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Showing papers on "Monte Carlo molecular modeling published in 2014"


Book ChapterDOI
01 Jan 2014
TL;DR: In this article, a Monte Carlo simulation is used to evaluate the physical quantities related to the interaction of electrons with a solid target, and the cross-sections and mean free paths have to be previously accurately calculated: they are then used in the Monte Carlo code in order to obtain the macroscopic characteristics of the interaction processes.
Abstract: Monte Carlo is one of the most powerful theoretical methods for evaluating the physical quantities related to the interaction of electrons with a solid target. A Monte Carlo simulation can be considered as an idealized experiment. The simulation does not investigate the fundamental principles of the interaction. It is necessary to have a good knowledge of them – in particular of the energy loss and angular deflection phenomena – to produce a good simulation. All the cross-sections and mean free paths have to be previously accurately calculated: they are then used in the Monte Carlo code in order to obtain the macroscopic characteristics of the interaction processes by simulating a large number of single particle trajectories and then averaging them. Due to the recent evolution in computer calculation capability, we are now able to obtain statistically significant results in very short calculation times.

268 citations


Journal ArticleDOI
TL;DR: In this article, the derivation of local chiral effective field theory interactions to next-to-next-to leading order was presented and results for nucleon-nucleon phase shifts and deuteron properties for these potentials were obtained.
Abstract: We present details of the derivation of local chiral effective field theory interactions to next-to-next-to-leading order and show results for nucleon-nucleon phase shifts and deuteron properties for these potentials. We then perform systematic auxiliary-field diffusion Monte Carlo calculations for neutron matter based on the developed local chiral potentials at different orders. This includes studies of the effects of the spectral-function regularization and of the local regulators. For all orders, we compare the quantum Monte Carlo results with perturbative many-body calculations and find excellent agreement for low cutoffs.

179 citations


Journal ArticleDOI
TL;DR: A Hamiltonian Monte Carlo algorithm to sample from multivariate Gaussian distributions in which the target space is constrained by linear and quadratic inequalities or products thereof is presented.
Abstract: We present a Hamiltonian Monte Carlo algorithm to sample from multivariate Gaussian distributions in which the target space is constrained by linear and quadratic inequalities or products thereof. The Hamiltonian equations of motion can be integrated exactly and there are no parameters to tune. The algorithm mixes faster and is more efficient than Gibbs sampling. The runtime depends on the number and shape of the constraints but the algorithm is highly parallelizable. In many cases, we can exploit special structure in the covariance matrices of the untruncated Gaussian to further speed up the runtime. A simple extension of the algorithm permits sampling from distributions whose log-density is piecewise quadratic, as in the “Bayesian Lasso” model.

179 citations


Journal ArticleDOI
TL;DR: PGAS provides the data analyst with an off-the-shelf class of Markov kernels that can be used to simulate, for instance, the typically high-dimensional and highly autocorrelated state trajectory in a state-space model.
Abstract: Particle Markov chain Monte Carlo (PMCMC) is a systematic way of combining the two main tools used for Monte Carlo statistical inference: sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC). We present a new PMCMC algorithm that we refer to as particle Gibbs with ancestor sampling (PGAS). PGAS provides the data analyst with an off-the-shelf class of Markov kernels that can be used to simulate, for instance, the typically high-dimensional and highly autocorrelated state trajectory in a state-space model. The ancestor sampling procedure enables fast mixing of the PGAS kernel even when using seemingly few particles in the underlying SMC sampler. This is important as it can significantly reduce the computational burden that is typically associated with using SMC. PGAS is conceptually similar to the existing PG with backward simulation (PGBS) procedure. Instead of using separate forward and backward sweeps as in PGBS, however, we achieve the same effect in a single forward sweep. This makes PGAS well suited for addressing inference problems not only in state-space models, but also in models with more complex dependencies, such as non-Markovian, Bayesian nonparametric, and general probabilistic graphical models.

