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2020 – today
- 2024
[j63]Yuan Chen
, Dongbin Xiu:
Learning stochastic dynamical system via flow map operator. J. Comput. Phys. 508: 112984 (2024)- [i25]Yuan Chen, Dongbin Xiu, Xiangxiong Zhang:
On enforcing non-negativity in polynomial approximations in high dimensions. CoRR abs/2401.12415 (2024) - [i24]Yuan Chen, Dongbin Xiu:
Modeling Unknown Stochastic Dynamical System Subject to External Excitation. CoRR abs/2406.15747 (2024) - [i23]Yuan Chen, Dongbin Xiu:
Data-driven Effective Modeling of Multiscale Stochastic Dynamical Systems. CoRR abs/2408.14821 (2024) - [i22]Zhongshu Xu, Yuan Chen, Dongbin Xiu:
Chebyshev Feature Neural Network for Accurate Function Approximation. CoRR abs/2409.19135 (2024) - [i21]Yanfang Liu, Yuan Chen, Dongbin Xiu, Guannan Zhang:
A Training-Free Conditional Diffusion Model for Learning Stochastic Dynamical Systems. CoRR abs/2410.03108 (2024) - 2023
- [j62]Victor Churchill, Steve Manns, Zhen Chen, Dongbin Xiu:
Robust modeling of unknown dynamical systems via ensemble averaged learning. J. Comput. Phys. 474: 111842 (2023) - [j61]Victor Churchill, Yuan Chen, Zhongshu Xu, Dongbin Xiu:
DNN modeling of partial differential equations with incomplete data. J. Comput. Phys. 493: 112502 (2023) - [i20]Yuan Chen, Dongbin Xiu:
Learning Stochastic Dynamical System via Flow Map Operator. CoRR abs/2305.03874 (2023) - [i19]Victor Churchill, Dongbin Xiu:
Flow Map Learning for Unknown Dynamical Systems: Overview, Implementation, and Benchmarks. CoRR abs/2307.11013 (2023) - [i18]Zhongshu Xu, Yuan Chen, Qifan Chen, Dongbin Xiu:
Modeling Unknown Stochastic Dynamical System via Autoencoder. CoRR abs/2312.10001 (2023) - 2022
- [j60]Zhen Chen, Victor Churchill, Kailiang Wu, Dongbin Xiu:
Deep neural network modeling of unknown partial differential equations in nodal space. J. Comput. Phys. 449: 110782 (2022) - [j59]Shuyi Wang, Zixu Zhou, Lo-Bin Chang, Dongbin Xiu:
Construction of discontinuity detectors using convolutional neural networks. J. Sci. Comput. 91(2): 40 (2022) - [i17]Xiaohan Fu, Weize Mao, Lo-Bin Chang, Dongbin Xiu:
Modeling unknown dynamical systems with hidden parameters. CoRR abs/2202.01858 (2022) - [i16]Victor Churchill, Steve Manns, Zhen Chen, Dongbin Xiu:
Robust Modeling of Unknown Dynamical Systems via Ensemble Averaged Learning. CoRR abs/2203.03458 (2022) - [i15]Victor Churchill, Dongbin Xiu:
Deep Learning of Chaotic Systems from Partially-Observed Data. CoRR abs/2205.08384 (2022) - [i14]Victor Churchill, Dongbin Xiu:
Learning Fine Scale Dynamics from Coarse Observations via Inner Recurrence. CoRR abs/2206.01807 (2022) - 2021
- [j58]Zhen Chen, Dongbin Xiu:
On generalized residual network for deep learning of unknown dynamical systems. J. Comput. Phys. 438: 110362 (2021) - [j57]Tong Qin, Zhen Chen, John D. Jakeman, Dongbin Xiu:
Data-Driven Learning of Nonautonomous Systems. SIAM J. Sci. Comput. 43(3): A1607-A1624 (2021) - [i13]Zhen Chen, Victor Churchill, Kailiang Wu, Dongbin Xiu:
Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Space. CoRR abs/2106.03603 (2021) - 2020
- [j56]Kailiang Wu, Dongbin Xiu:
Data-driven deep learning of partial differential equations in modal space. J. Comput. Phys. 408: 109307 (2020) - [j55]Zhen Chen, Kailiang Wu, Dongbin Xiu:
Methods to Recover Unknown Processes in Partial Differential Equations Using Data. J. Sci. Comput. 85(2): 23 (2020) - [j54]Kailiang Wu, Tong Qin, Dongbin Xiu:
