105 citations · 149 across the 31 of their papers we have counts for
31 papers
A convergent interacting particle method for computing KPP front speeds in random flows
Tan Zhang, Zhongjian Wang, Jack Xin +1
We aim to efficiently compute spreading speeds of reaction-diffusion-advection (RDA) fronts in divergence free random flows under the Kolmogorov-Petrovsky-Piskunov (KPP) nonlineari…
Randomized methods for computing optimal transport without regularization and their convergence analysis
Yue Xie, Zhongjian Wang, Zhiwen Zhang
The optimal transport (OT) problem can be reduced to a linear programming (LP) problem through discretization. In this paper, we introduced the random block coordinate descent (RBC…
Deterministic-Statistical Approach for an Inverse Acoustic Source Problem using Multiple Frequency Limited Aperture Data
Yanfang Liu, Zhizhang Wu, Jiguang Sun +1
We propose a deterministic-statistical method for an inverse source problem using multiple frequency limited aperture far field data. The direct sampling method is used to obtain a…
A variational neural network approach for glacier modelling with nonlinear rheology
Tiangang Cui, Zhongjian Wang, Zhiwen Zhang
In this paper, we propose a mesh-free method to solve full stokes equation which models the glacier movement with nonlinear rheology. Our approach is inspired by the Deep-Ritz meth…
A DeepParticle method for learning and generating aggregation patterns in multi-dimensional Keller-Segel chemotaxis systems
Zhongjian Wang, Jack Xin, Zhiwen Zhang
We study a regularized interacting particle method for computing aggregation patterns and near singular solutions of a Keller-Segal (KS) chemotaxis system in two and three space di…
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 +1
In this paper, we combine the Smolyak technique for multi-dimensional interpolation with the Filon-Clenshaw-Curtis (FCC) rule for one-dimensional oscillatory integration, to obtain…
A Deep Learning Approach to Nonconvex Energy Minimization for Martensitic Phase Transitions
Xiaoli Chen, Phoebus Rosakis, Zhizhang Wu +1
We propose a mesh-free method to solve nonconvex energy minimization problems for martensitic phase transitions and twinning in crystals, using the deep learning approach. These pr…
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
We introduce the so called DeepParticle method to learn and generate invariant measures of stochastic dynamical systems with physical parameters based on data computed from an inte…
A data-driven model reduction method for parabolic inverse source problems and its convergence analysis
Zhongjian Wang, Wenlong Zhang, Zhiwen Zhang
In this paper, we propose a data-driven model reduction method to solve parabolic inverse source problems efficiently. Our method consists of offline and online stages. In the off-…
Convergence analysis of an operator-compressed multiscale finite element method for Schrödinger equations with multiscale potentials
Zhizhang Wu, Zhiwen Zhang
In this paper, we analyze the convergence of the operator-compressed multiscale finite element method (OC MsFEM) for Schrödinger equations with general multiscale potentials in the…
Convergence analysis of a Lagrangian numerical scheme in computing effective diffusivity of 3D time-dependent flows
Zhongjian Wang, Jack Xin, Zhiwen Zhang
In this paper, we study the convergence analysis for a robust stochastic structure-preserving Lagrangian numerical scheme in computing effective diffusivity of time-dependent chaot…
A data-driven and model-based accelerated Hamiltonian Monte Carlo method for Bayesian elliptic inverse problems
Sijing Li, Cheng Zhang, Zhiwen Zhang +1
In this paper, we consider a Bayesian inverse problem modeled by elliptic partial differential equations (PDEs). Specifically, we propose a data-driven and model-based approach to…
A convergent interacting particle method and computation of KPP front speeds in chaotic flows
Junlong Lyu, Zhongjian Wang, Jack Xin +1
In this paper, we study the propagation speeds of reaction-diffusion-advection (RDA) fronts in time-periodic cellular and chaotic flows with Kolmogorov-Petrovsky-Piskunov (KPP) non…
A QMC-deep learning method for diffusivity estimation in random domains
Liyao Lyu, Zhiwen Zhang, Jingrun Chen
Exciton diffusion plays a vital role in the function of many organic semiconducting opto-electronic devices, where an accurate description requires precise control of heterojunctio…
Efficient multiscale methods for the semiclassical Schrödinger equation with time-dependent potentials
Jingrun Chen, Sijing Li, Zhiwen Zhang
The semiclassical Schrödinger equation with time-dependent potentials is an important model to study electron dynamics under external controls in the mean-field picture. In this pa…
A class of robust numerical methods for solving dynamical systems with multiple time scales
Thomas Y. Hou, Zhongjian Wang, Zhiwen Zhang
In this paper, we develop a class of robust numerical methods for solving dynamical systems with multiple time scales. We first represent the solution of a multiscale dynamical sys…
Solving high-dimensional nonlinear filtering problems using a tensor train decomposition method
Sijing Li, Zhongjian Wang, Stephen S. T. Yau +1
In this paper, we propose an efficient numerical method to solve high-dimensional nonlinear filtering (NLF) problems. Specifically, we use the tensor train decomposition method to…
A data-driven approach for multiscale elliptic PDEs with random coefficients based on intrinsic dimension reduction
Sijing Li, Zhiwen Zhang, Hongkai Zhao
We propose a data-driven approach to solve multiscale elliptic PDEs with random coefficients based on the intrinsic low dimension structure of the underlying elliptic differential…
A multiscale reduced basis method for Schrödinger equation with multiscale and random potentials
Jingrun Chen, Dingjiong Ma, Zhiwen Zhang
The semiclassical Schrödinger equation with multiscale and random potentials often appears when studying electron dynamics in heterogeneous quantum systems. As time evolves, the wa…
Convergence of stochastic structure-preserving schemes for computing effective diffusivity in random flows
Junlong Lyu, Zhongjian Wang, Jack Xin +1
In this paper, we propose stochastic structure-preserving schemes to compute the effective diffusivity for particles moving in random flows. We first introduce the motion of partic…
A mesh-free method for interface problems using the deep learning approach
Zhongjian Wang, Zhiwen Zhang
In this paper, we propose a mesh-free method to solve interface problems using the deep learning approach. Two interface problems are considered. The first one is an elliptic PDE w…
A multiscale finite element method for the Schrödinger equation with multiscale potentials
Jingrun Chen, Dingjiong Ma, Zhiwen Zhang
In recent years, an increasing attention has been paid to quantum heterostructures with tailored functionalities, such as heterojunctions and quantum matematerials, in which quantu…
Error estimates for a POD method for solving viscous G-equations in incompressible cellular flows
Haotian Gu, Jack Xin, Zhiwen Zhang
The G-equation is a well-known model for studying front propagation in turbulent combustion. In this paper, we develop an efficient model reduction method for computing \textcolor{…
An adaptive dynamically low-dimensional approximation method for multiscale stochastic diffusion equations
Eric T. Chung, Sai-Mang Pun, Zhiwen Zhang
In this paper, we propose a dynamically low-dimensional approximation method to solve a class of time-dependent multiscale stochastic diffusion equations. A dynamically bi-orthogon…