174 citations


Journal ArticleDOI
TL;DR: In this paper, a hybrid Monte Carlo/deterministic method for increasing the efficiency of Monte Carlo calculations of distributions, such as flux or dose rate distributions (e.g., mesh talli...
Abstract: This paper presents a hybrid (Monte Carlo/deterministic) method for increasing the efficiency of Monte Carlo calculations of distributions, such as flux or dose rate distributions (e.g., mesh talli...

121 citations


Journal ArticleDOI
TL;DR: An event-driven algorithm is presented that generalizes the recent hard-sphere event-chain Monte Carlo method without introducing discretizations in time or in space and breaks detailed balance, but satisfies maximal global balance.
Abstract: In this article, we present an event-driven algorithm that generalizes the recent hard-sphere event-chain Monte Carlo method without introducing discretizations in time or in space. A factorization of the Metropolis filter and the concept of infinitesimal Monte Carlo moves are used to design a rejection-free Markov-chain Monte Carlo algorithm for particle systems with arbitrary pairwise interactions. The algorithm breaks detailed balance, but satisfies maximal global balance and performs better than the classic, local Metropolis algorithm in large systems. The new algorithm generates a continuum of samples of the stationary probability density. This allows us to compute the pressure and stress tensor as a byproduct of the simulation without any additional computations.

120 citations


Journal ArticleDOI
TL;DR: Monte Carlo methods for solving the Boltzmann equation for applications to small-scale transport processes, with particular emphasis on nanoscale heat transport as mediated by phonons are reviewed.
Abstract: We review Monte Carlo methods for solving the Boltzmann equation for applications to small-scale transport processes, with particular emphasis on nanoscale heat transport as mediated by phonons. Our discussion reviews the numerical foundations of Monte Carlo algorithms, basic simulation methodology, as well as recent developments in the field. Examples of the latter include formulations for calculating the effective thermal conductivity of periodically nanostructured materials and variance-reduction methodologies for reducing the computational cost associated with statistical sampling of field properties of interest, such as the temperature and heat flux. Recent developments are presented in the context of applications of current practical interest, including multiscale problems that have motivated some of the most recent developments.

102 citations


Journal ArticleDOI
TL;DR: A novel sequential Monte Carlo approach for joint state and parameter estimation that can deal efficiently with abruptly changing parameters which is a common case when tracking maneuvering targets is developed.
Abstract: This paper develops a novel sequential Monte Carlo (SMC) approach for joint state and parameter estimation that can deal efficiently with abruptly changing parameters which is a common case when tracking maneuvering targets. The approach combines Bayesian methods for dealing with change-points with methods for estimating static parameters within the SMC framework. The result is an approach that adaptively estimates the model parameters in accordance with changes to the target's trajectory. The developed approach is compared against the Interacting Multiple Model (IMM) filter for tracking a maneuvering target over a complex maneuvering scenario with nonlinear observations. In the IMM filter a large combination of models is required to account for unknown parameters. In contrast, the proposed approach circumvents the combinatorial complexity of applying multiple models in the IMM filter through Bayesian parameter estimation techniques. The developed approach is validated over complex maneuvering scenarios where both the system parameters and measurement noise parameters are unknown. Accurate estimation results are presented.

80 citations


Journal ArticleDOI
TL;DR: In this article, a new and faster Total Monte Carlo (TMC) method for the propagation of nuclear data uncertainties in Monte Carlo nuclear simulations is presented, which addresses the main drawba...
Abstract: A new and faster Total Monte Carlo (TMC) method for the propagation of nuclear data uncertainties in Monte Carlo nuclear simulations is presented (the fast TMC method). It addresses the main drawba...

