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Stein variational gradient descent with local approximations 期刊论文
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2021, 卷号: 386, 页码: 20
作者:  Yan, Liang;  Zhou, Tao
收藏  |  浏览/下载：102/0  |  提交时间：2022/04/02
Stein variational gradient decent  Bayesian inference  Deep learning  Local approximation  
Optimal design for kernel interpolation: Applications to uncertainty quantification 期刊论文
JOURNAL OF COMPUTATIONAL PHYSICS, 2021, 卷号: 430, 页码: 19
作者:  Narayan, Akil;  Yan, Liang;  Zhou, Tao
收藏  |  浏览/下载：138/0  |  提交时间：2021/04/26
Kernel interpolation  Fekete points  Cholesky decomposition with pivoting  Hermite interpolation  Uncertainty quantification  
AN ACCELERATION STRATEGY FOR RANDOMIZE-THEN-OPTIMIZE SAMPLING VIA DEEP NEURAL NETWORKS* 期刊论文
JOURNAL OF COMPUTATIONAL MATHEMATICS, 2021, 卷号: 39, 期号: 6, 页码: 848-864
作者:  Yan, Liang;  Zhou, Tao
收藏  |  浏览/下载：122/0  |  提交时间：2022/04/02
Bayesian inverse problems  Deep neural network  Markov chain Monte Carlo  
AN ENERGY STABLE AND MAXIMUM BOUND PRESERVING SCHEME WITH VARIABLE TIME STEPS FOR TIME FRACTIONAL ALLEN--CAHN EQUATION 期刊论文
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2021, 卷号: 43, 期号: 5, 页码: A3503-A3526
作者:  Liao, Hong-lin;  Tang, Tao;  Zhou, Tao
收藏  |  浏览/下载：85/0  |  提交时间：2022/04/02
time-fractional Allen--Cahn equation  asymptotic preserving  energy stability  adaptive time stepping  max-imum principle  
Diagonalization-based parallel-in-time algorithms for parabolic PDE-constrained optimization problems 期刊论文
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2020, 卷号: 26, 页码: 26
作者:  Wu, Shu-Lin;  Zhou, Tao
收藏  |  浏览/下载：145/0  |  提交时间：2021/04/26
Parabolic PDE-constrained optimization  PinT algorithm  diagonalization technique  preconditioner  GMRES  BiCGStab  
A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations 期刊论文
JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 卷号: 414, 页码: 16
作者:  Liao, Hong-lin;  Tang, Tao;  Zhou, Tao
收藏  |  浏览/下载：158/0  |  提交时间：2020/06/30
Time-fractional Allen-Cahn equation  Alikhanov formula  Adaptive time-stepping strategy  Discrete maximum principle  Sharp error estimate  
Constructing Least-Squares Polynomial Approximations 期刊论文
SIAM REVIEW, 2020, 卷号: 62, 期号: 2, 页码: 483-508
作者:  Guo, Ling;  Narayan, Akil;  Zhou, Tao
收藏  |  浏览/下载：129/0  |  提交时间：2020/09/23
least-squares approximations  optimal sampling  polynomial approximations  
RATIONAL SPECTRAL METHODS FOR PDEs INVOLVING FRACTIONAL LAPLACIAN IN UNBOUNDED DOMAINS 期刊论文
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2020, 卷号: 42, 期号: 2, 页码: A585-A611
作者:  Tang, Tao;  Wang, Li-Lian;  Yuan, Huifang;  Zhou, Tao
收藏  |  浏览/下载：148/0  |  提交时间：2020/09/23
fractional Laplacian  Gegenbauer polynomials  modified rational functions  unbounded domains  Fourier transforms  spectral methods  
Efficient Stochastic Galerkin Methods for Maxwell's Equations with Random Inputs 期刊论文
JOURNAL OF SCIENTIFIC COMPUTING, 2019, 卷号: 80, 期号: 1, 页码: 248-267
作者:  Fang, Zhiwei;  Li, Jichun;  Tang, Tao;  Zhou, Tao
收藏  |  浏览/下载：159/0  |  提交时间：2020/01/10
Maxwell's equations  Finite element method  Random inputs  Polynomial chaos methods  Stochastic Galerkin  
Explicit Deferred Correction Methods for Second-Order Forward Backward Stochastic Differential Equations 期刊论文
JOURNAL OF SCIENTIFIC COMPUTING, 2019, 卷号: 79, 期号: 3, 页码: 1409-1432
作者:  Yang, Jie;  Zhao, Weidong;  Zhou, Tao
收藏  |  浏览/下载：152/0  |  提交时间：2020/01/10
Deferred correction method  Second-order forward backward stochastic differential equations  Euler scheme  High-order rate of convergence