Structure-Preserving Method for Reconstructing Unknown Hamiltonian Systems From Trajectory Data. SIAM J. Sci. Comput. 42(6): A3704-A3729 (2020) - [i12]Zhen Chen, Dongbin Xiu:
On generalized residue network for deep learning of unknown dynamical systems. CoRR abs/2002.02528 (2020) - [i11]Jun Hou, Tong Qin, Kailiang Wu, Dongbin Xiu:
A Non-Intrusive Correction Algorithm for Classification Problems with Corrupted Data. CoRR abs/2002.04658 (2020) - [i10]Zhen Chen, Kailiang Wu, Dongbin Xiu:
Methods to Recover Unknown Processes in Partial Differential Equations Using Data. CoRR abs/2003.02387 (2020) - [i9]Xiaohan Fu, Lo-Bin Chang, Dongbin Xiu:
Learning reduced systems via deep neural networks with memory. CoRR abs/2003.09451 (2020) - [i8]Tong Qin, Zhen Chen, John D. Jakeman, Dongbin Xiu:
Data-driven learning of non-autonomous systems. CoRR abs/2006.02392 (2020)
2010 – 2019
- 2019
- [j53]Ching-Shan Chou, Yukun Li, Dongbin Xiu:
Energy conserving Galerkin approximation of two dimensional wave equations with random coefficients. J. Comput. Phys. 381: 52-66 (2019) - [j52]Kailiang Wu, Dongbin Xiu:
Numerical aspects for approximating governing equations using data. J. Comput. Phys. 384: 200-221 (2019) - [j51]Tong Qin, Kailiang Wu, Dongbin Xiu:
Data driven governing equations approximation using deep neural networks. J. Comput. Phys. 395: 620-635 (2019) - [j50]Claudio Canuto, Sandra Pieraccini, Dongbin Xiu:
Uncertainty quantification of discontinuous outputs via a non-intrusive bifidelity strategy. J. Comput. Phys. 398 (2019) - [i7]Kailiang Wu, Tong Qin, Dongbin Xiu:
Structure-preserving Method for Reconstructing Unknown Hamiltonian Systems from Trajectory Data. CoRR abs/1905.10396 (2019) - [i6]Kailiang Wu, Dongbin Xiu:
Data-Driven Deep Learning of Partial Differential Equations in Modal Space. CoRR abs/1910.06948 (2019) - [i5]Tong Qin, Zhen Chen, John D. Jakeman, Dongbin Xiu:
A neural network approach for uncertainty quantification for time-dependent problems with random parameters. CoRR abs/1910.07096 (2019) - 2018
- [j49]Kailiang Wu, Dongbin Xiu:
Sequential function approximation on arbitrarily distributed point sets. J. Comput. Phys. 354: 370-386 (2018) - [j48]Yeonjong Shin, Kailiang Wu, Dongbin Xiu:
Sequential function approximation with noisy data. J. Comput. Phys. 371: 363-381 (2018) - [j47]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) - [i4]Tong Qin, Ling Zhou, Dongbin Xiu:
Reducing Parameter Space for Neural Network Training. CoRR abs/1805.08340 (2018) - [i3]Kailiang Wu, Dongbin Xiu:
An Explicit Neural Network Construction for Piecewise Constant Function Approximation. CoRR abs/1808.07390 (2018) - [i2]Kailiang Wu, Dongbin Xiu:
Numerical Aspects for Approximating Governing Equations Using Data. CoRR abs/1809.09170 (2018) - [i1]Tong Qin, Kailiang Wu, Dongbin Xiu:
Data Driven Governing Equations Approximation Using Deep Neural Networks. CoRR abs/1811.05537 (2018) - 2017
- [j46]Xueyu Zhu, Erin M. Linebarger, Dongbin Xiu:
Multi-fidelity stochastic collocation method for computation of statistical moments. J. Comput. Phys. 341: 386-396 (2017) - [j45]Kailiang Wu, Huazhong Tang, Dongbin Xiu:
A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty. J. Comput. Phys. 345: 224-244 (2017) - [j44]Liang Yan, Yeonjong Shin, Dongbin Xiu:
