8 papers
Long time asymptotics of mixed-type Kimura diffusions
Guillaume Bal, Binglu Chen, Zhongjian Wang
This paper concerns the long-time asymptotics of diffusions with degenerate coefficients at the domain's boundary. Degenerate diffusion operators with mixed linear and quadratic de…
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 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 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 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…