Size and temperature dependent shapes of copper nanocrystals using parallel tempering molecular dynamics
Parallel-tempering molecular dynamics simulations reveal the temperature- and size-dependent shapes of Cu nanocrystals.
36 MATERIALS SCIENCE↗
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Optimizing temperature distributions for training neural quantum states using parallel tempering
Parametrized artificial neural networks (ANNs) can be very expressive ansatzes for variational algorithms, reaching state-of-the-art energies on many quantum many-body Hamiltonians. Nevertheless, the training of the ANN can be slow and stymied by the presence of local minima in the parameter landscape. One approach to mitigate this issue is to use parallel tempering methods, and in this work, we focus on the role played by the temperature distribution of the parallel tempering replicas. Using an adaptive method that adjusts the temperatures in order to equate the exchange probability between neighboring replicas, we show that this temperature optimization can significantly increase the success rate of the variational algorithm with negligible computational cost by eliminating bottlenecks in the replicas' random walk. Furthermore, we demonstrate this using two different neural networks, a restricted Boltzmann machine and a feedforward network, which we use to study a toy problem based on a permutation invariant Hamiltonian with a pernicious local minimum and the 𝐽 1 −𝐽 2 model on a rectangular lattice.
Neural network simulations↗
Bug fixes / enhancements to Parallel tempering Markov chain Monte Carlo sampler (PTMCMCSampler) v3
Markov chain Monte Carlo sampler useful for a variety of problems for optimization, numerical integration, and generating draws from a probability distribution. They are often used in physical and mathematical problems, especially when it is difficult or impossible to use other approaches. This disclosure is for new bug fixes and enhancements to an existing open source library that is already in the public domain under the MIT license. https://github.com/jellis18/PTMCMCSampler
Forrer, Mark↗
Temperature Optimization for Parallel Tempering in Neural Networks
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Albash, Tameem↗
Precision study of the continuum SU(3) Yang-Mills theory: How to use parallel tempering to improve on supercritical slowing down for first order phase transitions
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S. Borsányi↗
Quantum-inspired tempering for ground state approximation using artificial neural networks
A large body of work has demonstrated that parameterized artificial neural networks (ANNs) can efficiently describe ground states of numerous interesting quantum many-body Hamiltonians. However, the standard variational algorithms used to update or train the ANN parameters can get trapped in local minima, especially for frustrated systems and even if the representation is sufficiently expressive. We propose a parallel tempering method that facilitates escape from such local minima. This methods involves training multiple ANNs independently, with each simulation governed by a Hamiltonian with a different "driver" strength, in analogy to quantum parallel tempering, and it incorporates an update step into the training that allows for the exchange of neighboring ANN configurations. We study instances from two classes of Hamiltonians to demonstrate the utility of our approach using Restricted Boltzmann Machines as our parameterized ANN. The first instance is based on a permutation-invariant Hamiltonian whose landscape stymies the standard training algorithm by drawing it increasingly to a false local minimum. The second instance is four hydrogen atoms arranged in a rectangle, which is an instance of the second quantized electronic structure Hamiltonian discretized using Gaussian basis functions. We study this problem in a minimal basis set, which exhibits false minima that can trap the standard variational algorithm despite the problem’s small size. We show that augmenting the training with quantum parallel tempering becomes useful to finding good approximations to the ground states of these problem instances.
Albash, Tameem↗
Minimum Free-Energy Shapes of Ag Nanocrystals: Vacuum vs Solution
Here, we use two variants of replica-exchange molecular dynamics (MD) simulations, parallel tempering MD and partial replica exchange MD, to probe the minimum free-energy shapes of Ag nanocrystals containing 100–200 atoms in a vacuum, ethylene glycol (EG) solvent, and EG solvent with a PVP polymer containing 100 repeat units. Our simulations reveal a shape intermediate between a Dh and an Ih, a Dh-Ih, that has distinct structural signatures and magic sizes. We find several prominent features associated with entropy: pure FCC nanocrystals are less common than FCC crystals containing stacking faults, and crystals with the minimum potential energy are not always preferred over the range of relevant temperatures. The shapes of the nanocrystals in solution are influenced by the chemical identities of the solution-phase molecules. Comparing Ag nanocrystal shapes in EG to those in an EG+PVP solution, we find more icosahedra in EG and more decahedra in EG+PVP across all of the nanocrystal sizes probed in this study. At certain critical sizes, nanocrystal shapes can change dramatically with the addition and removal of a single atom or with a change in temperature at a fixed size. The information in our study could be useful in efforts to devise processing routes to achieve selective nanocrystal shapes.