79 citations


Journal ArticleDOI
TL;DR: It is shown that both of these splitting approaches can reduce the computational cost of sampling from the posterior distribution for a logistic regression model, using either a Gaussian approximation centered on the posterior mode, or a Hamiltonian split into a term that depends on only a small number of critical cases, and another term that involves the larger number of cases whose influence on the anterior distribution is small.
Abstract: We show how the Hamiltonian Monte Carlo algorithm can sometimes be speeded up by “splitting” the Hamiltonian in a way that allows much of the movement around the state space to be done at low computational cost. One context where this is possible is when the log density of the distribution of interest (the potential energy function) can be written as the log of a Gaussian density, which is a quadratic function, plus a slowly-varying function. Hamiltonian dynamics for quadratic energy functions can be analytically solved. With the splitting technique, only the slowly-varying part of the energy needs to be handled numerically, and this can be done with a larger stepsize (and hence fewer steps) than would be necessary with a direct simulation of the dynamics. Another context where splitting helps is when the most important terms of the potential energy function and its gradient can be evaluated quickly, with only a slowly-varying part requiring costly computations. With splitting, the quick portion can be handled with a small stepsize, while the costly portion uses a larger stepsize. We show that both of these splitting approaches can reduce the computational cost of sampling from the posterior distribution for a logistic regression model, using either a Gaussian approximation centered on the posterior mode, or a Hamiltonian split into a term that depends on only a small number of critical cases, and another term that involves the larger number of cases whose influence on the posterior distribution is small.

74 citations


Journal ArticleDOI
TL;DR: Numerical results show the computational efficiency of the Interval Monte Carlo approach and its superiority to the alternative search approaches such as optimization and genetic algorithms and results show how that Interval Carlo approach provides guaranteed and sharp enclosure to the system solution.
Abstract: In this work structural reliability assessment is presented for structures with uncertain loads and mate- rial properties. Uncertain variables are modeled as fuzzy random variables and Interval Monte Carlo Simulation along with interval finite element method is used to evalu- ate failure probability. Interval Monte Carlo is compared with existing search algorithms used in the reliability as- sessment of fuzzy random structural systems for both ef- ficiency and accuracy. The genetic algorithm as one of the well developed approaches is selected for compari- son. Fuzzy randomness is used as a model for handling both aleatory and epistemic uncertainties. Fuzzy quanti- ties are calculated using the α-cut approach. In the case of Interval Monte Carlo, bounds on response quantities are obtained for each α-cut using only one run of interval fi- nite element method, however genetic approach requires performing Monte Carlo Simulation for each of the con- sidered different possible combinations within the search domain (α-cut) and running finite element for each of the Monte Carlo realizations. In the presented examples both load and material uncertainties are considered. Numeri- cal results show the computational efficiency of the In-

Posted Content
TL;DR: In this article, the authors used the underlying geometry of Hamiltonian Monte Carlo to construct a universal optimization criteria for tuning the step size of the symplectic integrator crucial to any implementation of the algorithm and diagnostics to monitor for any signs of invalidity.
Abstract: Hamiltonian Monte Carlo can provide powerful inference in complex statistical problems, but ultimately its performance is sensitive to various tuning parameters. In this paper we use the underlying geometry of Hamiltonian Monte Carlo to construct a universal optimization criteria for tuning the step size of the symplectic integrator crucial to any implementation of the algorithm as well as diagnostics to monitor for any signs of invalidity. An immediate outcome of this result is that the suggested target average acceptance probability of 0.651 can be relaxed to $0.6 \lesssim a \lesssim 0.9$ with larger values more robust in practice.

Journal ArticleDOI
TL;DR: In this paper, the Particle-In-Cell method is used to treat the collisionless Vlasov-Maxwell system, while neutral reactive flows are treated by the Direct Simulation Monte Carlo method.

Journal ArticleDOI
TL;DR: In this paper, two methods for computing two-time correlation functions or Green's functions from real-time bold-line continuous-time quantum Monte Carlo are presented, one is a formally exact generalized auxiliary lead formalism by which spectral properties may be obtained from single-time observables.
Abstract: We present two methods for computing two-time correlation functions or Green's functions from real-time bold-line continuous-time quantum Monte Carlo. One method is a formally exact generalized auxiliary lead formalism by which spectral properties may be obtained from single-time observables. The other involves the evaluation of diagrams contributing to two-time observables directly on the Keldysh contour. Additionally, we provide a detailed description of the bold-line Monte Carlo method. Our methods are general and numerically exact, and able to reliably resolve high-energy features such as band edges. We compare the spectral functions obtained from real-time methods to analytically continued spectral functions obtained from imaginary-time Monte Carlo, thus probing the limits of analytic continuation.

