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pro vyhledávání: '"Zhang,Zhiwen"'
The Random Batch Method (RBM) is an effective technique to reduce the computational complexity when solving certain stochastic differential problems (SDEs) involving interacting particles. It can transform the computational complexity from O(N^2) to
Externí odkaz:
http://arxiv.org/abs/2412.15581
We propose and rigorously analyze a finite element method for the approximation of stationary Fokker--Planck--Kolmogorov (FPK) equations subject to periodic boundary conditions in two settings: one with weakly differentiable coefficients, and one wit
Externí odkaz:
http://arxiv.org/abs/2409.07371
Autor:
Lin, Alvey Qianli, Zhang, Zhiwen
In this paper, we provide an optimisation approach motivated by the Blind Source Separation, or also known as Independent Component Analysis, for cointegration between financial time series. Two methods for cointegration tests are introduced, namely
Externí odkaz:
http://arxiv.org/abs/2409.02552
The investigation of tumor invasion and metastasis dynamics is crucial for advancements in cancer biology and treatment. Many mathematical models have been developed to study the invasion of host tissue by tumor cells. In this paper, we develop a nov
Externí odkaz:
http://arxiv.org/abs/2407.05626
Autor:
Duan, Renjun, Zhang, Zhiwen
In this note we adopt an approach by Grenier, Nguyen and Rodnianski in \cite{GNR} for studying the nonlinear Landau damping of the two-species Vlasov-Poisson system in the phase space $\mathbb{T}^d_x \times \mathbb{R}^d_v$ with the dimension $d\geq 1
Externí odkaz:
http://arxiv.org/abs/2407.02822
Autor:
Zhang, Wenlong, Zhang, Zhiwen
In this paper, we propose novel proper orthogonal decomposition (POD)--based model reduction methods that effectively address the issue of inverse crime in solving parabolic inverse problems. Both the inverse initial value problems and inverse source
Externí odkaz:
http://arxiv.org/abs/2406.02119
This paper aims to investigate the diffusion behavior of particles moving in stochastic flows under a structure-preserving scheme. We compute the effective diffusivity for normal diffusive random flows and establish the power law between spatial and
Externí odkaz:
http://arxiv.org/abs/2405.19003
We study an interacting particle method (IPM) for computing the large deviation rate function of entropy production for diffusion processes, with emphasis on the vanishing-noise limit and high dimensions. The crucial ingredient to obtain the rate fun
Externí odkaz:
http://arxiv.org/abs/2403.19223
Autor:
Zhang, Zhiwen
In light of recent work in the global well-posedness of solutions for an ionic Vlasov-Poisson system, as demonstrated by Griffin-Pickering and Iacobelli, the current work focuses on the moment propagation of the corresponding system in quasi-neutral
Externí odkaz:
http://arxiv.org/abs/2402.02786
In this paper, we consider the numerical solution of a nonlinear Schrodinger equation with spatial random potential. The randomly shifted quasi-Monte Carlo (QMC) lattice rule combined with the time-splitting pseudospectral discretization is applied a
Externí odkaz:
http://arxiv.org/abs/2311.11336