24 citations · 69 across the 15 of their papers we have counts for
15 papers
Solving eigenvalue PDEs of metastable diffusion processes using artificial neural networks
Wei Zhang, Tiejun Li, Christof Schütte
In this paper, we consider the eigenvalue PDE problem of the infinitesimal generators of metastable diffusion processes. We propose a numerical algorithm based on training artifici…
Global Solutions of Stochastic Stackelberg Differential Games under Convex Control Constraint
Liangquan Zhang, Wei Zhang
This paper is concerned with a Stackelberg stochastic differential game, where the systems are driven by stochastic differential equation (SDE for short), in which the control ente…
Non-reversible sampling schemes on submanifolds
Upanshu Sharma, Wei Zhang
Calculating averages with respect to probability measures on submanifolds is often necessary in various application areas such as molecular dynamics, computational statistical mech…
A theoretical framework for Koopman analyses of fluid flows, part 2: from linear to nonlinear dynamics
Wei Zhang, Mingjun Wei
A theoretic framework for dynamics is obtained by transferring dynamics from state space to its dual space. As a result, the linear structure where dynamics are analytically decomp…
A theoretical framework for Koopman analyses of fluid flows, part 1: local Koopman spectrum and properties
Wei Zhang, Mingjun Wei
Local Koopman spectral problem is studied to resolve all dynamics for a nonlinear system. The proposed spectral problem is compatible with the linear spectral theory for various li…
Some new results on relative entropy production, time reversal, and optimal control of time-inhomogeneous diffusion processes
Wei Zhang
This paper studies time-inhomogeneous nonequilibrium diffusion processes, including both Brownian dynamics and Langevin dynamics. We derive upper bounds of the relative entropy pro…
Moderate deviation and central limit theorem for SDDEs with plynomial growth
Yongqiang Suo, Jin Tao, Wei Zhang
In this paper, employing the weak convergence method, based on a variational representation for expected values of positive functionals of a Brownian motion, we investigate moderat…
Pathwise estimates for effective dynamics: the case of nonlinear vectorial reaction coordinates
Tony Lelièvre, Wei Zhang
Effective dynamics using conditional expectation was proposed in [F. Legoll and T. Lelièvre, Nonlinearity, 2010] to approximate the essential dynamics of high-dimensional diffusion…
Jarzynski's equality, fluctuation theorems, and variance reduction: Mathematical analysis and numerical algorithms
Carsten Hartmann, Christof Schuette, Wei Zhang
In this paper, we study Jarzynski's equality and fluctuation theorems for diffusion processes. While some of the results considered in the current work are known in the (mainly phy…
Ergodic SDEs on submanifolds and related numerical sampling schemes
Wei Zhang
In many applications, it is often necessary to sample the mean value of certain quantity with respect to a probability measure μ on the level set of a smooth function $ξ: \mathbb{R…
Statistical analysis of the first passage path ensemble of jump processes
Max von Kleist, Christof Schütte, Wei Zhang
The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted conside…
Asymptotic Analysis of Multiscale Markov Chain
Wei Zhang
We consider continuous-time Markov chain on a finite state space X. We assume X can be clustered into several subsets such that the intra-transition rates within these subsets are…
Optimal control of Markov jump processes : Asymptotic analysis, algorithms and applications to the modelling of chemical reaction systems
Wei Zhang, Carsten Hartmann, Max von Kleist
Markov jump processes are widely used to model natural and engineered processes. In the context of biological or chemical applications one typically refers to the chemical master e…
Importance sampling in path space for diffusion processes with slow-fast variables
Carsten Hartmann, Christof Schütte, Marcus Weber +1
Importance sampling is a widely used technique to reduce the variance of a Monte Carlo estimator by an appropriate change of measure. In this work, we study importance sam- pling i…
Optimal control of multiscale systems using reduced-order models
Wei Zhang, Juan C. Latorre, Grigorios A. Pavliotis +1
We study optimal control of diffusions with slow and fast variables and address a question raised by practitioners: is it possible to first eliminate the fast variables before solv…