Book ChapterDOI
01 Jan 2014
TL;DR: The aim of this contribution is to provide a readable account of Markov Chain Monte Carlo methods, with particular emphasis on their relations with the numerical integration of deterministic and stochastic differential equations.
Abstract: The aim of this contribution is to provide a readable account of Markov Chain Monte Carlo methods, with particular emphasis on their relations with the numerical integration of deterministic and stochastic differential equations. The exposition is largely based on numerical experiments and avoids mathematical technicalities. The presentation is largely self-contained and includes tutorial sections on stochastic processes, Markov chains, stochastic differential equations and Hamiltonian dynamics. The Metropolis Random-Walk algorithm, Metropolis adjusted Langevin algorithm and Hybrid Monte Carlo are discussed in detail, including some recent results.

Journal ArticleDOI
TL;DR: This work presents a C++ code based on the application of the Monte Carlo method in combination with variance reduction techniques, with a description of sample geometry based on quadric surfaces that makes XRMC able to accurately simulate X-ray photon transport and interactions with matter up to any order of interaction.

Journal ArticleDOI
TL;DR: In this article, the authors explored the application of Monte Carlo transport methods to solving coupled radiation-hydrodynamics problems, using a timedependent, frequency-dependent, 3D radiation transport code, that is special relativistic and includes some detailed microphysical interactions such as resonant line scattering.
Abstract: We explore the application of Monte Carlo transport methods to solving coupled radiation-hydrodynamics problems. We use a time-dependent, frequency-dependent, 3-dimensional radiation transport code, that is special relativistic and includes some detailed microphysical interactions such as resonant line scattering. We couple the transport code to two different 1-dimensional (non-relativistic) hydrodynamics solvers: a spherical Lagrangian scheme and a Eulerian Godunov solver. The gas-radiation energy coupling is treated implicitly, allowing us to take hydrodyanimcal time-steps that are much longer than the radiative cooling time. We validate the code and assess its performance using a suite of radiation hydrodynamical test problems, including ones in the radiation energy dominated regime. We also develop techniques that reduce the noise of the Monte Carlo estimated radiation force by using the spatial divergence of the radiation pressure tensor. The results suggest that Monte Carlo techniques hold promise for simulating the multi-dimensional radiation hydrodynamics of astrophysical systems.

Journal ArticleDOI
TL;DR: In this article, an empirical space correlation function is proposed as a diagnostic tool for detecting clustering in criticality simulations, which is based on a simplified Brownian transport model coupled with a Galton-Watson birth and death process.

Journal ArticleDOI
TL;DR: The pitfalls of using the method as a replacement or complement of molecular dynamics simulations, its ability to explicitly describe correct dynamics and reaction mechanisms, and the association of timescales to MC simulations in general are addressed.
Abstract: Uniform-acceptance force-bias Monte Carlo (fbMC) methods have been shown to be a powerful technique to access longer timescales in atomistic simulations allowing, for example, phase transitions and growth Recently, a new fbMC method, the time-stamped force-bias Monte Carlo (tfMC) method, was derived with inclusion of an estimated effective timescale; this timescale, however, does not seem able to explain some of the successes the method In this contribution, we therefore explicitly quantify the effective timescale tfMC is able to access for a variety of systems, namely a simple single-particle, one-dimensional model system, the Lennard-Jones liquid, an adatom on the Cu(100) surface, a silicon crystal with point defects and a highly defected graphene sheet, in order to gain new insights into the mechanisms by which tfMC operates It is found that considerable boosts, up to three orders of magnitude compared to molecular dynamics, can be achieved for solid state systems by lowering of the apparent activation barrier of occurring processes, while not requiring any system-specific input or modifications of the method We furthermore address the pitfalls of using the method as a replacement or complement of molecular dynamics simulations, its ability to explicitly describe correct dynamics and reaction mechanisms, and the association of timescales to MC simulations in general


Journal ArticleDOI
TL;DR: In this article, a brief historical review on analytic, Monte Carlo and renormalization group (RG) approaches to some lattice critical systems in memory of late Professors Shang-keng Ma (1940-1983) and Yu-Ming Shih (1942-2005), who played some key roles in early developments of statistical physics of critical phenomena in Taiwan.