36 MATERIALS SCIENCE↗
3-regular three-XORSAT planted solutions benchmark of classical and quantum heuristic optimizers
With current semiconductor technology reaching its physical limits, special-purpose hardware has emerged as an option to tackle specific computing-intensive challenges. Optimization in the form of solving quadratic unconstrained binary optimization problems, or equivalently Ising spin glasses, has been the focus of several new dedicated hardware platforms. These platforms come in many different flavors, from highly-efficient hardware implementations on digital-logic of established algorithms to proposals of analog hardware implementing new algorithms. In this work, we use a mapping of a specific class of linear equations whose solutions can be found efficiently, to a hard constraint satisfaction problem (three-regular three-XORSAT, or an Ising spin glass) with a 'golf-course' shaped energy landscape, to benchmark several of these different approaches. We perform a scaling and prefactor analysis of the performance of Fujitsu's digital annealer unit (DAU), the D-Wave advantage quantum annealer, a virtual MemComputing machine, Toshiba's simulated bifurcation machine (SBM), the SATonGPU algorithm from Bernaschi et al, and our implementation of parallel tempering. We identify the SATonGPU and DAU as currently having the smallest scaling exponent for this benchmark, with SATonGPU having a small scaling advantage and in addition having by far the smallest prefactor thanks to its use of massive parallelism. Furthermore, our work provides an objective assessment and a snapshot of the promise and limitations of dedicated optimization hardware relative to a particular class of optimization problems.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Crystal structure of perfluorononanoic acid, C 9 HF 17 O 2
The crystal structure of perfluorononanoic acid (PFNA) was solved via parallel tempering using synchrotron powder diffraction data obtained from the Brockhouse X-ray Diffraction and Scattering (BXDS) Wiggler Lower Energy (WLE) beamline at the Canadian Light Source. PFNA crystallizes in monoclinic space group P2 1 /c (#14) with lattice parameters a = 26.172(1) Å, b = 5.6345(2) Å, c = 10.9501(4) Å, and β = 98.752(2)°. The crystal structure is composed of dimers, with pairs of PFNA molecules connected by hydrogen bonds via the carboxylic acid functional groups. The Rietveld-refined structure was compared to a density functional theory-optimized structure, and the root-mean-square Cartesian difference was larger than normally observed for correct powder structures. The powder data likely exhibited evidence of disorder which was not successfully modeled.
38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
A Computational Study of RNA Tetraloop Thermodynamics, Including Misfolded States
An important characteristic of RNA folding is the adoption of alternative configurations of similar stability, often referred to as misfolded configurations. These configurations are considered to compete with correctly folded configurations, although their rigorous thermodynamic and structural characterization remains elusive. Tetraloop motifs found in large ribozymes are ideal systems for an atomistically detailed computational quantification of folding free energy landscapes and the structural characterization of their constituent free energy basins, including nonnative states. In this work, we studied a group of closely related 10-mer tetraloops using a combined parallel tempering and metadynamics technique that allows a reliable sampling of the free energy landscapes, requiring only knowledge that the stem folds into a canonical A-RNA configuration. Here we isolated and analyzed unfolded, folded, and misfolded populations that correspond to different free energy basins. We identified a distinct misfolded state that has a stability very close to that of the correctly folded state. This misfolded state contains a predominant population that shares the same structural features across all tetraloops studied here and lacks the noncanonical A-G base pair in its loop portion. Further analysis performed with biased trajectories showed that although this competitive misfolded state is not an essential intermediate, it is visited in most of the transitions from unfolded to correctly folded states. Moreover, the tetraloops can transition from this misfolded state to the correctly folded state without requiring extensive unfolding.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Water–Hydrocarbon Interactions in Anionic Pyrene Monohydrate
