Split local absorbing conditions for one-dimensional nonlinear Klein-Gordon equation on unbounded domain. - Houde Han; Zhiwen Zhang 001 (J. Comput. Phys., 2008)

Adaptive artificial boundary condition for the two-level Schrödinger equation with conical crossings. - Houde Han; Zhiwen Zhang 001 (J. Comput. Phys., 2011)

An Eulerian Surface Hopping Method for the Schrödinger Equation with Conical Crossings. - Shi Jin 003; Peng Qi; Zhiwen Zhang 001 (Multiscale Model. Simul., 2011)

A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations II: Adaptivity and generalizations. - Mulin Cheng; Thomas Y. Hou 001; Zhiwen Zhang 001 (J. Comput. Phys., 2013)

A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations I: Derivation and algorithms. - Mulin Cheng; Thomas Y. Hou 001; Zhiwen Zhang 001 (J. Comput. Phys., 2013)

A Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients. - Mulin Cheng; Thomas Y. Hou 001; Mike P. Yan; Zhiwen Zhang 001 (SIAM/ASA J. Uncertain. Quantification, 2013)

A Multiscale Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients. - Zhiwen Zhang 001; Maolin Ci; Thomas Y. Hou 001 (Multiscale Model. Simul., 2015)

GPS trajectory data segmentation based on probabilistic logic. - Sini Guo; Xiang Li 006; Wai-Ki Ching; Dan A. Ralescu; Wai-Keung Li; Zhiwen Zhang 001 (Int. J. Approx. Reason., 2018)

Cluster-based generalized multiscale finite element method for elliptic PDEs with random coefficients. - Eric T. Chung 001; Yalchin Efendiev; Wing Tat Leung; Zhiwen Zhang 001 (J. Comput. Phys., 2018)

Computing Effective Diffusivity of Chaotic and Stochastic Flows Using Structure-Preserving Schemes. - Zhongjian Wang; Jack Xin; Zhiwen Zhang 001 (SIAM J. Numer. Anal., 2018)

Convergence of stochastic structure-preserving schemes for computing effective diffusivity in random flows. - Junlong Lyu; Zhongjian Wang; Jack Xin; Zhiwen Zhang 001 (CoRR, 2019)

Solving high-dimensional nonlinear filtering problems using a tensor train decomposition method. - Sijing Li; Zhongjian Wang; Stephen S.-T. Yau; Zhiwen Zhang 001 (CoRR, 2019)

A class of robust numerical methods for solving dynamical systems with multiple time scales. - Thomas Y. Hou 001; Zhongjian Wang; Zhiwen Zhang 001 (CoRR, 2019)

Efficient multiscale methods for the semiclassical Schrödinger equation with time-dependent potentials. - Jingrun Chen; Sijing Li; Zhiwen Zhang 001 (CoRR, 2019)

Connecting exciton diffusion with surface roughness via deep learning. - Liyao Lyu; Zhiwen Zhang 001; Jingrun Chen (CoRR, 2019)

An adaptive dynamically low-dimensional approximation method for multiscale stochastic diffusion equations. - Eric T. Chung 001; Sai-Mang Pun; Zhiwen Zhang 001 (J. Comput. Appl. Math., 2019)

Estimation of exciton diffusion lengths of organic semiconductors in random domains. - Jingrun Chen; Ling Lin 002; Zhiwen Zhang 001; Xiang Zhou 001 (J. Comput. Phys., 2019)

A Model Reduction Method for Multiscale Elliptic Pdes with Random Coefficients Using an Optimization Approach. - Thomas Y. Hou 001; Dingjiong Ma; Zhiwen Zhang 001 (Multiscale Model. Simul., 2019)

A Multiscale Finite Element Method for the Schrödinger Equation with Multiscale Potentials. - Jingrun Chen; Dingjiong Ma; Zhiwen Zhang 001 (SIAM J. Sci. Comput., 2019)