Journal Article
TL;DR: This work extends the regime where signful simulations are possible through a novel permutation sampling scheme and discusses a method to variationally improve the nodal surface by minimizing a free energy during simulation.
Abstract: In general, Quantum Monte Carlo methods suffer from a sign problem when simulating fermionic systems. This causes the efficiency of a simulation to decrease exponentially with the number of particles and inverse temperature. To circumvent this issue, a nodal constraint is often implemented, restricting the Monte Carlo procedure from sampling paths that cause the many-body density matrix to change sign. Unfortunately, this high-dimensional nodal surface is not a priori known unless the system is exactly solvable, resulting in uncontrolled errors. We will discuss two possible routes to extend the applicability of finite-temperatue path integral Monte Carlo. First we extend the regime where signful simulations are possible through a novel permutation sampling scheme. Afterwards, we discuss a method to variationally improve the nodal surface by minimizing a free energy during simulation. Applications of these methods will include both free and interacting electron gases, concluding with discussion concerning extension to inhomogeneous systems.

Journal ArticleDOI
TL;DR: The results confirm the necessity of a three-body force for correct reproduction of experimental binding energies and radii, and pave the way for studying few- and many-nucleon systems using quantum Monte Carlo methods with chiral interactions.
Abstract: We present the first Green's function Monte Carlo calculations of light nuclei with nuclear interactions derived from chiral effective field theory up to next-to-next-to-leading order. Up to this order, the interactions can be constructed in a local form and are therefore amenable to quantum Monte Carlo calculations. We demonstrate a systematic improvement with each order for the binding energies of $A=3$ and $A=4$ systems. We also carry out the first few-body tests to study perturbative expansions of chiral potentials at different orders, finding that higher-order corrections are more perturbative for softer interactions. Our results confirm the necessity of a three-body force for correct reproduction of experimental binding energies and radii, and pave the way for studying few- and many-nucleon systems using quantum Monte Carlo methods with chiral interactions.

Journal ArticleDOI
03 Jun 2014-Entropy
TL;DR: A full exposition of Markov chains and their use in Monte Carlo simulation for statistical inference and molecular dynamics is provided, with particular emphasis on methods based on Langevin diffusions.
Abstract: Recent work incorporating geometric ideas in Markov chain Monte Carlo is reviewed in order to highlight these advances and their possible application in a range of domains beyond statistics. A full exposition of Markov chains and their use in Monte Carlo simulation for statistical inference and molecular dynamics is provided, with particular emphasis on methods based on Langevin diffusions. After this, geometric concepts in Markov chain Monte Carlo are introduced. A full derivation of the Langevin diffusion on a Riemannian manifold is given, together with a discussion of the appropriate Riemannian metric choice for different problems. A survey of applications is provided, and some open questions are discussed.

Journal ArticleDOI
TL;DR: This work presents a general framework for constructing hybrid Monte Carlo methods under relaxed conditions: the only geometric property needed is (weakened) reversibility; volume preservation is not needed.
Abstract: One of the most demanding calculations is to generate random samples from a specified probability distribution (usually with an unknown normalizing prefactor) in a high-dimensional configuration space. One often has to resort to using a Markov chain Monte Carlo method, which converges only in the limit to the prescribed distribution. Such methods typically inch through configuration space step by step, with acceptance of a step based on a Metropolis(-Hastings) criterion. An acceptance rate of 100% is possible in principle by embedding configuration space in a higher-dimensional phase space and using ordinary differential equations. In practice, numerical integrators must be used, lowering the acceptance rate. This is the essence of hybrid Monte Carlo methods. Presented is a general framework for constructing such methods under relaxed conditions: the only geometric property needed is (weakened) reversibility; volume preservation is not needed. The possibilities are illustrated by deriving a couple of explicit hybrid Monte Carlo methods, one based on barrier-lowering variable-metric dynamics and another based on isokinetic dynamics.