Interactions between water and polycyclic aromatic hydrocarbons are essential in many aspects of chemistry, from interstellar and atmospheric processes to interfacial hydrophobicity and wetting phenomena. Despite their growing importance, the intermolecular potentials of the water-hydrocarbon interactions are underdeveloped compared to water-water potentials, and there are similarly few experimental probes that are sensitive to the details of the water-hydrocarbon potential. We present a combined experimental and computational study of anionic pyrene monohydrate, one of the simplest water/hydrocarbon clusters. The action spectrum in the OH region of the mass-selected cluster ion provides a rigorous benchmark for intermolecular potentials and computational methodologies. We identify missing intermolecular interactions and shortcomings in conventional dynamics calculations by comparing experimental data to density functional theory and classical molecular dynamics calculations. Kinetic trapping is prevalent, even for one water molecule and one pyrene molecule, leading to slow equilibration in conventional molecular dynamics calculations, even on nanosecond timescales and at low temperatures (50 K). At constant energy, temperature fluctuations for the pair of molecules are substantial. Immersing the system in a bath of soft spheres and employing parallel tempering alleviates kinetic trapping and dampens temperature fluctuations, bringing the system closer to the thermodynamic limit. With such augmented sampling, a simple, flexible water model reproduces the linewidth and the asymmetric broadening of the symmetric OH stretching mode, which we assign to spectral diffusion. In the OH stretching region, dynamics calculations predict a more intense antisymmetric peak than experiments observe but do not predict the bimodal split symmetric peak that the experiments show. Furthermore, our work suggests that electronic polarization, missing in the empirical force field, is responsible for the first discrepancy and that quantum nuclear effects, captured neither in density functional theory nor in classical dynamics, may be responsible for the second.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Variational inference of effective range parameters for 3 He− 4 He scattering
We use two different methods, Monte Carlo sampling and variational inference (VI), to perform a Bayesian calibration of the effective-range parameters in 3 He– 4 He elastic scattering. The parameters are calibrated to data from a recent set of 3 He– 4 He elastic scattering differential cross section measurements. Analysis of these data for E lab ≤ 4.3 MeV yields a unimodal posterior for which both methods obtain the same structure. However, the effective-range expansion amplitude does not account for the 7/2 − state of 7 Be so, even after calibration, the description of data at the upper end of this energy range is poor. The data up to E lab = 2.6 MeV can be well described, but calibration to this lower-energy subset of the data yields a bimodal posterior. After adapting VI to treat such a multi-modal posterior we find good agreement between the VI results and those obtained with parallel-tempered Monte Carlo sampling.
effective field theory↗
Umbrella sampling: a powerful method to sample tails of distributions
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. In this approach sampling of the target likelihood is split into sampling of multiple biased likelihoods confined within individual umbrella windows. We show that the US algorithm is efficient and highly parallel and that it can be easily used with other existing Markov Chain Monte Carlo (MCMC) samplers. The method allows the user to capitalize on their intuition and define umbrella windows and increase sampling accuracy along specific directions in the parameter space. Alternatively, one can define umbrella windows using an approach similar to parallel tempering. We provide a public code that implements US as a standalone PYTHON package. We present a number of tests illustrating the power of the US method in sampling low-probability areas of the posterior and show that this ability allows a considerably more robust sampling of multimodal distributions compared to standard sampling methods. We also present an application of the method in a real world example of deriving cosmological constraints using the supernova type Ia data. We show that US can sample the posterior accurately down to the approximate to 15 sigma credible region in the Omega(m) - Omega(Lambda) plane, while for the same computational effort the affine-invariant MCMC sampling implemented in the emcee code samples the posterior reliably only to approximate to 3 sigma.
cosmology: cosmological parameters↗
Spirals and skyrmions in antiferromagnetic triangular lattices
In this work, we study realizations of spirals and skyrmions in two-dimensional antiferromagnets with a triangular lattice on an inversion-symmetry-breaking substrate. As a possible material realization, we investigate the adsorption of transition-metal atoms (Cr, Mn, Fe, or Co) on a monolayer of MoS 2 , WS 2 , or WSe 2 and obtain the exchange, anisotropy, and Dzyaloshinskii-Moriya interaction parameters using first-principles calculations. Using energy minimization and parallel-tempering Monte Carlo simulations, we determine the magnetic phase diagrams for a wide range of interaction parameters. We find that skyrmion lattices can appear even with weak Dzyaloshinskii-Moriya interactions, but their stability is hindered by magnetic anisotropy. However, a weak easy plane magnetic anisotropy can be beneficial for stabilizing the skyrmion phase. Our results suggest that Cr/MoS 2 , Fe/MoS 2 , and Fe/WSe 2 interfaces can host spin spirals formed from the 120 degrees antiferromagnetic states. Our results further suggest that for interfaces, such as Fe/MoS 2 , the Dzyaloshinskii-Moriya interaction is strong enough to drive the system into a three-sublattice skyrmion lattice in the presence of experimentally feasible external magnetic field.
