Showing papers on "Monte Carlo molecular modeling published in 2018"
TL;DR: This work has investigated the critical behavior of the simple cubic Ising Model, using Monte Carlo simulation that employs the Wolff cluster flipping algorithm with both 32-bit and 53-bit random number generators and data analysis with histogram reweighting and quadruple precision arithmetic.
Abstract: While the three-dimensional Ising model has defied analytic solution, various numerical methods like Monte Carlo, Monte Carlo renormalization group, and series expansion have provided precise information about the phase transition. Using Monte Carlo simulation that employs the Wolff cluster flipping algorithm with both 32-bit and 53-bit random number generators and data analysis with histogram reweighting and quadruple precision arithmetic, we have investigated the critical behavior of the simple cubic Ising Model, with lattice sizes ranging from ${16}^{3}$ to ${1024}^{3}$. By analyzing data with cross correlations between various thermodynamic quantities obtained from the same data pool, e.g., logarithmic derivatives of magnetization and derivatives of magnetization cumulants, we have obtained the critical inverse temperature ${K}_{c}=0.221\phantom{\rule{0.16em}{0ex}}654\phantom{\rule{0.16em}{0ex}}626(5)$ and the critical exponent of the correlation length $\ensuremath{
u}=0.629\phantom{\rule{0.16em}{0ex}}912(86)$ with precision that exceeds all previous Monte Carlo estimates.
127 citations
TL;DR: The usefulness and effectiveness of the proposed EPFM is investigated by applying the technique on a conceptual and highly nonlinear hydrologic model over four river basins located in different climate and geographical regions of the United States.
95 citations
TL;DR: An informal introduction to piecewise deterministic Markov processes is given, covering the aspects relevant to these new Monte Carlo algorithms, with a view to making the development of new continuoustime Monte Carlo more accessible.
Abstract: Recently, there have been conceptually new developments in Monte Carlo methods through the introduction of new MCMC and sequential Monte Carlo (SMC) algorithms which are based on continuous-time, rather than discrete-time, Markov processes. This has led to some fundamentally new Monte Carlo algorithms which can be used to sample from, say, a posterior distribution. Interestingly, continuous-time algorithms seem particularly well suited to Bayesian analysis in big-data settings as they need only access a small sub-set of data points at each iteration, and yet are still guaranteed to target the true posterior distribution. Whilst continuous-time MCMC and SMC methods have been developed independently we show here that they are related by the fact that both involve simulating a piecewise deterministic Markov process. Furthermore, we show that the methods developed to date are just specific cases of a potentially much wider class of continuous-time Monte Carlo algorithms. We give an informal introduction to piecewise deterministic Markov processes, covering the aspects relevant to these new Monte Carlo algorithms, with a view to making the development of new continuous-time Monte Carlo more accessible. We focus on how and why sub-sampling ideas can be used with these algorithms, and aim to give insight into how these new algorithms can be implemented, and what are some of the issues that affect their efficiency.
85 citations
TL;DR: In this paper, a hybrid quantum Monte Carlo (HQMC) method is used to simulate negative sign free lattice fermion models with subcubic scaling in system size.
Abstract: A unique feature of the hybrid quantum Monte Carlo (HQMC) method is the potential to simulate negative sign free lattice fermion models with subcubic scaling in system size. Here we will revisit the algorithm for various models. We will show that for the Hubbard model the HQMC suffers from ergodicity issues and unbounded forces in the effective action. Solutions to these issues can be found in terms of a complexification of the auxiliary fields. This implementation of the HQMC that does not attempt to regularize the fermionic matrix so as to circumvent the aforementioned singularities does not outperform single spin flip determinantal methods with cubic scaling. On the other hand we will argue that there is a set of models for which the HQMC is very efficient. This class is characterized by effective actions free of singularities. Using the Majorana representation, we show that models such as the Su-Schrieffer-Heeger Hamiltonian at half filling and on a bipartite lattice belong to this class. For this specific model subcubic scaling is achieved.
65 citations
TL;DR: In this paper, piecewise deterministic Monte Carlo (DMMC) algorithms are implemented in settings where the parameters live on a restricted domain, and shown how they can be implemented in the restricted domain.
52 citations
TL;DR: This work addresses the approximation of functionals depending on a system of particles, described by stochastic differential equations (SDEs), in the mean-field limit when the number of particles approaches infinity, and considers different variants of the Monte Carlo and Multilevel Monte Carlo methods.
