250 citations · 626 across the 10 of their papers we have counts for
10 papers
Partitioned integrators for thermodynamic parameterization of neural networks
Benedict Leimkuhler, Charles Matthews, Tiffany Vlaar
Traditionally, neural networks are parameterized using optimization procedures such as stochastic gradient descent, RMSProp and ADAM. These procedures tend to drive the parameters…
Simulating the stochastic dynamics and cascade failure of power networks
Charles Matthews, Bradly Stadie, Jonathan Weare +2
For large-scale power networks, the failure of particular transmission lines can offload power to other lines and cause self-protection trips to activate, instigating a cascade of…
Langevin Markov Chain Monte Carlo with stochastic gradients
Charles Matthews, Jonathan Weare
Monte Carlo sampling techniques have broad applications in machine learning, Bayesian posterior inference, and parameter estimation. Often the target distribution takes the form of…
MIST: A Simple and Efficient Molecular Dynamics Abstraction Library for Integrator Development
Iain Bethune, Ralf Banisch, Elena Breitmoser +6
We present MIST, the Molecular Integration Simulation Toolkit, a lightweight and efficient software library written in C++ which provides an abstract in- terface to common molecula…
Umbrella sampling: a powerful method to sample tails of distributions
Charles Matthews, Jonathan Weare, Andrey Kravtsov +1
We present the umbrella sampling (US) technique and show that it can be used to sample extremely low probability areas of the posterior distribution that may be required in statist…
Ensemble preconditioning for Markov chain Monte Carlo simulation
Charles Matthews, Jonathan Weare, Benedict Leimkuhler
We describe parallel Markov chain Monte Carlo methods that propagate a collective ensemble of paths, with local covariance information calculated from neighboring replicas. The use…
On the long-time integration of stochastic gradient systems
B. Leimkuhler, C. Matthews, M. V. Tretyakov
This article addresses the weak convergence of numerical methods for Brownian dynamics. Typical analyses of numerical methods for stochastic differential equations focus on propert…
The computation of averages from equilibrium and nonequilibrium Langevin molecular dynamics
Benedict Leimkuhler, Charles Matthews, Gabriel Stoltz
We consider numerical methods for thermodynamic sampling, i.e. computing sequences of points distributed according to the Gibbs-Boltzmann distribution, using Langevin dynamics and…
Robust and efficient configurational molecular sampling via Langevin Dynamics
Benedict Leimkuhler, Charles Matthews
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 app…
Rational Construction of Stochastic Numerical Methods for Molecular Sampling
Benedict Leimkuhler, Charles Matthews
In this article, we focus on the sampling of the configurational Gibbs-Boltzmann distribution, that is, the calculation of averages of functions of the position coordinates of a mo…