xiu, Jie Shen
Efficient stochastic Galerkin methods for random diffusion equations. J. Comput. Phys. 228 (2) (2009)
Rick Archibald, Anne Gelb, Rishu Saxena, Dongbin Xiu
Discontinuity detection in multivariate space for stochastic simulations. J. Comput. Phys. 228 (7) (2009)
Jia Li, Dongbin Xiu
A generalized polynomial chaos based ensemble Kalman filter with high accuracy. J. Comput. Phys. 228 (15) (2009)
Dongbin Xiu, Spencer J. Sherwin
Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network. J. Comput. Phys. 226 (2) (2007)
Daniel M. Tartakovsky, Dongbin Xiu
Guest Editors' Introduction: Stochastic Modeling of Complex Systems. Comput. Sci. Eng. 9 (2) (2007)
Daniel M. Tartakovsky, Dongbin Xiu
Stochastic analysis of transport in tubes with rough walls. J. Comput. Phys. 217 (1) (2006)
Dongbin Xiu, Daniel M. Tartakovsky
Numerical Methods for Differential Equations in Random Domains. SIAM J. Sci. Comput. 28 (3) (2006)
Dongbin Xiu, Jan S. Hesthaven
High-Order Collocation Methods for Differential Equations with Random Inputs. SIAM J. Sci. Comput. 27 (3) (2005)
Dongbin Xiu, Ioannis G. Kevrekidis, Roger G. Ghanem
An equation-free, multiscale approach to uncertainty quantification. Comput. Sci. Eng. 7 (3) (2005)
Dongbin Xiu, Ioannis G. Kevrekidis
Equation-Free, Multiscale Computation for Unsteady Random Diffusion. Multiscale Model. Simul. 4 (3) (2005)
Dongbin Xiu, Spencer J. Sherwin, Suchuan Dong, George E. Karniadakis
Strong and Auxiliary Forms of the Semi-Lagrangian Method for Incompressible Flows. J. Sci. Comput. 25 (1-2) (2005)
Dongbin Xiu, Daniel M. Tartakovsky
A Two-Scale Nonperturbative Approach to Uncertainty Analysis of Diffusion in Random Composites. Multiscale Model. Simul. 2 (4) (2004)
Xiaoliang Wan, Dongbin Xiu, George E. Karniadakis
Stochastic Solutions for the Two-Dimensional Advection-Diffusion Equation. SIAM J. Sci. Comput. 26 (2) (2004)
Dongbin Xiu, Didier Lucor, Chau-Hsing Su, George E. Karniadakis
Performance Evaluation of Generalized Polynomial Chaos. International Conference on Computational Science (2003)
Dongbin Xiu, George E. Karniadakis
The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations. SIAM J. Sci. Comput. 24 (2) (2002)
Jin Xu, Dongbin Xiu, George E. Karniadakis
A Semi-Lagrangian Method for Turbulence Simulations Using Mixed Spectral Discretizations. J. Sci. Comput. 17 (1-4) (2002)