Fuzzy hidden Markov-switching portfolio selection with capital gain tax. - Sini Guo; Wai-Ki Ching; Wai-Keung Li; Tak Kuen Siu; Zhiwen Zhang 001 (Expert Syst. Appl., 2020)

Proper orthogonal decomposition method for multiscale elliptic PDEs with random coefficients. - Dingjiong Ma; Wai-Ki Ching; Zhiwen Zhang 001 (J. Comput. Appl. Math., 2020)

A mesh-free method for interface problems using the deep learning approach. - Zhongjian Wang; Zhiwen Zhang 001 (J. Comput. Phys., 2020)

A Multiscale Reduced Basis Method for the Schrödinger Equation With Multiscale and Random Potentials. - Jingrun Chen; Dingjiong Ma; Zhiwen Zhang 001 (Multiscale Model. Simul., 2020)

A Data-Driven Approach for Multiscale Elliptic PDEs with Random Coefficients Based on Intrinsic Dimension Reduction. - Sijing Li; Zhiwen Zhang 001; Hongkai Zhao (Multiscale Model. Simul., 2020)

Convergence Analysis of Stochastic Structure-Preserving Schemes for Computing Effective Diffusivity in Random Flows. - Junlong Lyu; Zhongjian Wang; Jack Xin; Zhiwen Zhang 001 (SIAM J. Numer. Anal., 2020)

Proper Orthogonal Decomposition Method to Nonlinear Filtering Problems in Medium-High Dimension. - Zhongjian Wang; Xue Luo; Stephen S.-T. Yau; Zhiwen Zhang 001 (IEEE Trans. Autom. Control., 2020)

Convergence analysis of a Lagrangian numerical scheme in computing effective diffusivity of 3D time-dependent flows. - Zhongjian Wang; Jack Xin; Zhiwen Zhang 001 (CoRR, 2021)

Convergence analysis of an operator-compressed multiscale finite element method for Schrödinger equations with multiscale potentials. - Zhizhang Wu; Zhiwen Zhang 001 (CoRR, 2021)

A second order accuracy preserving method for moving contact lines with Stokes flow. - Shuqing Chai; Zhen Zhang 018; Zhiwen Zhang 001 (J. Comput. Phys., 2021)

Sharp Error Estimates on a Stochastic Structure-Preserving Scheme in Computing Effective Diffusivity of 3D Chaotic Flows. - Zhongjian Wang; Jack Xin; Zhiwen Zhang 001 (Multiscale Model. Simul., 2021)

Error Estimates for a POD Method for Solving Viscous G-Equations in Incompressible Cellular Flows. - Haotian Gu; Jack Xin; Zhiwen Zhang 001 (SIAM J. Sci. Comput., 2021)

A Deep Learning Approach to Nonconvex Energy Minimization for Martensitic Phase Transitions. - Xiaoli Chen; Phoebus Rosakis; Zhizhang Wu; Zhiwen Zhang 001 (CoRR, 2022)

A DeepParticle method for learning and generating aggregation patterns in multi-dimensional Keller-Segel chemotaxis systems. - Zhongjian Wang; Jack Xin; Zhiwen Zhang 001 (CoRR, 2022)

A variational neural network approach for glacier modelling with nonlinear rheology. - Tiangang Cui; Zhongjian Wang; Zhiwen Zhang 001 (CoRR, 2022)

Deterministic-Statistical Approach for an Inverse Acoustic Source Problem using Multiple Frequency Limited Aperture Data. - Yanfang Liu; Zhizhang Wu; Jiguang Sun; Zhiwen Zhang 001 (CoRR, 2022)

DeepParticle: Learning invariant measure by a deep neural network minimizing Wasserstein distance on data generated from an interacting particle method. - Zhongjian Wang; Jack Xin; Zhiwen Zhang 001 (J. Comput. Phys., 2022)

Convergence Analysis of the Localized Orthogonal Decomposition Method for the Semiclassical Schrödinger Equations with Multiscale Potentials. - Zhizhang Wu; Zhiwen Zhang 001 (J. Sci. Comput., 2022)

