A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations. I: Derivation and algorithms. Zbl 1297.65008
Cheng, Mulin; Hou, Thomas Y.; Zhang, Zhiwen |
|
2013
|
A mesh-free method for interface problems using the deep learning approach. Zbl 1454.65173
Wang, Zhongjian; Zhang, Zhiwen |
|
2020
|
A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations. II: Adaptivity and generalizations. Zbl 1297.65007
Cheng, Mulin; Hou, Thomas Y.; Zhang, Zhiwen |
|
2013
|
Split local absorbing conditions for one-dimensional nonlinear Klein-Gordon equation on unbounded domain. Zbl 1152.65092
Han, Houde; Zhang, Zhiwen |
|
2008
|
A data-driven stochastic method for elliptic PDEs with random coefficients. Zbl 1290.60068
Cheng, Mulin; Hou, Thomas Y.; Yan, Mike; Zhang, Zhiwen |
|
2013
|
A model reduction method for multiscale elliptic PDEs with random coefficients using an optimization approach. Zbl 1420.35083
Hou, Thomas Y.; Ma, Dingjiong; Zhang, Zhiwen |
|
2019
|
An Eulerian surface hopping method for the Schrödinger equation with conical crossings. Zbl 1219.35202
Jin, Shi; Qi, Peng; Zhang, Zhiwen |
|
2011
|
An analysis of the finite-difference method for one-dimensional Klein-Gordon equation on unbounded domain. Zbl 1162.65377
Han, Houde; Zhang, Zhiwen |
|
2009
|
Cluster-based generalized multiscale finite element method for elliptic PDEs with random coefficients. Zbl 1415.65251
Chung, Eric T.; Efendiev, Yalchin; Leung, Wing Tat; Zhang, Zhiwen |
|
2018
|
A data-driven approach for multiscale elliptic PDEs with random coefficients based on intrinsic dimension reduction. Zbl 1459.35194
Li, Sijing; Zhang, Zhiwen; Zhao, Hongkai |
|
2020
|
Computing effective diffusivity of chaotic and stochastic flows using structure-preserving schemes. Zbl 1404.65209
Wang, Zhongjian; Xin, Jack; Zhang, Zhiwen |
|
2018
|
A multiscale finite element method for the Schrödinger equation with multiscale potentials. Zbl 1428.35111
Chen, Jingrun; Ma, Dingjiong; Zhang, Zhiwen |
|
2019
|
Proper orthogonal decomposition method to nonlinear filtering problems in medium-high dimension. Zbl 1533.93818
Wang, Zhongjian; Luo, Xue; Yau, Stephen S.-T.; Zhang, Zhiwen |
|
2020
|
Computing eigenvalues and eigenfunctions of Schrödinger equations using a model reduction approach. Zbl 1475.65183
Li, Shuangping; Zhang, Zhiwen |
|
2018
|
DeepParticle: learning invariant measure by a deep neural network minimizing Wasserstein distance on data generated from an interacting particle method. Zbl 07540355
Wang, Zhongjian; Xin, Jack; Zhang, Zhiwen |
|
2022
|
Efficient multiscale methods for the semiclassical Schrödinger equation with time-dependent potentials. Zbl 1506.81008
Chen, Jingrun; Li, Sijing; Zhang, Zhiwen |
|
2020
|
Error estimates for a POD method for solving viscous G-equations in incompressible cellular flows. Zbl 1469.65156
Gu, Haotian; Xin, Jack; Zhang, Zhiwen |
|
2021
|
Sharp error estimates on a stochastic structure-preserving scheme in computing effective diffusivity of 3D chaotic flows. Zbl 1496.65192
Wang, Zhongjian; Xin, Jack; Zhang, Zhiwen |
|
2021
|
A model reduction method for elliptic PDEs with random input using the heterogeneous stochastic FEM framework. Zbl 1341.65004
Hou, Thomas Y.; Liu, Pengfei; Zhang, Zhiwen |
|
2016
|
An adaptive ANOVA-based data-driven stochastic method for elliptic PDEs with random coefficient. Zbl 1388.65178
Zhang, Zhiwen; Hu, Xin; Hou, Thomas Y.; Lin, Guang; Yan, Mike |
