Showing papers on "Monte Carlo molecular modeling published in 2013"

Monte Carlo methods

Abstract: Bayesian inference often requires integrating some function with respect to a posterior distribution. Monte Carlo methods are sampling algorithms that allow to compute these integrals numerically when they are not analytically tractable. We review here the basic principles and the most common Monte Carlo algorithms, among which rejection sampling, importance sampling and Monte Carlo Markov chain (MCMC) methods. We give intuition on the theoretical justification of the algorithms as well as practical advice, trying to relate both. We discuss the application of Monte Carlo in experimental physics, and point to landmarks in the literature for the curious reader.

On the inner workings of Monte Carlo codes

Abstract: We review state-of-the-art Monte Carlo (MC) techniques for computing fluid coexistence properties (Gibbs simulations) and adsorption simulations in nanoporous materials such as zeolites and metal–o...

MCCCS Towhee: a tool for Monte Carlo molecular simulation

Abstract: The history of the Monte Carlo for complex chemical systems Towhee open source Monte Carlo molecular simulation tool is discussed. A proof is given that the Widom insertion method for computing the...

Mean Field Simulation for Monte Carlo Integration

Abstract: In the last three decades, there has been a dramatic increase in the use of interacting particle methods as a powerful tool in real-world applications of Monte Carlo simulation in computational physics, population biology, computer sciences, and statistical machine learning. Ideally suited to parallel and distributed computation, these advanced particle algorithms include nonlinear interacting jump diffusions; quantum, diffusion, and resampled Monte Carlo methods; Feynman-Kac particle models; genetic and evolutionary algorithms; sequential Monte Carlo methods; adaptive and interacting Markov chain Monte Carlo models; bootstrapping methods; ensemble Kalman filters; and interacting particle filters.

Monte Carlo methods in Materials Studio

Abstract: We survey the use of the Monte Carlo method within the Materials Studio application, which integrates a large number of modules for molecular simulation. Several of these modules work by generating...

Hard-disk equation of state: first-order liquid-hexatic transition in two dimensions with three simulation methods.

Abstract: We report large-scale computer simulations of the hard-disk system at high densities in the region of the melting transition. Our simulations reproduce the equation of state, previously obtained using the event-chain Monte Carlo algorithm, with a massively parallel implementation of the local Monte Carlo method and with event-driven molecular dynamics. We analyze the relative performance of these simulation methods to sample configuration space and approach equilibrium. Our results confirm the first-order nature of the melting phase transition in hard disks. Phase coexistence is visualized for individual configurations via the orientational order parameter field. The analysis of positional order confirms the existence of the hexatic phase.

A warp-speed method for conducting monte carlo experiments involving bootstrap estimators

Abstract: We analyze fast procedures for conducting Monte Carlo experiments involving bootstrap estimators, providing formal results establishing the properties of these methods under general conditions.

Backward Simulation Methods for Monte Carlo Statistical Inference

Abstract: Monte Carlo methods, in particular those based on Markov chains and on interacting particle systems, are by now tools that are routinely used in machine learning. These methods have had a profound impact on statistical inference in a wide range of application areas where probabilistic models are used. Moreover, there are many algorithms in machine learning which are based on the idea of processing the data sequentially, first in the forward direction and then in the backward direction. In this tutorial, we will review a branch of Monte Carlo methods based on the forward–backward idea, referred to as backward simulators. These methods are useful for learning and inference in probabilistic models containing latent stochastic processes. The theory and practice of backward simulation algorithms have undergone a significant development in recent years and the algorithms keep finding new applications. The foundation for these methods is sequential Monte Carlo (SMC). SMC-based backward simulators are capable of addressing smoothing problems in sequential latent variable models, such as general, nonlinear/non-Gaussian state-space models (SSMs). However, we will also clearly show that the underlying backward simulation idea is by no means restricted to SSMs. Furthermore, backward simulation plays an important role in recent developments of Markov chain Monte Carlo (MCMC) methods. Particle MCMC is a systematic way of using SMC within MCMC. In this framework, backward simulation gives us a way to significantly improve the performance of the samplers. We review and discuss several related backward-simulation-based methods for state inference as well as learning of static parameters, both using a frequentistic and a Bayesian approach.

Using perturbatively selected configuration interaction in quantum Monte Carlo calculations

Abstract: Defining accurate and compact trial wavefunctions leading to small statistical and fixed-node errors in quantum Monte Carlo (QMC) calculations is still a challenging problem. Here we propose to mak...

Multi-Determinant Wave-functions in Quantum Monte Carlo

Abstract: Quantum Monte Carlo (QMC) methods have received considerable attention over the last decades due to their great promise for providing a direct solution to the many-body Schrodinger equation in electronic systems. Thanks to their low scaling with number of particles, QMC methods present a compelling competitive alternative for the accurate study of large molecular systems and solid state calculations. In spite of such promise, the method has not permeated the quantum chemistry community broadly, mainly because of the fixed-node error, which can be large and whose control is difficult. In this Perspective, we present a systematic application of large scale multi-determinant expansions in QMC, and report on its impressive performance with first row dimers and the 55 molecules of the G1 test set. We demonstrate the potential of this strategy for systematically reducing the fixed-node error in the wave function and for achieving chemical accuracy in energy predictions. When compared to traditional quantum chemistry methods like MP2, CCSD(T), and various DFT approximations, the QMC results show a marked improvement over all of them. In fact, only the explicitly-correlated CCSD(T) method with a large basis set produces more accurate results. Further developments in trial wave functions and algorithmic improvements appear promising for rendering QMC as the benchmark standard in large electronic systems.