Abstract: We address the approximation of functionals depending on a system of particles, described by stochastic differential equations (SDEs), in the mean-field limit when the number of particles approaches infinity This problem is equivalent to estimating the weak solution of the limiting McKean–Vlasov SDE To that end, our approach uses systems with finite numbers of particles and a time-stepping scheme In this case, there are two discretization parameters: the number of time steps and the number of particles Based on these two parameters, we consider different variants of the Monte Carlo and Multilevel Monte Carlo (MLMC) methods and show that, in the best case, the optimal work complexity of MLMC, to estimate the functional in one typical setting with an error tolerance of $$\mathrm {TOL}$$
, is when using the partitioning estimator and the Milstein time-stepping scheme We also consider a method that uses the recent Multi-index Monte Carlo method and show an improved work complexity in the same typical setting of Our numerical experiments are carried out on the so-called Kuramoto model, a system of coupled oscillators
36 citations
TL;DR: This tutorial will provide a self-contained introduction to one of the state-of-the-art methods—the particle Metropolis-Hastings algorithm—which has proven to offer a practical approximation to the problem of learning probabilistic nonlinear state-space models.
35 citations
TL;DR: Various ways of optimizing population annealing Monte Carlo are presented using 2-local spin-glass Hamiltonians as a case study to demonstrate how the algorithm can be optimized from an implementation, algorithmic accelerator, as well as scalable parallelization point of view.
Abstract: Population annealing Monte Carlo is an efficient sequential algorithm for simulating k-local Boolean Hamiltonians. Because of its structure, the algorithm is inherently parallel and therefore well suited for large-scale simulations of computationally hard problems. Here we present various ways of optimizing population annealing Monte Carlo using 2-local spin-glass Hamiltonians as a case study. We demonstrate how the algorithm can be optimized from an implementation, algorithmic accelerator, as well as scalable parallelization points of view. This makes population annealing Monte Carlo perfectly suited to study other frustrated problems such as pyrochlore lattices, constraint-satisfaction problems, as well as higher-order Hamiltonians commonly found in, e.g., topological color codes.
33 citations
TL;DR: This article considers static Bayesian parameter estimation for partially observed diffusions that are discretely observed under the assumption that one must resort to discretizing the underlying diffusion process, for instance, using the Euler--Maruyama method.
Abstract: In this article we consider static Bayesian parameter estimation for partially observed diffusions that are discretely observed. We work under the assumption that one must resort to discretizing the underlying diffusion process, for instance, using the Euler--Maruyama method. Given this assumption, we show how one can use Markov chain Monte Carlo (MCMC) and particularly particle MCMC [C. Andrieu, A. Doucet, and R. Holenstein, J. R. Stat. Soc. Ser. B Stat. Methodol., 72 (2010), 269--342] to implement a new approximation of the multilevel (ML) Monte Carlo (MC) collapsing sum identity. Our approach comprises constructing an approximate coupling of the posterior density of the joint distribution over parameter and hidden variables at two different discretization levels and then correcting by an importance sampling method. The variance of the weights are independent of the length of the observed data set. The utility of such a method is that, for a prescribed level of mean square error, the cost of this MLMC m...
32 citations
TL;DR: In this article, the authors use the Gutzwiller Monte Carlo approach to simulate the dissipative $XYZ$ model in the vicinity of a dissipative phase transition and identify a ferromagnetic and two paramagnetic phases.
Abstract: We use the Gutzwiller Monte Carlo approach to simulate the dissipative $XYZ$ model in the vicinity of a dissipative phase transition. This approach captures classical spatial correlations together with the full on-site quantum behavior while neglecting nonlocal quantum effects. By considering finite two-dimensional lattices of various sizes, we identify a ferromagnetic and two paramagnetic phases, in agreement with earlier studies. The greatly reduced numerical complexity of the Gutzwiller Monte Carlo approach facilitates efficient simulation of relatively large lattice sizes. The inclusion of the spatial correlations allows to capture parts of the phase diagram that are completely missed by the widely applied Gutzwiller decoupling of the density matrix.
31 citations
TL;DR: The aim of this review is to provide a comprehensive introduction to the geometric tools used in Hamiltonian Monte Carlo at a level accessible to statisticians, machine learners, and other users of the methodology with only a basic understanding of Monte Carlo methods.
