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Monte Carlo fPINNs: Deep learning method for forward and inverse problems involving high dimensional fractional partial differential equations 期刊论文
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2022, 卷号: 400, 页码: 17
Authors:  Guo, Ling;  Wu, Hao;  Yu, Xiaochen;  Zhou, Tao
Favorite  |  View/Download:76/0  |  Submit date:2023/02/07
Physics -informed neural networks  Fractional Laplacian  Nonlocal operators  Uncertainty quantification  

Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow models

期刊论文

JOURNAL OF COMPUTATIONAL PHYSICS, 2022, 卷号: 461, 页码: 18
Authors:  Guo, Ling;  Wu, Hao;  Zhou, Tao
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Data -driven modeling  Normalizing flows  Uncertainty quantification  Random fields  
A well-conditioned direct PinT algorithm for first- and second-order evolutionary equations 期刊论文
ADVANCES IN COMPUTATIONAL MATHEMATICS, 2022, 卷号: 48, 期号: 3, 页码: 29
Authors:  Liu, Jun;  Wang, Xiang-Sheng;  Wu, Shu-Lin;  Zhou, Tao
Favorite  |  View/Download:123/0  |  Submit date:2022/04/29
Direct PinT algorithms  Diagonalization technique  Condition number  Wave-type equations  
A UNIFORM SPECTRAL ANALYSIS FOR A PRECONDITIONED ALL-AT-ONCE SYSTEM FROM FIRST-ORDER AND SECOND-ORDER EVOLUTIONARY PROBLEMS 期刊论文
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2022, 卷号: 43, 期号: 3, 页码: 1331-1353
Authors:  Wu, Shu-Lin;  Zhou, Tao;  Zhou, Zhi
Favorite  |  View/Download:89/0  |  Submit date:2023/02/07
time-parallel algorithm  diagonalization technique  alpha-circulant preconditioner  stability  spectral analysis  Runge-Kutta method  two-step methods  
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
Authors:  Yan, Liang;  Zhou, Tao
Favorite  |  View/Download:115/0  |  Submit date: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
Authors:  Narayan, Akil;  Yan, Liang;  Zhou, Tao
Favorite  |  View/Download:163/0  |  Submit date:2021/04/26
Kernel interpolation  Fekete points  Cholesky decomposition with pivoting  Hermite interpolation  Uncertainty quantification  
AN EXPLICIT MULTISTEP SCHEME FOR MEAN-FIELD FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS 期刊论文
JOURNAL OF COMPUTATIONAL MATHEMATICS, 2021, 页码: 25
Authors:  Sun, Yabing;  Yang, Jie;  Zhao, Weidong;  Zhou, Tao
Favorite  |  View/Download:132/0  |  Submit date:2022/04/02
Mean-field forward backward stochastic differential equations  Explicit multistep scheme  Error estimates  
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
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molecular beam epitaxial growth  variable-step BDF2 scheme  discrete orthogonal convolution kernels  energy stability  convergence analysis  
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
Authors:  Yan, Liang;  Zhou, Tao
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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
Authors:  Liao, Hong-lin;  Tang, Tao;  Zhou, Tao
Favorite  |  View/Download:110/0  |  Submit date:2022/04/02
time-fractional Allen--Cahn equation  asymptotic preserving  energy stability  adaptive time stepping  max-imum principle