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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：53/0  |  提交时间：2023/02/07
Physics -informed neural networks  Fractional Laplacian  Nonlocal operators  Uncertainty quantification  
Collective stochastic dynamics of the Cucker-Smale ensemble under uncertain communication 期刊论文
JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 卷号: 284, 页码: 39-82
作者:  Ha, Seung-Yeal;  Jung, Jinwook;  Rockner, Michael
收藏  |  浏览/下载：152/0  |  提交时间：2021/06/01
Cucker-Smale model  Emergence  Flocking  Random communication  Stochastic kinetic Cucker-Smale equation  
Ornstein-Uhlenbeck processes with singular drifts: integral estimates and Girsanov densities 期刊论文
PROBABILITY THEORY AND RELATED FIELDS, 2020, 页码: 31
作者:  Gordina, Maria;  Roeckner, Michael;  Teplyaev, Alexander
收藏  |  浏览/下载：140/0  |  提交时间：2020/09/23
Ornstein-Uhlenbeck process  Singular perturbation  Nonlinear infinite-dimensional stochastic differential equations  Non-Lipschitz monotone coefficients  Girsanov theorem  
Ergodicity for a class of semilinear stochastic partial differential equations 期刊论文
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2019, 页码: 20
作者:  Dong, Zhao;  Zhang, Rangrang
收藏  |  浏览/下载：196/0  |  提交时间：2020/05/24
invariant measures  irreducibility  semilinear partial differential equations  space-time white noise  strong Feller property  
Shadowing orbits of a class of random differential equations 期刊论文
APPLIED NUMERICAL MATHEMATICS, 2019, 卷号: 136, 页码: 206-214
作者:  Zhan, Qingyi
收藏  |  浏览/下载：142/0  |  提交时间：2019/03/05
Random differential equation  Random dynamical system  Shadowing  Brouwer's fixed point theorem  Random Lorenz equations  
ERGODIC APPROXIMATION TO CHEMICAL REACTION SYSTEM WITH DELAY 期刊论文
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2019, 卷号: 57, 期号: 1, 页码: 70-95
作者:  Chen, Chuchu;  Liu, Di
收藏  |  浏览/下载：141/0  |  提交时间：2020/01/10
stochastic delay differential equation  invariant measure  ergodicity  weak convergence order  Malliavin calculus  Poisson random measure  
Averaging principle for one dimensional stochastic Burgers equation 期刊论文
JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 卷号: 265, 期号: 10, 页码: 4749-4797
作者:  Dong, Zhao;  Sun, Xiaobin;  Xiao, Hui;  Zhai, Jianliang
收藏  |  浏览/下载：402/0  |  提交时间：2018/10/07
Stochastic Burgers' equation  Averaging principle  Ergodicity  Invariant measure  Strong convergence  Weak convergence  
Existence of solution to parabolic equations with mixed boundary condition on non-cylindrical domains 期刊论文
JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 卷号: 265, 期号: 6, 页码: 2648-2670
作者:  Kim, Tujin;  Cao, Daomin
收藏  |  浏览/下载：187/0  |  提交时间：2018/07/30
Parabolic equation  Non-cylindrical domain  Mixed boundary condition  Existence  
Distributed resource allocation over random networks based on stochastic approximation 期刊论文
SYSTEMS & CONTROL LETTERS, 2018, 卷号: 114, 页码: 44-51
作者:  Yi, Peng;  Lei, Jinlong;  Hong, Yiguang
收藏  |  浏览/下载：153/0  |  提交时间：2018/07/30
Distributed optimization  Resource allocation  Stochastic approximation  Random graph  Demand response  
Inverse random source scattering for the Helmholtz equation in inhomogeneous media 期刊论文
INVERSE PROBLEMS, 2018, 卷号: 34, 期号: 1, 页码: 19
作者:  Li, Ming;  Chen, Chuchu;  Li, Peijun
收藏  |  浏览/下载：149/0  |  提交时间：2018/07/30
inverse source scattering problem  the Helmholtz equation  stochastic partial differential equation