78 research outputs found
Phase space sampling and operator confidence with generative adversarial networks
We demonstrate that a generative adversarial network can be trained to
produce Ising model configurations in distinct regions of phase space. In
training a generative adversarial network, the discriminator neural network
becomes very good a discerning examples from the training set and examples from
the testing set. We demonstrate that this ability can be used as an anomaly
detector, producing estimations of operator values along with a confidence in
the prediction
Deep neural networks for direct, featureless learning through observation: the case of 2d spin models
We demonstrate the capability of a convolutional deep neural network in
predicting the nearest-neighbor energy of the 4x4 Ising model. Using its
success at this task, we motivate the study of the larger 8x8 Ising model,
showing that the deep neural network can learn the nearest-neighbor Ising
Hamiltonian after only seeing a vanishingly small fraction of configuration
space. Additionally, we show that the neural network has learned both the
energy and magnetization operators with sufficient accuracy to replicate the
low-temperature Ising phase transition. We then demonstrate the ability of the
neural network to learn other spin models, teaching the convolutional deep
neural network to accurately predict the long-range interaction of a screened
Coulomb Hamiltonian, a sinusoidally attenuated screened Coulomb Hamiltonian,
and a modified Potts model Hamiltonian. In the case of the long-range
interaction, we demonstrate the ability of the neural network to recover the
phase transition with equivalent accuracy to the numerically exact method.
Furthermore, in the case of the long-range interaction, the benefits of the
neural network become apparent; it is able to make predictions with a high
degree of accuracy, and do so 1600 times faster than a CUDA-optimized exact
calculation. Additionally, we demonstrate how the neural network succeeds at
these tasks by looking at the weights learned in a simplified demonstration
Sampling algorithms for validation of supervised learning models for Ising-like systems
In this paper, we build and explore supervised learning models of
ferromagnetic system behavior, using Monte-Carlo sampling of the spin
configuration space generated by the 2D Ising model. Given the enormous size of
the space of all possible Ising model realizations, the question arises as to
how to choose a reasonable number of samples that will form physically
meaningful and non-intersecting training and testing datasets. Here, we propose
a sampling technique called ID-MH that uses the Metropolis-Hastings algorithm
creating Markov process across energy levels within the predefined
configuration subspace. We show that application of this method retains phase
transitions in both training and testing datasets and serves the purpose of
validation of a machine learning algorithm. For larger lattice dimensions,
ID-MH is not feasible as it requires knowledge of the complete configuration
space. As such, we develop a new "block-ID" sampling strategy: it decomposes
the given structure into square blocks with lattice dimension no greater than 5
and uses ID-MH sampling of candidate blocks. Further comparison of the
performance of commonly used machine learning methods such as random forests,
decision trees, k nearest neighbors and artificial neural networks shows that
the PCA-based Decision Tree regressor is the most accurate predictor of
magnetizations of the Ising model. For energies, however, the accuracy of
prediction is not satisfactory, highlighting the need to consider more
algorithmically complex methods (e.g., deep learning).Comment: 43 pages and 16 figure
A note on the metallization of compressed liquid hydrogen
We examine the molecular-atomic transition in liquid hydrogen as it relates
to metallization. Pair potentials are obtained from first principles molecular
dynamics and compared with potentials derived from quadratic response. The
results provide insight into the nature of covalent bonding under extreme
conditions. Based on this analysis, we construct a schematic
dissociation-metallization phase diagram and suggest experimental approaches
that should significantly reduce the pressures necessary for the realization of
the elusive metallic phase of hydrogen.Comment: 11 pages, 4 figure
Neuroevolutionary learning of particles and protocols for self-assembly
Within simulations of molecules deposited on a surface we show that
neuroevolutionary learning can design particles and time-dependent protocols to
promote self-assembly, without input from physical concepts such as thermal
equilibrium or mechanical stability and without prior knowledge of candidate or
competing structures. The learning algorithm is capable of both directed and
exploratory design: it can assemble a material with a user-defined property, or
search for novelty in the space of specified order parameters. In the latter
mode it explores the space of what can be made rather than the space of
structures that are low in energy but not necessarily kinetically accessible
Structure and phase boundaries of compressed liquid hydrogen
We have mapped the molecular-atomic transition in liquid hydrogen using first
principles molecular dynamics. We predict that a molecular phase with
short-range orientational order exists at pressures above 100 GPa. The presence
of this ordering and the structure emerging near the dissociation transition
provide an explanation for the sharpness of the molecular-atomic crossover and
the concurrent pressure drop at high pressures. Our findings have non-trivial
implications for simulations of hydrogen; previous equation of state data for
the molecular liquid may require revision. Arguments for the possibility of a
order liquid-liquid transition are discussed
Controlled Online Optimization Learning (COOL): Finding the ground state of spin Hamiltonians with reinforcement learning
Reinforcement learning (RL) has become a proven method for optimizing a
procedure for which success has been defined, but the specific actions needed
to achieve it have not. We apply the so-called "black box" method of RL to what
has been referred as the "black art" of simulated annealing (SA), demonstrating
that an RL agent based on proximal policy optimization can, through experience
alone, arrive at a temperature schedule that surpasses the performance of
standard heuristic temperature schedules for two classes of Hamiltonians. When
the system is initialized at a cool temperature, the RL agent learns to heat
the system to "melt" it, and then slowly cool it in an effort to anneal to the
ground state; if the system is initialized at a high temperature, the algorithm
immediately cools the system. We investigate the performance of our RL-driven
SA agent in generalizing to all Hamiltonians of a specific class; when trained
on random Hamiltonians of nearest-neighbour spin glasses, the RL agent is able
to control the SA process for other Hamiltonians, reaching the ground state
with a higher probability than a simple linear annealing schedule. Furthermore,
the scaling performance (with respect to system size) of the RL approach is far
more favourable, achieving a performance improvement of one order of magnitude
on L=14x14 systems. We demonstrate the robustness of the RL approach when the
system operates in a "destructive observation" mode, an allusion to a quantum
system where measurements destroy the state of the system. The success of the
RL agent could have far-reaching impact, from classical optimization, to
quantum annealing, to the simulation of physical systems
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