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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
作者:  Guo, Ling;  Wu, Hao;  Yu, Xiaochen;  Zhou, Tao
收藏  |  浏览/下载:49/0  |  提交时间: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
作者:  Zhao, Yue;  Mao, Zhiping;  Guo, Ling;  Tang, Yifa;  Karniadakis, George Em
收藏  |  浏览/下载:58/0  |  提交时间: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
作者:  Guo, Ling;  Wu, Hao;  Zhou, Tao
收藏  |  浏览/下载:115/0  |  提交时间: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
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  
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
作者:  Zhang, Yue;  Luo, Shunlong
收藏  |  浏览/下载:147/0  |  提交时间: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
作者:  Fu, Shuangshuang;  Luo, Shunlong;  Zhang, Yue
收藏  |  浏览/下载:168/0  |  提交时间: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
作者:  Wei, Yunfei;  Xiong, Shifeng
收藏  |  浏览/下载:181/0  |  提交时间: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
作者:  Zhou, Heng;  Xu, Zhiqiang
收藏  |  浏览/下载:159/0  |  提交时间: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
作者:  Guo, Ling;  Liu, Yongle;  Zhou, Tao
收藏  |  浏览/下载:160/0  |  提交时间: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
作者:  Wan, Xiaoliang;  Yu, Haijun
收藏  |  浏览/下载:143/0  |  提交时间:2020/01/10
Wiener chaos expansion  Wick product  stochastic elliptic PDE  uncertainty quantification  log-normal random coefficient