This paper surveys in detail the relations between numerical integration and the Hamiltonian
(or hybrid) Monte Carlo method (HMC). Since the computational cost of HMC mainly lies in …

For a number of years, we have been exploring the underpinnings of algorithms for
simulating molecular dynamics from a mathematics perspective, ie as outsiders. We have …

On the one hand, the explicit Euler scheme fails to converge strongly to the exact solution of
a stochastic differential equation (SDE) with a superlinearly growing and globally one-sided …

This monograph provides a general introduction to advanced computational methods for
free energy calculations, from the systematic and rigorous point of view of applied …

A wide variety of numerical methods are evaluated and compared for solving the stochastic
differential equations encountered in molecular dynamics. The methods are based on the …

One of the main challenges in molecular dynamics is overcoming the 'timescale barrier': in
many realistic molecular systems, biologically important rare transitions occur on timescales …

We consider numerical methods for thermodynamic sampling, ie, computing sequences of
points distributed according to the Gibbs–Boltzmann distribution, using Langevin dynamics …

Applications in modern biotechnology and molecular medicine often require simulation of
biomolecular systems in atomic representation with immense length and timescales that are …

Numerical approximation of the long time behavior of a stochastic differential equation
(SDE) is considered. Error estimates for time-averaging estimators are obtained and then …

Discretizations of the Langevin diffusion have been proven very useful for developing and
analyzing algorithms for sampling and stochastic optimization. We present an improved non …