384 research outputs found
Variance Reduction Result for a Projected Adaptive Biasing Force Method
This paper is committed to investigate an extension of the classical adaptive
biasing force method, which is used to compute the free energy related to the
Boltzmann-Gibbs measure and a reaction coordinate function. The issue of this
technique is that the approximated gradient of the free energy, called biasing
force, is not a gradient. The commitment to this field is to project the
estimated biasing force on a gradient using the Helmholtz decomposition. The
variance of the biasing force is reduced using this technique, which makes the
algorithm more efficient than the standard ABF method. We prove exponential
convergence to equilibrium of the estimated free energy, with a precise rate of
convergence in function of Logarithmic Sobolev inequality constants
A mathematical formalization of the parallel replica dynamics
The purpose of this article is to lay the mathematical foundations of a well
known numerical approach in computational statistical physics and molecular
dynamics, namely the parallel replica dynamics introduced by A.F. Voter. The
aim of the approach is to efficiently generate a coarse-grained evolution (in
terms of state-to-state dynamics) of a given stochastic process. The approach
formally consists in concurrently considering several realizations of the
stochastic process, and tracking among the realizations that which, the
soonest, undergoes an important transition. Using specific properties of the
dynamics generated, a computational speed-up is obtained. In the best cases,
this speed-up approaches the number of realizations considered. By drawing
connections with the theory of Markov processes and, in particular, exploiting
the notion of quasi-stationary distribution, we provide a mathematical setting
appropriate for assessing theoretically the performance of the approach, and
possibly improving it
Efficiency of the Wang-Landau algorithm: a simple test case
We analyze the efficiency of the Wang-Landau algorithm to sample a multimodal
distribution on a prototypical simple test case. We show that the exit time
from a metastable state is much smaller for the Wang Landau dynamics than for
the original standard Metropolis-Hastings algorithm, in some asymptotic regime.
Our results are confirmed by numerical experiments on a more realistic test
case
Micro-macro models for viscoelastic fluids: modelling, mathematics and numerics
This paper is an introduction to the modelling of viscoelastic fluids, with
an emphasis on micro-macro (or multiscale) models. Some elements of
mathematical and numerical analysis are provided. These notes closely follow
the lectures delivered by the second author at the Chinese Academy of Science
during the Workshop "Stress Tensor Effects on Fluid Mechanics", in January
2010
Virtual gardening: Identifying problems and potential directions for 'ecological awareness' through soil management and plant recognition gaming
Games are increasingly proven to be effective learning tools through a multitude of methodologies and approaches and this is no different for issues relating to the environment and the place of humans within it. We collaborated with the Eden Project to create a mobile game addressing some concerns on the ecological awareness of visitors that they raised with us: a mobile garden management game with a plant recognition technology. Such a project proved a valuable opportunity to understand how a game for smart devices might promote short-term ecological awareness for a general audience. Using a research creation methodology, we analyse, document and run a limited empirical study through user experience testing on players to investigate if the game had an effect on their ecological awareness
Measurement of the neutron electric dipole moment via spin rotation in a non-centrosymmetric crystal
We have measured the neutron electric dipole moment using spin rotation in a
non-centrosymmetric crystal. Our result is d_n = (2.5 +- 6.5(stat) +-
5.5(syst)) 10^{-24} e cm. The dominating contribution to the systematic
uncertainty is statistical in nature and will reduce with improved statistics.
The statistical sensitivity can be increased to 2 10^{-26} e cm in 100 days
data taking with an improved setup. We state technical requirements for a
systematic uncertainty at the same level.Comment: submitted to Phys. Lett.
Optimal importance sampling for overdamped Langevin dynamics
Calculating averages with respect to multimodal probability distributions is
often necessary in applications. Markov chain Monte Carlo (MCMC) methods to
this end, which are based on time averages along a realization of a Markov
process ergodic with respect to the target probability distribution, are
usually plagued by a large variance due to the metastability of the process. In
this work, we mathematically analyze an importance sampling approach for MCMC
methods that rely on the overdamped Langevin dynamics. Specifically, we study
an estimator based on an ergodic average along a realization of an overdamped
Langevin process for a modified potential. The estimator we consider
incorporates a reweighting term in order to rectify the bias that would
otherwise be introduced by this modification of the potential. We obtain an
explicit expression in dimension 1 for the biasing potential that minimizes the
asymptotic variance of the estimator for a given observable, and propose a
general numerical approach for approximating the optimal potential in the
multi-dimensional setting. We also investigate an alternative approach where,
instead of the asymptotic variance for a given observable, a weighted average
of the asymptotic variances corresponding to a class of observables is
minimized. Finally, we demonstrate the capabilities of the proposed method by
means of numerical experiments
Optimal friction matrix for underdamped Langevin sampling
A systematic procedure for optimising the friction coefficient in underdamped Langevin dynamics as a sampling tool is given by taking the gradient of the associated asymptotic variance with respect to friction. We give an expression for this gradient in terms of the solution to an appropriate Poisson equation and show that it can be approximated by short simulations of the associated first variation/tangent process under concavity assumptions on the log density. Our algorithm is applied to the estimation of posterior means in Bayesian inference problems and reduced variance is demonstrated when compared to the original underdamped and overdamped Langevin dynamics in both full and stochastic gradient cases
Approaching a parameter-free metadynamics
We present a unique derivation of metadynamics. The starting point for the
derivation is an on-the-fly reweighting scheme but through an approximation we
recover the standard metadynamics and the well-tempered metadynamics in a
general form while never appealing to the extended Lagrangian framework. This
work leads to a more robust understanding of the error in the computed free
energy than what has been obtained previously. Moreover, a formula for the
exact free energy is introduced. The formula can be used to post-process any
existing well-tempered metadynamics data allowing one, in principle, to obtain
an exact free energy regardless the metadynamics parameters.Comment: 4 pages, 1 figur
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