A Convergent Interacting Particle Method and Computation of KPP Front Speeds in Chaotic Flows. - Junlong Lyu; Zhongjian Wang; Jack Xin; Zhiwen Zhang 001 (SIAM J. Numer. Anal., 2022)

Stochastic convergence of regularized solutions for backward heat conduction problems. - Zhongjian Wang; Wenlong Zhang; Zhiwen Zhang 001 (CoRR, 2023)

A data-driven model reduction method for parabolic inverse source problems and its convergence analysis. - Zhongjian Wang; Wenlong Zhang; Zhiwen Zhang 001 (J. Comput. Phys., 2023)

Solving Nonlinear Filtering Problems Using a Tensor Train Decomposition Method. - Sijing Li; Zhongjian Wang; Stephen S.-T. Yau; Zhiwen Zhang 001 (IEEE Trans. Autom. Control., 2023)

A data-driven and model-based accelerated Hamiltonian Monte Carlo method for Bayesian elliptic inverse problems. - Sijing Li; Cheng Zhang; Zhiwen Zhang 001; Hongkai Zhao (Stat. Comput., 2023)

Computing large deviation rate functions of entropy production for diffusion processes in the vanishing-noise limit and high dimensions by an interacting particle method. - Zhizhang Wu; Renaud Raquépas; Jack Xin; Zhiwen Zhang 001 (CoRR, 2024)

A structure-preserving scheme for computing effective diffusivity and anomalous diffusion phenomena of random flows. - Tan Zhang; Zhongjian Wang; Jack Xin; Zhiwen Zhang 001 (CoRR, 2024)

A novel model reduction method to solve inverse problems of parabolic type. - Wenlong Zhang; Zhiwen Zhang 001 (CoRR, 2024)

A Stochastic Interacting Particle-Field Algorithm for a Haptotaxis Advection-Diffusion System Modeling Cancer Cell Invasion. - Boyi Hu; Zhongjian Wang; Jack Xin; Zhiwen Zhang 001 (CoRR, 2024)

A Filon-Clenshaw-Curtis-Smolyak rule for multi-dimensional oscillatory integrals with application to a UQ problem for the Helmholtz equation. - Zhizhang Wu; Ivan G. Graham; Dingjiong Ma; Zhiwen Zhang 001 (Math. Comput., 2024)

Error Estimate of a Quasi-Monte Carlo Time-Splitting Pseudospectral Method for Nonlinear Schrödinger Equation with Random Potentials. - Zhizhang Wu; Zhiwen Zhang 001; Xiaofei Zhao (SIAM/ASA J. Uncertain. Quantification, 2024)

Reduced-order model-based variational inference with normalizing flows for Bayesian elliptic inverse problems. - Zhizhang Wu; Cheng Zhang; Zhiwen Zhang 001 (J. Comput. Appl. Math., 2024)

Randomized Methods for Computing Optimal Transport Without Regularization and Their Convergence Analysis. - Yue Xie; Zhongjian Wang; Zhiwen Zhang 001 (J. Sci. Comput., 2024)

Discontinuous extreme learning machine for interface and free boundary problems. - Anci Lin; Zhiwen Zhang 001; Weidong Zhao; Wenju Zhao (J. Comput. Phys., 2025)

A Convergent Interacting Particle Method for Computing KPP Front Speeds in Random Flows. - Tan Zhang; Zhongjian Wang; Jack Xin; Zhiwen Zhang 001 (SIAM/ASA J. Uncertain. Quantification, 2025)

Finite Element Approximation of Stationary Fokker-Planck-Kolmogorov Equations with Application to Periodic Numerical Homogenization. - Timo Sprekeler; Endre Süli; Zhiwen Zhang 001 (SIAM J. Numer. Anal., 2025)

A Novel Stochastic Interacting Particle-Field Algorithm for 3D Parabolic-Parabolic Keller-Segel Chemotaxis System. - Zhongjian Wang; Jack Xin; Zhiwen Zhang 001 (J. Sci. Comput., 2025)