70 citations · 380 across the 25 of their papers we have counts for
18 papers · 1 filter
A deep learning method for solving Fokker-Planck equations
Jiayu Zhai, Matthew Dobson, Yao Li
The time evolution of the probability distribution of a stochastic differential equation follows the Fokker-Planck equation, which usually has an unbounded, high-dimensional domain…
Using coupling methods to estimate sample quality for stochastic differential equations
Matthew Dobson, Jiayu Zhai, Yao Li
A probabilistic approach for estimating sample qualities for stochastic differential equations is introduced in this paper. The aim is to provide a quantitative upper bound of the…
An efficient data-driven solver for Fokker-Planck equations: algorithm and analysis
Matthew Dobson, Yao Li, Jiayu Zhai
Computing the invariant probability measure of a randomly perturbed dynamical system usually means solving the stationary Fokker-Planck equation. This paper studies several key pro…
Strong Convergence of Integrators for Nonequilibrium Langevin Dynamics`
Matthew Dobson, Abdel Kader Geraldo
Several numerical schemes are proposed for the solution of Nonequilibrium Langevin Dynamics (NELD), and the rate of convergence is analyzed. Due to the special deforming boundary c…
On assessing the accuracy of defect free energy computations
Matthew Dobson, Manh Hong Duong, Christoph Ortner
We develop a rigorous error analysis for coarse-graining of defect-formation free energy. For a one-dimensional constrained atomistic system, we establish the thermodynamic limit o…
Cell List Algorithms for Nonequilibrium Molecular Dynamics
Matthew Dobson, Ian Fox, Alexandra Saracino
We present two modifications of the standard cell list algorithm for nonequilibrium molecular dynamics simulations of homogeneous, linear flows. When such a flow is modeled with pe…