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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：17/0  |  Submit date：2023/02/07
Physics -informed neural networks  Fractional Laplacian  Nonlocal operators  Uncertainty quantification  
A spectral method for stochastic fractional PDEs using dynamically-orthogonal/bi-orthogonal decomposition 期刊论文
JOURNAL OF COMPUTATIONAL PHYSICS, 2022, 卷号: 461, 页码: 17
Authors:  Zhao, Yue;  Mao, Zhiping;  Guo, Ling;  Tang, Yifa;  Karniadakis, George Em
Favorite  |  View/Download：20/0  |  Submit date：2023/02/07
Uncertainty quantification  Anomalous transport  Quasi Monte Carlo simulation  Generalized polynomial chaos  Long-time integration  Poly-fractonomials  

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
Favorite  |  View/Download：62/0  |  Submit date：2023/02/07
Data -driven modeling  Normalizing flows  Uncertainty quantification  Random fields  
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：99/0  |  Submit date：2021/04/26
Kernel interpolation  Fekete points  Cholesky decomposition with pivoting  Hermite interpolation  Uncertainty quantification  
Quantum states as observables: Their variance and nonclassicality 期刊论文
PHYSICAL REVIEW A, 2020, 卷号: 102, 期号: 6, 页码: 6
Authors:  Zhang, Yue;  Luo, Shunlong
Favorite  |  View/Download：112/0  |  Submit date：2021/04/26
Quantifying non-Gaussianity of bosonic fields via an uncertainty relation 期刊论文
PHYSICAL REVIEW A, 2020, 卷号: 101, 期号: 1, 页码: 8
Authors:  Fu, Shuangshuang;  Luo, Shunlong;  Zhang, Yue
Favorite  |  View/Download：131/0  |  Submit date：2020/05/24
Bayesian integrative analysis for multi-fidelity computer experiments 期刊论文
JOURNAL OF APPLIED STATISTICS, 2019, 卷号: 46, 期号: 11, 页码: 1973-1987
Authors:  Wei, Yunfei;  Xiong, Shifeng
Favorite  |  View/Download：138/0  |  Submit date：2020/01/10
Correlated priors  Gaussian process  Kriging  penalization  uncertainty quantification  
On Generalizations of p-Sets and their Applications 期刊论文
NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2019, 卷号: 12, 期号: 2, 页码: 453-466
Authors:  Zhou, Heng;  Xu, Zhiqiang
Favorite  |  View/Download：128/0  |  Submit date：2019/03/05
p-set  deterministic sampling  numerical integral  exponential sum  
Data-driven polynomial chaos expansions: A weighted least-square approximation 期刊论文
JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 卷号: 381, 页码: 129-145
Authors:  Guo, Ling;  Liu, Yongle;  Zhou, Tao
Favorite  |  View/Download：124/0  |  Submit date：2019/03/11
Uncertainty quantification  Data-driven polynomial chaos expansions  Weighted least-squares  Equilibrium measure  
NUMERICAL APPROXIMATION OF ELLIPTIC PROBLEMS WITH LOG-NORMAL RANDOM COEFFICIENTS 期刊论文
INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION, 2019, 卷号: 9, 期号: 2, 页码: 161-186
Authors:  Wan, Xiaoliang;  Yu, Haijun
Favorite  |  View/Download：97/0  |  Submit date：2020/01/10
Wiener chaos expansion  Wick product  stochastic elliptic PDE  uncertainty quantification  log-normal random coefficient