Abstract: Markov chain Monte Carlo methods have revolutionized mathematical computation and enabled statistical inference within many previously intractable models. In this context, Hamiltonian dynamics have been proposed as an efficient way of building chains that can explore probability densities efficiently. The method emerges from physics and geometry, and these links have been extensively studied over the past thirty years. The aim of this review is to provide a comprehensive introduction to the geometric tools used in Hamiltonian Monte Carlo at a level accessible to statisticians, machine learners, and other users of the methodology with only a basic understanding of Monte Carlo methods. This will be complemented with some discussion of the most recent advances in the field, which we believe will become increasingly relevant to scientists.
TL;DR: In this paper, the phase diagrams and the magnetic properties of a single nano-graphene layer with next-nearest neighbors coupling J 2 and four-spin interaction J 4 were studied.
TL;DR: A new, asymptotic-preserving Monte Carlo method that is stable independently of the scaling parameter and degenerates to a standard probabilistic approach for solving the limiting equation in the diffusion limit.
Abstract: We develop a new Monte Carlo method that solves hyperbolic transport equations with stiff terms, characterized by a (small) scaling parameter. In particular, we focus on systems which lead to a reduced problem of parabolic type in the limit when the scaling parameter tends to zero. Classical Monte Carlo methods suffer severe time step limitations in these situations, due to the fact that the characteristic speeds go to infinity in the diffusion limit. This makes the problem a real challenge, since the scaling parameter may differ by several orders of magnitude in the domain. To circumvent these time step limitations, we construct a new, asymptotic-preserving Monte Carlo method that is stable independently of the scaling parameter and degenerates to a standard probabilistic approach for solving the limiting equation in the diffusion limit. The method uses an implicit time discretization to formulate a modified equation in which the characteristic speeds do not grow indefinitely when the scaling factor tend...
TL;DR: A modification of the MIMC method is developed which allows one to use standard Markov chain Monte Carlo (MCMC) algorithms to replace independent and coupled sampling, in certain contexts, and a variance theorem is proved which shows that using this method is preferable to i.i.t.d.~sampling from the most accurate approximation of the probability law.
Abstract: In this article we consider computing expectations w.r.t.~probability laws associated to a certain class of stochastic systems. In order to achieve such a task, one must not only resort to numerical approximation of the expectation, but also to a biased discretization of the associated probability. We are concerned with the situation for which the discretization is required in multiple dimensions, for instance in space and time. In such contexts, it is known that the multi-index Monte Carlo (MIMC) method can improve upon i.i.d.~sampling from the most accurate approximation of the probability law. Indeed by a non-trivial modification of the multilevel Monte Carlo (MLMC) method and it can reduce the work to obtain a given level of error, relative to the afore mentioned i.i.d.~sampling and relative even to MLMC. In this article we consider the case when such probability laws are too complex to sampled independently. We develop a modification of the MIMC method which allows one to use standard Markov chain Monte Carlo (MCMC) algorithms to replace independent and coupled sampling, in certain contexts. We prove a variance theorem which shows that using our MIMCMC method is preferable, in the sense above, to i.i.d.~sampling from the most accurate approximation, under assumptions. The method is numerically illustrated on a problem associated to a stochastic partial differential equation (SPDE).
TL;DR: In this article, a differentially weighted operator splitting Monte Carlo (DWOSMC) method was developed to solve complex aerosol dynamic processes by coupling the DWOSMC method and the operator splitting technique.
TL;DR: In this paper, the authors investigated the tunneling time of projective QMC simulations based on the diffusion Monte Carlo (DMC) algorithm without guiding functions, showing that it scales as $1/
Abstract: In simple ferromagnetic quantum Ising models characterized by an effective double-well energy landscape the characteristic tunneling time of path-integral Monte Carlo (PIMC) simulations has been shown to scale as the incoherent quantum-tunneling time, i.e., as $1/{\mathrm{\ensuremath{\Delta}}}^{2}$, where $\mathrm{\ensuremath{\Delta}}$ is the tunneling gap. Since incoherent quantum tunneling is employed by quantum annealers (QAs) to solve optimization problems, this result suggests that there is no quantum advantage in using QAs with respect to quantum Monte Carlo (QMC) simulations. A counterexample is the recently introduced shamrock model (Andriyash and Amin, arXiv:1703.09277), where topological obstructions cause an exponential slowdown of the PIMC tunneling dynamics with respect to incoherent quantum tunneling, leaving open the possibility for potential quantum speedup, even for stoquastic models. In this work we investigate the tunneling time of projective QMC simulations based on the diffusion Monte Carlo (DMC) algorithm without guiding functions, showing that it scales as $1/\mathrm{\ensuremath{\Delta}}$, i.e., even more favorably than the incoherent quantum-tunneling time, both in a simple ferromagnetic system and in the more challenging shamrock model. However, a careful comparison between the DMC ground-state energies and the exact solution available for the transverse-field Ising chain indicates an exponential scaling of the computational cost required to keep a fixed relative error as the system size increases.
