58,705 research outputs found
Near-optimal protocols in complex nonequilibrium transformations
The development of sophisticated experimental means to control nanoscale
systems has motivated efforts to design driving protocols which minimize the
energy dissipated to the environment. Computational models are a crucial tool
in this practical challenge. We describe a general method for sampling an
ensemble of finite-time, nonequilibrium protocols biased towards a low average
dissipation. We show that this scheme can be carried out very efficiently in
several limiting cases. As an application, we sample the ensemble of
low-dissipation protocols that invert the magnetization of a 2D Ising model and
explore how the diversity of the protocols varies in response to constraints on
the average dissipation. In this example, we find that there is a large set of
protocols with average dissipation close to the optimal value, which we argue
is a general phenomenon.Comment: 6 pages and 3 figures plus 4 pages and 5 figures of supplemental
materia
Reweighting for Nonequilibrium Markov Processes Using Sequential Importance Sampling Methods
We present a generic reweighting method for nonequilibrium Markov processes.
With nonequilibrium Monte Carlo simulations at a single temperature, one
calculates the time evolution of physical quantities at different temperatures,
which greatly saves the computational time. Using the dynamical finite-size
scaling analysis for the nonequilibrium relaxation, one can study the dynamical
properties of phase transitions together with the equilibrium ones. We
demonstrate the procedure for the Ising model with the Metropolis algorithm,
but the present formalism is general and can be applied to a variety of systems
as well as with different Monte Carlo update schemes.Comment: accepted for publication in Phys. Rev. E (Rapid Communications
Boosting Monte Carlo simulations of spin glasses using autoregressive neural networks
The autoregressive neural networks are emerging as a powerful computational
tool to solve relevant problems in classical and quantum mechanics. One of
their appealing functionalities is that, after they have learned a probability
distribution from a dataset, they allow exact and efficient sampling of typical
system configurations. Here we employ a neural autoregressive distribution
estimator (NADE) to boost Markov chain Monte Carlo (MCMC) simulations of a
paradigmatic classical model of spin-glass theory, namely the two-dimensional
Edwards-Anderson Hamiltonian. We show that a NADE can be trained to accurately
mimic the Boltzmann distribution using unsupervised learning from system
configurations generated using standard MCMC algorithms. The trained NADE is
then employed as smart proposal distribution for the Metropolis-Hastings
algorithm. This allows us to perform efficient MCMC simulations, which provide
unbiased results even if the expectation value corresponding to the probability
distribution learned by the NADE is not exact. Notably, we implement a
sequential tempering procedure, whereby a NADE trained at a higher temperature
is iteratively employed as proposal distribution in a MCMC simulation run at a
slightly lower temperature. This allows one to efficiently simulate the
spin-glass model even in the low-temperature regime, avoiding the divergent
correlation times that plague MCMC simulations driven by local-update
algorithms. Furthermore, we show that the NADE-driven simulations quickly
sample ground-state configurations, paving the way to their future utilization
to tackle binary optimization problems.Comment: 13 pages, 14 figure
Hamiltonian Monte Carlo Without Detailed Balance
We present a method for performing Hamiltonian Monte Carlo that largely
eliminates sample rejection for typical hyperparameters. In situations that
would normally lead to rejection, instead a longer trajectory is computed until
a new state is reached that can be accepted. This is achieved using Markov
chain transitions that satisfy the fixed point equation, but do not satisfy
detailed balance. The resulting algorithm significantly suppresses the random
walk behavior and wasted function evaluations that are typically the
consequence of update rejection. We demonstrate a greater than factor of two
improvement in mixing time on three test problems. We release the source code
as Python and MATLAB packages.Comment: Accepted conference submission to ICML 2014 and also featured in a
special edition of JMLR. Since updated to include additional literature
citation
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