36 MATERIALS SCIENCE↗
Scale setting of SU(𝑁) Yang–Mills theory, topology and large-𝑁 volume independence
We set the scale of SU(𝑁) Yang-Mills theories for 𝑁 =3, 5, 8 and in the large-𝑁 limit via gradient flow, as a first step towards the computation of the large-𝑁 Λ-parameter using step scaling. We adopt twisted boundary conditions to achieve large-𝑁 volume reduction and the Parallel Tempering on Boundary Conditions algorithm to tame topological freezing. This setup allows accurate determinations of the gradient-flow scales down to lattice spacings as fine as ∼0.025 fm for all the explored values of 𝑁, a regime that has never been reached with ergodic algorithms. Moreover, we are able to precisely estimate the finite-size systematics related to topological freezing, and to show the suppression of finite-volume effects expected by virtue of large-𝑁 twisted volume reduction.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
ORNL_AISD_NiPt
This dataset describes the nickel-platinum (NiPt) solid solution binary alloy, where the two constituent elements nickel (Ni) and platinum (Pt) are randomly placed on the face centered cubic (FCC) crystal structure, with the lattice constant of 3.840 angstroms. The dataset comprises data for three different sizes of the crystal structure: 256 atoms, 864 atoms, and 2,048 atoms, each of which contains 1900 configurations. For each size of the crystal structure, the data set was generated for concentrations ranging from 0at% of Pt to 100at% of Pt in the NiPt binary system, with increasing the concentration of Pt in the system every 5at%. For each one of the chemical compositions, 100 random configurations were generated, each with a different random seed. Each of the output files contains the mass, type, atomic coordinates, energy per atom, and forces in x, y, and z directions respectively. For each atomic configuration, the output was collected every 150 steps during the minimization stage and every 1000 steps during the replica exchange stage. Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [1], which is a molecular dynamics code, was used to generate data for NiPt alloy. The simulation used the interatomic potential for NiPt binary system MEAM_LAMMPS_KimSeolJi_2017_PtNi__MO_020840179467_001 [3] from the OpenKIM library (Open Knowledgebase of Interatomic Models) [2]. This potential was developed based on the second nearest-neighbor modified embedded-atom method (2NN MEAM). The simulation process begins with the generation of the random NiPt structure and follows with the short minimization and replica exchange simulation. The minimization procedure adjusts atomic coordinates and performs energy minimization, which typically leads to a local potential energy minimum. The method used for the minimization was the conjugate gradient algorithm. A short replica exchange (parallel tempering) simulation involves four replicas (ensembles) of a system and follows the minimization stage. Multiple snapshots of the configuration were collected during the minimization and replica exchange stages. NiPt alloy is interesting due to its magnetic and charge transfer properties [4]. The data is provided in three compressed zipped folders: atoms256.zip, atoms864.zip, atoms2048.zip Each zipped folder contains the data that describes crystals of size 256 atoms, 864 atoms, and 2,048 atoms respectively. Each one of the three zipped folders contains the data structured in the following way: -Ni_ground_state.cfg --> atomic configuration for the pure nickel -Pt_ground_state.cfg --> atomic configuration for the pure platinum -Pt#_filtered --> folders containing atomic configurations for #at% concentration of platinum. The folder contains 100 atomic configurations, each saved in a subfolder. Each subfolder named config* is associated with a specific atomic configuration. Each of these subfolders contains files with .cfg format, corresponding to outputs for each atomic configuration The total number of atomic configurations contained in atoms256.zip is 65,046. The total number of atomic configurations contained in atoms864.zip is 63,936. The total number of atomic configurations contained in atoms2048.zip is 61,997. The total number of atomic configurations spanned by the entire dataset is 190,979. References [1] https://www.lammps.org/ [2] https://openkim.org/ [3] https://openkim.org/id/MEAM_LAMMPS_KimSeolJi_2017_PtNi__MO_020840179467_001 [4] El-Gendy, Ahmed A. and Hampel, Silke and Büccchner, Bernd and Klingeler, Rüdiger, Tuneable magnetic properties of carbon-shielded NiPt-nanoalloys, RSC Adv., volume 6, issue 57, pages 52427-52433, 2016, The Royal Society of Chemistry, doi:10.1039/C6RA05910D
36 MATERIALS SCIENCE↗