TL;DR: In this article, the authors showed how the clusters free energies are constrained by the coagulation probability, and explained various anomalies observed during the precipitation kinetics in coagulated water.
Abstract: In a recent paper, the authors showed how the clusters free energies are constrained by the coagulation probability, and explained various anomalies observed during the precipitation kinetics in co...
TL;DR: In this paper, the authors proposed a Monte Carlo test that is able to control Type I error with more accuracy compared to existing approaches in both normal and nonnormally distributed data at small sample sizes.
Abstract: Statistical theories of goodness-of-fit tests in structural equation modeling are based on asymptotic distributions of test statistics. When the model includes a large number of variables or the population is not from a multivariate normal distribution, the asymptotic distributions do not approximate the distribution of the test statistics very well at small sample sizes. A variety of methods have been developed to improve the accuracy of hypothesis testing at small sample sizes. However, all these methods have their limitations, specially for nonnormal distributed data. We propose a Monte Carlo test that is able to control Type I error with more accuracy compared to existing approaches in both normal and nonnormally distributed data at small sample sizes. Extensive simulation studies show that the suggested Monte Carlo test has a more accurate observed significance level as compared to other tests with a reasonable power to reject misspecified models.
TL;DR: This work proposes a classification and regression trees (CART) approach from the statistical learning and data mining field to analyze Monte Carlo simulation data and suggests that CART is able to arrive at the same conclusions as current descriptive and inferential approaches.
Abstract: Monte Carlo simulations are an important tool for researchers to study statistical properties of estimators, such as parameter bias, or the limits of various modeling approaches. Typically, the imm...
TL;DR: Upper and lower bounds for the additional error caused by this are determined and compared to those of |E-N [Y - Y-n]|, which are found to be smaller than the corresponding results for multilevel Monte Carlo estimators.
TL;DR: An update to the pysimm Python molecular simulation API is presented, with a major part of the implementation of a new interface with CASSANDRA — a modern, versatile Monte Carlo molecular simulation program.
TL;DR: In this paper, a generalized perturbation theory (GPT) formulation suited for the Monte Carlo (MC) eigenvalue calculations is newly developed to estimate sensitivities of a general MC tally to input data.
Abstract: A generalized perturbation theory (GPT) formulation suited for the Monte Carlo (MC) eigenvalue calculations is newly developed to estimate sensitivities of a general MC tally to input data. In the ...
TL;DR: The consortium for Advanced Simulation of Light Water Reactors aims to provide real-time information about the design and operation of light water Reactors to improve the simulation quality of the Reactors.
TL;DR: For a nuclear system in which the entire -eigenvalue spectrum is known, eigenfunction expansion yields the time-dependent flux response to any arbitrary source as mentioned in this paper, and applications in which this response...
Abstract: For a nuclear system in which the entire -eigenvalue spectrum is known, eigenfunction expansion yields the time-dependent flux response to any arbitrary source. Applications in which this response ...
TL;DR: In this paper, the authors proposed an algorithm which initially assumes that there is a substantial amount of artificial measurement noise present, and then the variance of this noise is sequentially decreased in an adaptive fashion.
TL;DR: This work analyzes and compares the computational complexity of dierent simulation strategies for Monte Carlo in the setting of classically scaled population processes and introduces a novel asymptotic regime where the required accuracy is a function of the model scaling parameter.
