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Optimal design for kernel interpolation: Applications to uncertainty quantification 期刊论文
JOURNAL OF COMPUTATIONAL PHYSICS, 2021, 卷号: 430, 页码: 19
Authors:  Narayan, Akil;  Yan, Liang;  Zhou, Tao
Favorite  |  View/Download:11/0  |  Submit date:2021/04/26
Kernel interpolation  Fekete points  Cholesky decomposition with pivoting  Hermite interpolation  Uncertainty quantification  
Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection 期刊论文
SCIENCE CHINA-MATHEMATICS, 2021, 页码: 16
Authors:  Liao, Hong-Lin;  Song, Xuehua;  Tang, Tao;  Zhou, Tao
Favorite  |  View/Download:8/0  |  Submit date:2021/04/26
molecular beam epitaxial growth  variable-step BDF2 scheme  discrete orthogonal convolution kernels  energy stability  convergence analysis  
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
Authors:  Wu, Shu-Lin;  Zhou, Tao
Favorite  |  View/Download:4/0  |  Submit date:2021/04/26
Parabolic PDE-constrained optimization  PinT algorithm  diagonalization technique  preconditioner  GMRES  BiCGStab  
An Efficient Numerical Algorithm for Solving Data Driven Feedback Control Problems 期刊论文
JOURNAL OF SCIENTIFIC COMPUTING, 2020, 卷号: 85, 期号: 2, 页码: 27
Authors:  Archibald, Richard;  Bao, Feng;  Yong, Jiongmin;  Zhou, Tao
Favorite  |  View/Download:4/0  |  Submit date:2021/01/14
Stochastic optimal control  Nonlinear filtering  Data driven  Maximum principle  Stochastic optimization  
An Adaptive Surrogate Modeling Based on Deep Neural Networks for Large-Scale Bayesian Inverse Problems 期刊论文
COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2020, 卷号: 28, 期号: 5, 页码: 2180-2205
Authors:  Yan, Liang;  Zhou, Tao
Favorite  |  View/Download:6/0  |  Submit date:2021/01/14
Bayesian inverse problems  deep neural networks  multi-fidelity surrogate modeling  Markov chain Monte Carlo  
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
Authors:  Liao, Hong-lin;  Tang, Tao;  Zhou, Tao
Favorite  |  View/Download:19/0  |  Submit date: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
Authors:  Guo, Ling;  Narayan, Akil;  Zhou, Tao
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least-squares approximations  optimal sampling  polynomial approximations  
Highly Accurate Numerical Schemes for Stochastic Optimal Control Via FBSDEs 期刊论文
NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2020, 卷号: 13, 期号: 2, 页码: 296-319
Authors:  Fu, Yu;  Zhao, Weidong;  Zhou, Tao
Favorite  |  View/Download:18/0  |  Submit date:2020/05/24
Forward backward stochastic differential equations  stochastic optimal control  stochastic maximum principle  projected quasi-Newton methods  
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
Authors:  Tang, Tao;  Wang, Li-Lian;  Yuan, Huifang;  Zhou, Tao
Favorite  |  View/Download:11/0  |  Submit date:2020/09/23
fractional Laplacian  Gegenbauer polynomials  modified rational functions  unbounded domains  Fourier transforms  spectral methods  
ON ENERGY STABLE, MAXIMUM-PRINCIPLE PRESERVING, SECOND-ORDER BDF SCHEME WITH VARIABLE STEPS FOR THE ALLEN-CAHN EQUATION 期刊论文
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2020, 卷号: 58, 期号: 4, 页码: 2294-2314
Authors:  Liao, Hong-lin;  Tang, Tao;  Zhou, Tao
Favorite  |  View/Download:4/0  |  Submit date:2021/01/14
Allen-Cahn equation  nonuniform BDF2 scheme  energy stability  discrete maximum principle  convergence analysis