|
2014
|
An iterative algorithm for POD basis adaptation in solving parametric convection-diffusion equations. Zbl 1507.65192
Wu, Zhizhang; Zhang, Zhiwen |
|
2022
|
Multiscale tailored finite point method for second order elliptic equations with rough or highly oscillatory coefficients. Zbl 1416.65450
Han, Houde; Zhang, Zhiwen |
|
2012
|
Adaptive artificial boundary condition for the two-level Schrödinger equation with conical crossings. Zbl 1210.65155
Han, Houde; Zhang, Zhiwen |
|
2011
|
A convergent interacting particle method and computation of KPP front speeds in chaotic flows. Zbl 07538279
Lyu, Junlong; Wang, Zhongjian; Xin, Jack; Zhang, Zhiwen |
|
2022
|
Proper orthogonal decomposition method for multiscale elliptic PDEs with random coefficients. Zbl 1439.35588
Ma, Dingjiong; Ching, Wai-ki; Zhang, Zhiwen |
|
2020
|
Convergence analysis of stochastic structure-preserving schemes for computing effective diffusivity in random flows. Zbl 1509.37120
Lyu, Junlong; Wang, Zhongjian; Xin, Jack; Zhang, Zhiwen |
|
2020
|
Split local artificial boundary conditions for the two-dimensional sine-Gordon equation on \(\mathbb R^2\). Zbl 1388.65055
Han, Houde; Zhang, Zhiwen |
|
2011
|
A second order accuracy preserving method for moving contact lines with Stokes flow. Zbl 07515862
Chai, Shuqing; Zhang, Zhen; Zhang, Zhiwen |
|
2021
|
A multiscale reduced basis method for the Schrödinger equation with multiscale and random potentials. Zbl 1454.35070
Chen, Jingrun; Ma, Dingjiong; Zhang, Zhiwen |
|
2020
|
Deterministic-statistical approach for an inverse acoustic source problem using multiple frequency limited aperture data. Zbl 1520.35175
Liu, Yanfang; Wu, Zhizhang; Sun, Jiguang; Zhang, Zhiwen |
|
2023
|
A data-driven model reduction method for parabolic inverse source problems and its convergence analysis. Zbl 07690228
Wang, Zhongjian; Zhang, Wenlong; Zhang, Zhiwen |
|
2023
|
A QMC-deep learning method for diffusivity estimation in random domains. Zbl 1474.65007
Lv, Liyao; Zhang, Zhiwen; Chen, Jingrun |
|
2020
|
An adaptive dynamically low-dimensional approximation method for multiscale stochastic diffusion equations. Zbl 1435.65154
Chung, Eric T.; Pun, Sai-Mang; Zhang, Zhiwen |
|
2019
|
Computing effective diffusivities in 3D time-dependent chaotic flows with a convergent Lagrangian numerical method. Zbl 07598348
Wang, Zhongjian; Xin, Jack; Zhang, Zhiwen |
|
2022
|
A data-driven and model-based accelerated Hamiltonian Monte Carlo method for Bayesian elliptic inverse problems. Zbl 1517.62030
Li, Sijing; Zhang, Cheng; Zhang, Zhiwen; Zhao, Hongkai |
|
2023
|
Error estimate of a quasi-Monte Carlo time-splitting pseudospectral method for nonlinear Schrödinger equation with random potentials. Zbl 07827680
Wu, Zhizhang; Zhang, Zhiwen; Zhao, Xiaofei |
|
2024
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A pressure Poisson equation-based second-order method for solving two-dimensional moving contact line problems with topological changes. Zbl 07832223
Chai, Shuqing; Li, Zhilin; Zhang, Zhen; Zhang, Zhiwen |
|
2024
|
Reduced-order model-based variational inference with normalizing flows for Bayesian elliptic inverse problems. Zbl 1532.35539
Wu, Zhizhang; Zhang, Cheng; Zhang, Zhiwen |
|
2024
|
Convergence analysis of the localized orthogonal decomposition method for the semiclassical Schrödinger equations with multiscale potentials. Zbl 1503.65275