Abstract: We analyze and compare the computational complexity of dierent simulation strategies for Monte Carlo in the setting of classically scaled population processes. This setting includes stochastically modeled biochemical systems. We consider the task of approximating the expected value of some function of the state of the system at a xed time point. We study the use of standard Monte Carlo when samples are produced by exact simulation and by approximation with tau-leaping or an EulerMaruyama discretization of a diusion approximation. Appropriate modications of recently proposed multilevel Monte Carlo algorithms are also studied for the tau-leaping and Euler-Maruyama approaches. In order to quantify computational complexity in a tractable yet meaningful manner, we consider a parameterization that, in the mass action chemical kinetics setting, corresponds to the classical system size scaling. We then introduce a novel asymptotic regime where the required accuracy is a function of the model scaling parameter. Our new analysis shows that for this particular scaling a diusion approximation oers little from a computational standpoint. Instead, we nd
TL;DR: Modern variants of Monte Carlo methods for Uncertainty Quantification (UQ) of the Neutron Transport Equation, when it is approximated by the discrete ordinates method with diamond differencing are described.
Abstract: We describe modern variants of Monte Carlo methods for Uncertainty Quantification (UQ) of the Neutron Transport Equation, when it is approximated by the discrete ordinates method with diamond differencing. We focus on the mono-energetic 1D slab geometry problem, with isotropic scattering, where the cross-sections are log-normal correlated random fields of possibly low regularity. The paper includes an outline of novel theoretical results on the convergence of the discrete scheme, in the cases of both spatially variable and random cross-sections. We also describe the theory and practice of algorithms for quantifying the uncertainty of a functional of the scalar flux, using Monte Carlo and quasi-Monte Carlo methods, and their multilevel variants. A hybrid iterative/direct solver for computing each realisation of the functional is also presented. Numerical experiments show the effectiveness of the hybrid solver and the gains that are possible through quasi-Monte Carlo sampling and multilevel variance reduction. For the multilevel quasi-Monte Carlo method, we observe gains in the computational e-cost of up to two orders of magnitude over the standard Monte Carlo method, and we explain this theoretically. Experiments on problems with up to several thousand stochastic dimensions are included.
TL;DR: This paper evaluates the performance of Monte Carlo forecasting by analyzing it in the context of Markov chain Monte Carlo (MCMC) theory, and shows that for a special class of nonlinear systems that have zero divergence, the propagated kernel is in detailed balance with the true state probability density function.
TL;DR: In this paper, Monte Carlo (MC) simulations in the Gibbs ensemble are used to compute the VLE of multicomponent natural gas mixtures, and the results show that molecular simulation can be used to predict properties of multi-component systems relevant for the natural gas industry.
Abstract: Vapour–liquid equilibrium (VLE) and volumetric data of multicomponent mixtures are extremely important for natural gas production and processing, but it is time consuming and challenging to experimentally obtain these properties. An alternative tool is provided by means of molecular simulation. Here, Monte Carlo (MC) simulations in the Gibbs ensemble are used to compute the VLE of multicomponent natural gas mixtures. Two multicomponent systems, one containing a mixture of six components ((Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.)S, (Formula presented.)(Formula presented.) and (Formula presented.)(Formula presented.)), and the other containing a mixture of nine components ((Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.)S, (Formula presented.)(Formula presented.), (Formula presented.)(Formula presented.), (Formula presented.)(Formula presented.), (Formula presented.)(Formula presented.) and (Formula presented.)(Formula presented.)) are simulated. The computed VLE from the MC simulations is in good agreement with available experimental data and the GERG-2008 equation of state modelling. The results show that molecular simulation can be used to predict properties of multicomponent systems relevant for the natural gas industry. Guidelines are provided to setup Gibbs ensemble simulations for multicomponent systems, which is a challenging task due to the increased number of degrees of freedom.
TL;DR: Various new schemes such as deterministic decay of precursors in each time step, adjustment of weights of neutrons and precursor for population control, use of mean number of secondaries per collision, and particle splitting/Russian roulette to reduce the variance in neutron power are proposed.
Abstract: The use of the Monte Carlo (MC) method for space-time reactor kinetics is expected to be much more accurate than the presently used deterministic methods largely based on few-group diffusion theory. However, the development of the MC method for space-time reactor kinetics poses challenges because of the vastly different timescales of neutrons and delayed neutron precursors and their vastly different populations that also change with time by several orders of magnitude. In order to meet these challenges in MC-based space kinetics, we propose various new schemes such as deterministic decay of precursors in each time step, adjustment of weights of neutrons and precursors for population control, use of mean number of secondaries per collision, and particle splitting/Russian roulette to reduce the variance in neutron power. The efficacy of these measures is first tested in a simpler point-kinetics version of the MC method against analytical or accurate numerical solutions of point-kinetics equations. T...