Sparse Approximation using ℓ1-ℓ2 Minimization and Its Application to Stochastic Collocation. SIAM J. Sci. Comput. 39(1) (2017) - [j43]Yeonjong Shin, Dongbin Xiu:
A Randomized Algorithm for Multivariate Function Approximation. SIAM J. Sci. Comput. 39(3) (2017) - [j42]Kailiang Wu, Yeonjong Shin, Dongbin Xiu:
A Randomized Tensor Quadrature Method for High Dimensional Polynomial Approximation. SIAM J. Sci. Comput. 39(5) (2017) - 2016
- [j41]Yanyan He, Dongbin Xiu:
Numerical strategy for model correction using physical constraints. J. Comput. Phys. 313: 617-634 (2016) - [j40]Yeonjong Shin, Dongbin Xiu:
On a near optimal sampling strategy for least squares polynomial regression. J. Comput. Phys. 326: 931-946 (2016) - [j39]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): 1198-1218 (2016) - [j38]Yeonjong Shin, Dongbin Xiu:
Nonadaptive Quasi-Optimal Points Selection for Least Squares Linear Regression. SIAM J. Sci. Comput. 38(1) (2016) - [j37]Yeonjong Shin, Dongbin Xiu:
Correcting Data Corruption Errors for Multivariate Function Approximation. SIAM J. Sci. Comput. 38(4) (2016) - 2015
- [j36]Shi Jin, Dongbin Xiu, Xueyu Zhu:
Asymptotic-preserving methods for hyperbolic and transport equations with random inputs and diffusive scalings. J. Comput. Phys. 289: 35-52 (2015) - [j35]Tao Zhou, Akil Narayan, Dongbin Xiu:
Weighted discrete least-squares polynomial approximation using randomized quadratures. J. Comput. Phys. 298: 787-800 (2015) - [j34]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) - [j33]Jingwei Hu, Shi Jin, Dongbin Xiu:
A Stochastic Galerkin Method for Hamilton-Jacobi Equations with Uncertainty. SIAM J. Sci. Comput. 37(5) (2015) - [j32]Xiaoxiao Chen, Yanyan He, Dongbin Xiu:
An Efficient Method for Uncertainty Propagation using Fuzzy Sets. SIAM J. Sci. Comput. 37(6) (2015) - 2014
- [j31]Xueyu Zhu, Akil Narayan, Dongbin Xiu:
Computational Aspects of Stochastic Collocation with Multifidelity Models. SIAM/ASA J. Uncertain. Quantification 2(1): 444-463 (2014) - [j30]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) - [j29]Jing Li, Dongbin Xiu:
Surrogate Based Method for Evaluation of Failure Probability under Multiple Constraints. SIAM J. Sci. Comput. 36(2) (2014) - [j28]Akil Narayan, Claude Jeffrey Gittelson, Dongbin Xiu:
A Stochastic Collocation Algorithm with Multifidelity Models. SIAM J. Sci. Comput. 36(2) (2014) - 2013
- [j27]Xiaoxiao Chen, Eun-Jae Park, Dongbin Xiu:
A flexible numerical approach for quantification of epistemic uncertainty. J. Comput. Phys. 240: 211-224 (2013) - [j26]John D. Jakeman, Akil Narayan, Dongbin Xiu:
Minimal multi-element stochastic collocation for uncertainty quantification of discontinuous functions. J. Comput. Phys. 242: 790-808 (2013) - [j25]Akil Narayan, Dongbin Xiu:
Constructing Nested Nodal Sets for Multivariate Polynomial Interpolation. SIAM J. Sci. Comput. 35(5) (2013) - 2012
- [j24]Akil Narayan, Youssef M. Marzouk, Dongbin Xiu:
Sequential data assimilation with multiple models. J. Comput. Phys. 231(19): 6401-6418 (2012) - [j23]Roland Pulch, Dongbin Xiu:
Generalised Polynomial Chaos for a Class of Linear Conservation Laws. J. Sci. Comput. 51(2): 293-312 (2012) - [j22]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): 2659-2682 (2012) - [j21]Akil Narayan, Dongbin Xiu:
Stochastic Collocation Methods on Unstructured Grids in High Dimensions via Interpolation. SIAM J. Sci. Comput. 34(3) (2012) - [j20]Jing Li, Dongbin Xiu:
Computation of Failure Probability Subject to Epistemic Uncertainty. SIAM J. Sci. Comput. 34(6) (2012) - 2011
- [j19]John D. Jakeman, Richard Archibald, Dongbin Xiu:
Characterization of discontinuities in high-dimensional stochastic problems on adaptive sparse grids. J. Comput. Phys. 230(10): 3977-3997 (2011) - [j18]Jing Li, Jinglai Li, Dongbin Xiu:
An efficient surrogate-based method for computing rare failure probability. J. Comput. Phys. 230(24): 8683-8697 (2011) - 2010
- [j17]John D. Jakeman, Michael S. Eldred, Dongbin Xiu:
Numerical approach for quantification of epistemic uncertainty. J. Comput. Phys. 229(12): 4648-4663 (2010) - [j16]Jing Li, Dongbin Xiu:
Evaluation of failure probability via surrogate models. J. Comput. Phys. 229(23): 8966-8980 (2010)
2000 – 2009
- 2009
- [j15]Dongbin Xiu, Jie Shen:
Efficient stochastic Galerkin methods for random diffusion equations. J. Comput. Phys. 228(2): 266-281 (2009) - [j14]Rick Archibald, Anne Gelb, Rishu Saxena, Dongbin Xiu:
Discontinuity detection in multivariate space for stochastic simulations. J. Comput. Phys. 228(7): 2676-2689 (2009) - [j13]Jia Li, Dongbin Xiu:
A generalized polynomial chaos based ensemble Kalman filter with high accuracy. J. Comput. Phys. 228(15): 5454-5469 (2009) - 2007
- [j12]Daniel M. Tartakovsky, Dongbin Xiu:
Guest Editors' Introduction: Stochastic Modeling of Complex Systems. Comput. Sci. Eng. 9(2): 8-9 (2007) - [j11]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): 1385-1407 (2007) - 2006
- [j10]Daniel M. Tartakovsky, Dongbin Xiu:
Stochastic analysis of transport in tubes with rough walls. J. Comput. Phys. 217(1): 248-259 (2006) - [j9]Dongbin Xiu, Daniel M. Tartakovsky:
Numerical Methods for Differential Equations in Random Domains. SIAM J. Sci. Comput. 28(3): 1167-1185 (2006) - 2005
- [j8]Dongbin Xiu, Ioannis G. Kevrekidis, Roger G. Ghanem:
An equation-free, multiscale approach to uncertainty quantification. Comput. Sci. Eng. 7(3): 16-23 (2005) - [j7]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): 323-346 (2005) - [j6]Dongbin Xiu, Ioannis G. Kevrekidis:
Equation-Free, Multiscale Computation for Unsteady Random Diffusion. Multiscale Model. Simul. 4(3): 915-935 (2005) - [j5]Dongbin Xiu, Jan S. Hesthaven:
High-Order Collocation Methods for Differential Equations with Random Inputs. SIAM J. Sci. Comput. 27(3): 1118-1139 (2005) - 2004
- [j4]Dongbin Xiu, Daniel M. Tartakovsky:
A Two-Scale Nonperturbative Approach to Uncertainty Analysis of Diffusion in Random Composites. Multiscale Model. Simul. 2(4): 662-674 (2004) - [j3]Xiaoliang Wan, Dongbin Xiu, George E. Karniadakis:
Stochastic Solutions for the Two-Dimensional Advection-Diffusion Equation. SIAM J. Sci. Comput. 26(2): 578-590 (2004) - 2003
- [c1]Dongbin Xiu, Didier Lucor, Chau-Hsing Su, George E. Karniadakis:
Performance Evaluation of Generalized Polynomial Chaos. International Conference on Computational Science 2003: 346-354 - 2002
- [j2]Jin Xu, Dongbin Xiu, George E. Karniadakis:
A Semi-Lagrangian Method for Turbulence Simulations Using Mixed Spectral Discretizations. J. Sci. Comput. 17(1-4): 585-597 (2002) - [j1]Dongbin Xiu, George E. Karniadakis:
The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations. SIAM J. Sci. Comput. 24(2): 619-644 (2002)
Coauthor Index
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