Journal ArticleDOI
TL;DR: The capabilities of the Monte Carlo technique are demonstrated in obtaining absolute binding free energies for a series of benzamidine like inhibitors into trypsin in good agreement with experimental data and other molecular dynamics simulations, indicating that PELE can be a useful tool for quick estimates of binding free energy and mechanisms.
Abstract: Obtaining absolute binding free energies from unbiased ligand diffusion has attracted a significant amount of attention due to its implications in drug design. Several studies have used special purpose computers and software to achieve microsecond molecular dynamics which, combined with a Markov state model analysis, are capable of providing absolute binding free energies. We have recently developed a Monte Carlo based technique, PELE, capable of performing a dynamical exploration of the protein-ligand energy landscape including free ligand diffusion into the active site, at a fraction of the computational cost of molecular dynamics techniques. We demonstrate here the capabilities of our Monte Carlo technique in obtaining absolute binding free energies for a series of benzamidine like inhibitors into trypsin. Our results are in good agreement with experimental data and other molecular dynamics simulations, indicating that PELE can be a useful tool for quick estimates of binding free energies and mechanisms.

Journal ArticleDOI
TL;DR: The Monte Carlo implementation of this asymptotic-preserving Monte Carlo method for the Boltzmann equation is introduced, which, despite its lower order accuracy, is very efficient in higher dimensions or simulating some complicated chemical processes.

Journal ArticleDOI
TL;DR: A method for accelerating molecular dynamics simulations in rare event systems is described, and an estimator for the completeness of the calculated rate table in each state is derived.
Abstract: A method for accelerating molecular dynamics simulations in rare event systems is described. From each new state visited, high temperature molecular dynamics trajectories are used to discover the set of escape mechanisms and rates. This event table is provided to the adaptive kinetic Monte Carlo algorithm to model the evolution of the system from state to state. Importantly, an estimator for the completeness of the calculated rate table in each state is derived. The method is applied to three model systems: adatom diffusion on Al(100); island diffusion on Pt(111); and vacancy cluster ripening in bulk Fe. Connections to the closely related temperature accelerated dynamics method of Voter and co-workers is discussed.

Journal ArticleDOI
TL;DR: This work studies systematically the accuracy and reliability of a recently developed ab initio simulation scheme based on molecular dynamics and quantum Monte Carlo by targeting the vibrational frequencies of simple molecules, showing that all sources of systematic errors can be controlled and reliable frequencies can be obtained with a reasonable computational effort.
Abstract: We present a systematic study of a recently developed ab initio simulation scheme based on molecular dynamics and quantum Monte Carlo. In this approach, a damped Langevin molecular dynamics is employed by using a statistical evaluation of the forces acting on each atom by means of quantum Monte Carlo. This allows the use of an highly correlated wave function parametrized by several variational parameters and describing quite accurately the Born-Oppenheimer energy surface, as long as these parameters are determined at the minimum energy condition. However, in a statistical method both the minimization method and the evaluation of the atomic forces are affected by the statistical noise. In this work, we study systematically the accuracy and reliability of this scheme by targeting the vibrational frequencies of simple molecules such as the water monomer, hydrogen sulfide, sulfur dioxide, ammonia, and phosphine. We show that all sources of systematic errors can be controlled and reliable frequencies can be obtained with a reasonable computational effort. This work provides convincing evidence that this molecular dynamics scheme can be safely applied also to realistic systems containing several atoms.

Journal ArticleDOI
TL;DR: This paper extends the second approach to the Wigner equation for time-dependent simulations and presents a validation against a well-known benchmark model, the Schrödinger equation, demonstrating excellent quantitative agreement.
Abstract: The Wigner equation is a promising full quantum model for the simulation of nanodevices. It is also a challenging numerical problem. Two basic Monte Carlo approaches to this model exist exploiting, in the time-dependent case, the so-called particle affinity and, in the stationary case, integer particle signs. In this paper we extend the second approach for time-dependent simulations and present a validation against a well-known benchmark model, the Schrodinger equation. Excellent quantitative agreement is demonstrated by the compared results despite the very different numerical properties of the utilized stochastic and deterministic approaches.