Wu, Zhizhang; Zhang, Zhiwen |
|
2022
|
Error estimate of a quasi-Monte Carlo time-splitting pseudospectral method for nonlinear Schrödinger equation with random potentials. Zbl 07827680
Wu, Zhizhang; Zhang, Zhiwen; Zhao, Xiaofei |
|
2024
|
A pressure Poisson equation-based second-order method for solving two-dimensional moving contact line problems with topological changes. Zbl 07832223
Chai, Shuqing; Li, Zhilin; Zhang, Zhen; Zhang, Zhiwen |
|
2024
|
Reduced-order model-based variational inference with normalizing flows for Bayesian elliptic inverse problems. Zbl 1532.35539
Wu, Zhizhang; Zhang, Cheng; Zhang, Zhiwen |
|
2024
|
Deterministic-statistical approach for an inverse acoustic source problem using multiple frequency limited aperture data. Zbl 1520.35175
Liu, Yanfang; Wu, Zhizhang; Sun, Jiguang; Zhang, Zhiwen |
|
2023
|
A data-driven model reduction method for parabolic inverse source problems and its convergence analysis. Zbl 07690228
Wang, Zhongjian; Zhang, Wenlong; Zhang, Zhiwen |
|
2023
|
A data-driven and model-based accelerated Hamiltonian Monte Carlo method for Bayesian elliptic inverse problems. Zbl 1517.62030
Li, Sijing; Zhang, Cheng; Zhang, Zhiwen; Zhao, Hongkai |
|
2023
|
DeepParticle: learning invariant measure by a deep neural network minimizing Wasserstein distance on data generated from an interacting particle method. Zbl 07540355
Wang, Zhongjian; Xin, Jack; Zhang, Zhiwen |
|
2022
|
An iterative algorithm for POD basis adaptation in solving parametric convection-diffusion equations. Zbl 1507.65192
Wu, Zhizhang; Zhang, Zhiwen |
|
2022
|
A convergent interacting particle method and computation of KPP front speeds in chaotic flows. Zbl 07538279
Lyu, Junlong; Wang, Zhongjian; Xin, Jack; Zhang, Zhiwen |
|
2022
|
Computing effective diffusivities in 3D time-dependent chaotic flows with a convergent Lagrangian numerical method. Zbl 07598348
Wang, Zhongjian; Xin, Jack; Zhang, Zhiwen |
|
2022
|
Convergence analysis of the localized orthogonal decomposition method for the semiclassical Schrödinger equations with multiscale potentials. Zbl 1503.65275
Wu, Zhizhang; Zhang, Zhiwen |
|
2022
|
Error estimates for a POD method for solving viscous G-equations in incompressible cellular flows. Zbl 1469.65156
Gu, Haotian; Xin, Jack; Zhang, Zhiwen |
|
2021
|
Sharp error estimates on a stochastic structure-preserving scheme in computing effective diffusivity of 3D chaotic flows. Zbl 1496.65192
Wang, Zhongjian; Xin, Jack; Zhang, Zhiwen |
|
2021
|
A second order accuracy preserving method for moving contact lines with Stokes flow. Zbl 07515862
Chai, Shuqing; Zhang, Zhen; Zhang, Zhiwen |
|
2021
|
A mesh-free method for interface problems using the deep learning approach. Zbl 1454.65173
Wang, Zhongjian; Zhang, Zhiwen |
|
2020
|
A data-driven approach for multiscale elliptic PDEs with random coefficients based on intrinsic dimension reduction. Zbl 1459.35194
Li, Sijing; Zhang, Zhiwen; Zhao, Hongkai |
|
2020
|
Proper orthogonal decomposition method to nonlinear filtering problems in medium-high dimension. Zbl 1533.93818
Wang, Zhongjian; Luo, Xue; Yau, Stephen S.-T.; Zhang, Zhiwen |
|
2020
|
Efficient multiscale methods for the semiclassical Schrödinger equation with time-dependent potentials. Zbl 1506.81008
Chen, Jingrun; Li, Sijing; Zhang, Zhiwen |
|
2020
|
Proper orthogonal decomposition method for multiscale elliptic PDEs with random coefficients. Zbl 1439.35588
