Error analysis of the transport properties of Metropolized schemes
Provides theoretical error bounds for practitioners using Metropolis-adjusted Langevin algorithms to compute transport coefficients.
The paper analyzes discretization errors in transport coefficient estimation for Brownian dynamics using the Smart MC algorithm, proving first-order error in time step for both Green-Kubo and Einstein formulas, supported by numerical simulations.
We consider in this work the numerical computation of transport coefficients for Brownian dynamics. We investigate the discretization error arising when simulating the dynamics with the Smart MC algorithm (also known as Metropolis-adjusted Langevin algorithm). We prove that the error is of order one in the time step, when using either the Green-Kubo or the Einstein formula to estimate the transport coefficients. We illustrate our results with numerical simulations.