1 code implementation • 30 Aug 2019 • Benedict Leimkuhler, Charles Matthews, Tiffany Vlaar
We describe easy-to-implement hybrid partitioned numerical algorithms, based on discretized stochastic differential equations, which are adapted to feed-forward neural networks, including a multi-layer Langevin algorithm, AdLaLa (combining the adaptive Langevin and Langevin algorithms) and LOL (combining Langevin and Overdamped Langevin); we examine the convergence of these methods using numerical studies and compare their performance among themselves and in relation to standard alternatives such as stochastic gradient descent and ADAM.
1 code implementation • 13 Dec 2017 • Charles Matthews, Jonathan Weare, Andrey Kravtsov, Elise Jennings
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 statistical analyses of data.
Instrumentation and Methods for Astrophysics
1 code implementation • 13 Jul 2016 • 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.
1 code implementation • 24 Mar 2012 • Benedict Leimkuhler, Charles Matthews
We then compare Langevin dynamics integrators in terms of their invariant distributions and demonstrate a superconvergence property (4th order accuracy where only 2nd order would be expected) of one method in the high friction limit; this method, moreover, can be reduced to a simple modification of the Euler-Maruyama method for Brownian dynamics involving a non-Markovian (coloured noise) random process.
Numerical Analysis Statistical Mechanics Chemical Physics Computational Physics