Ma, Dingjiong; Ching, Wai-ki; Zhang, Zhiwen |
|
2020
|
Convergence analysis of stochastic structure-preserving schemes for computing effective diffusivity in random flows. Zbl 1509.37120
Lyu, Junlong; Wang, Zhongjian; Xin, Jack; Zhang, Zhiwen |
|
2020
|
A multiscale reduced basis method for the Schrödinger equation with multiscale and random potentials. Zbl 1454.35070
Chen, Jingrun; Ma, Dingjiong; Zhang, Zhiwen |
|
2020
|
A QMC-deep learning method for diffusivity estimation in random domains. Zbl 1474.65007
Lv, Liyao; Zhang, Zhiwen; Chen, Jingrun |
|
2020
|
A model reduction method for multiscale elliptic PDEs with random coefficients using an optimization approach. Zbl 1420.35083
Hou, Thomas Y.; Ma, Dingjiong; Zhang, Zhiwen |
|
2019
|
A multiscale finite element method for the Schrödinger equation with multiscale potentials. Zbl 1428.35111
Chen, Jingrun; Ma, Dingjiong; Zhang, Zhiwen |
|
2019
|
An adaptive dynamically low-dimensional approximation method for multiscale stochastic diffusion equations. Zbl 1435.65154
Chung, Eric T.; Pun, Sai-Mang; Zhang, Zhiwen |
|
2019
|
Cluster-based generalized multiscale finite element method for elliptic PDEs with random coefficients. Zbl 1415.65251
Chung, Eric T.; Efendiev, Yalchin; Leung, Wing Tat; Zhang, Zhiwen |
|
2018
|
Computing effective diffusivity of chaotic and stochastic flows using structure-preserving schemes. Zbl 1404.65209
Wang, Zhongjian; Xin, Jack; Zhang, Zhiwen |
|
2018
|
Computing eigenvalues and eigenfunctions of Schrödinger equations using a model reduction approach. Zbl 1475.65183
Li, Shuangping; Zhang, Zhiwen |
|
2018
|
A model reduction method for elliptic PDEs with random input using the heterogeneous stochastic FEM framework. Zbl 1341.65004
Hou, Thomas Y.; Liu, Pengfei; Zhang, Zhiwen |
|
2016
|
An adaptive ANOVA-based data-driven stochastic method for elliptic PDEs with random coefficient. Zbl 1388.65178
Zhang, Zhiwen; Hu, Xin; Hou, Thomas Y.; Lin, Guang; Yan, Mike |
|
2014
|
A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations. I: Derivation and algorithms. Zbl 1297.65008
Cheng, Mulin; Hou, Thomas Y.; Zhang, Zhiwen |
|
2013
|
A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations. II: Adaptivity and generalizations. Zbl 1297.65007
Cheng, Mulin; Hou, Thomas Y.; Zhang, Zhiwen |
|
2013
|
A data-driven stochastic method for elliptic PDEs with random coefficients. Zbl 1290.60068
Cheng, Mulin; Hou, Thomas Y.; Yan, Mike; Zhang, Zhiwen |
|
2013
|
Multiscale tailored finite point method for second order elliptic equations with rough or highly oscillatory coefficients. Zbl 1416.65450
Han, Houde; Zhang, Zhiwen |
|
2012
|
An Eulerian surface hopping method for the Schrödinger equation with conical crossings. Zbl 1219.35202
Jin, Shi; Qi, Peng; Zhang, Zhiwen |
|
2011
|
Adaptive artificial boundary condition for the two-level Schrödinger equation with conical crossings. Zbl 1210.65155
Han, Houde; Zhang, Zhiwen |
|
2011
|
Split local artificial boundary conditions for the two-dimensional sine-Gordon equation on \(\mathbb R^2\). Zbl 1388.65055
Han, Houde; Zhang, Zhiwen |
|
2011
|
An analysis of the finite-difference method for one-dimensional Klein-Gordon equation on unbounded domain. Zbl 1162.65377
Han, Houde; Zhang, Zhiwen |
|
2009
|
Split local absorbing conditions for one-dimensional nonlinear Klein-Gordon equation on unbounded domain. Zbl 1152.65092
Han, Houde; Zhang, Zhiwen |
|
2008
|