The Wiener-Askey polynomial chaos for stochastic differential equations D Xiu, GE Karniadakis SIAM Journal on Scientific Computing 24 (2), 614-644, 2002 | 5718 | 2002 |
Numerical methods for stochastic computations: a spectral method approach D Xiu Princeton university press, 2010 | 2300 | 2010 |
High-order collocation methods for differential equations with random inputs D Xiu, JS Hesthaven SIAM Journal on Scientific Computing 27 (3), 1118-1139, 2005 | 1946 | 2005 |
Modeling uncertainty in flow simulations via generalized polynomial chaos D Xiu, GE Karniadakis Journal of computational physics 187 (1), 137-167, 2003 | 1760 | 2003 |
Fast numerical methods for stochastic computations: a review D Xiu Communications in Computational Physics 5 (2-4), 242-272, 2009 | 867 | 2009 |
Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos D Xiu, GE Karniadakis Computer methods in applied mechanics and engineering 191 (43), 4927-4948, 2002 | 728 | 2002 |
Efficient collocational approach for parametric uncertainty analysis D Xiu Communications in Computational Physics 2 (2), 293-309, 2007 | 570 | 2007 |
Stochastic modeling of flow-structure interactions using generalized polynomial chaos D Xiu, D Lucor, CH Su, GE Karniadakis J. Fluids Eng. 124 (1), 51-59, 2002 | 374 | 2002 |
A stochastic collocation approach to Bayesian inference in inverse problems Y Marzouk, D Xiu Communications in Computational Physics 6 (4), 826-847, 2009 | 346 | 2009 |
Data driven governing equations approximation using deep neural networks T Qin, K Wu, D Xiu Journal of Computational Physics 395, 620-635, 2019 | 311 | 2019 |
A new stochastic approach to transient heat conduction modeling with uncertainty D Xiu, GE Karniadakis International Journal of Heat and Mass Transfer 46 (24), 4681-4693, 2003 | 287 | 2003 |
A semi-Lagrangian high-order method for Navier-Stokes equations D Xiu, GE Karniadakis Journal of Computational Physics 172 (2), 658-684, 2001 | 240 | 2001 |
Numerical methods for differential equations in random domains D Xiu, DM Tartakovsky SIAM Journal on Scientific Computing 28 (3), 1167-1185, 2006 | 233 | 2006 |
Evaluation of failure probability via surrogate models J Li, D Xiu Journal of Computational Physics 229 (23), 8966-8980, 2010 | 187 | 2010 |
Galerkin method for wave equations with uncertain coefficients D Gottlieb, D Xiu Communications in Computational Physics 3 (2), 505-518, 2008 | 178 | 2008 |
A generalized polynomial chaos based ensemble Kalman filter with high accuracy J Li, D Xiu Journal of Computational Physics 228 (15), 5454-5469, 2009 | 170 | 2009 |
A stochastic collocation algorithm with multifidelity models A Narayan, C Gittelson, D Xiu SIAM Journal on Scientific Computing 36 (2), A495-A521, 2014 | 166 | 2014 |
Data-driven deep learning of partial differential equations in modal space K Wu, D Xiu Journal of Computational Physics 408, 109307, 2020 | 156 | 2020 |
Stochastic Collocation Algorithms using l1--Minimization L Yan, L Guo, D Xiu International Journal for Uncertainty Quantification 2 (3), 279-293, 2012 | 149 | 2012 |
Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network D Xiu, SJ Sherwin Journal of Computational Physics 226 (2), 1385-1407, 2007 | 131 | 2007 |