Quantum Monte Carlo applied to solids

Abstract: We apply diffusion quantum Monte Carlo to a broad set of solids, benchmarking the method by comparing bulk structural properties (equilibrium volume and bulk modulus) to experiment and density functional theory (DFT) based theories. The test set includes materials with many different types of binding including ionic, metallic, covalent, and van der Waals. We show that, on average, the accuracy is comparable to or better than that of DFT when using the new generation of functionals, including one hybrid functional and two dispersion corrected functionals. The excellent performance of quantum Monte Carlo on solids is promising for its application to heterogeneous systems and high-pressure/high-density conditions. Important to the results here is the application of a consistent procedure with regards to the several approximations that are made, such as finite-size corrections and pseudopotential approximations. This test set allows for any improvements in these methods to be judged in a systematic way.

Integral formulation of null-collision Monte Carlo algorithms

Abstract: At the kinetic level, the meaning of null-collisions is straightforward: they correspond to pure-forward scattering events. We here discuss their technical significance in integral terms. We first consider a most standard null-collision Monte Carlo algorithm and show how it can be rigorously justified starting from a Fredholm equivalent to the radiative transfer equation. Doing so, we also prove that null-collision algorithms can be slightly modified so that they deal with unexpected occurrences of negative values of the null-collision coefficient (when the upper bound of the heterogeneous extinction coefficient is nonstrict). We then describe technically, in full details, the resulting algorithm, when applied to the evaluation of the local net-power density within a bounded, heterogeneous, multiple scattering and emitting/absorbing medium. The corresponding integral formulation is then explored theoretically in order to distinguish the statistical significance of introducing null-collisions from that of the integral-structure underlying modification.

Photon beam diffusion: a hybrid Monte Carlo method for subsurface scattering

Abstract: We present photon beam diffusion, an efficient numerical method for accurately rendering translucent materials. Our approach interprets incident light as a continuous beam of photons inside the material. Numerically integrating diffusion from such extended sources has long been assumed computationally prohibitive, leading to the ubiquitous single-depth dipole approximation and the recent analytic sum-of-Gaussians approach employed by Quantized Diffusion. In this paper, we show that numerical integration of the extended beam is not only feasible, but provides increased speed, flexibility, numerical stability, and ease of implementation, while retaining the benefits of previous approaches. We leverage the improved diffusion model, but propose an efficient and numerically stable Monte Carlo integration scheme that gives equivalent results using only 3--5 samples instead of 20--60 Gaussians as in previous work. Our method can account for finite and multi-layer materials, and additionally supports directional incident effects at surfaces. We also propose a novel diffuse exact single-scattering term which can be integrated in tandem with the multi-scattering approximation. Our numerical approach furthermore allows us to easily correct inaccuracies of the diffusion model and even combine it with more general Monte Carlo rendering algorithms. We provide practical details necessary for efficient implementation, and demonstrate the versatility of our technique by incorporating it on top of several rendering algorithms in both research and production rendering systems.

Parameter estimation in stochastic differential equations with Markov chain Monte Carlo and non-linear Kalman filtering

Abstract: This paper is concerned with parameter estimation in linear and non-linear Ito type stochastic differential equations using Markov chain Monte Carlo (MCMC) methods. The MCMC methods studied in this paper are the Metropolis–Hastings and Hamiltonian Monte Carlo (HMC) algorithms. In these kind of models, the computation of the energy function gradient needed by HMC and gradient based optimization methods is non-trivial, and here we show how the gradient can be computed with a linear or non-linear Kalman filter-like recursion. We shall also show how in the linear case the differential equations in the gradient recursion equations can be solved using the matrix fraction decomposition. Numerical results for simulated examples are presented and discussed in detail.

Adjoint-Based k-Eigenvalue Sensitivity Coefficients to Nuclear Data Using Continuous-Energy Monte Carlo

Abstract: A continuous-energy Monte Carlo method is developed to compute adjoint-based k-eigenvalue sensitivity coefficients with respect to nuclear data. The method is implemented into MCNP6 and is based upon similar methodologies used to compute other adjoint-weighted quantities. The Monte Carlo tallies employed are explained. Verification of the method is performed by comparing results to analytic solutions, direct density perturbations, and those from other software packages such as TSUNAMI-3D and MONK. Results of analytic solutions agree within a few tenths of a percent. Direct density perturbations and comparisons with other software generally agree within a few percent.

An Adaptive Sequential Monte Carlo Sampler

Abstract: Sequential Monte Carlo (SMC) methods are not only a popular tool in the analysis of state–space models, but offer an alternative to Markov chain Monte Carlo (MCMC) in situations where Bayesian inference must proceed via simulation. This paper introduces a new SMC method that uses adaptive MCMC kernels for particle dynamics. The proposed algorithm features an online stochastic optimization procedure to select the best MCMC kernel and simultaneously learn optimal tuning parameters. Theoretical results are presented that justify the approach and give guidance on how it should be implemented. Empirical results, based on analysing data from mixture models, show that the new adaptive SMC algorithm (ASMC) can both choose the best MCMC kernel, and learn an appropriate scaling for it. ASMC with a choice between kernels outperformed the adaptive MCMC algorithm of Haario et al. (1998) in 5 out of the 6 cases considered.

Combining molecular dynamics with Monte Carlo simulations: implementations and applications

Abstract: In this contribution, we present an overview of the various techniques for combining atomistic molecular dynamics with Monte Carlo simulations, mainly in the context of condensed matter systems, as well as a brief summary of the main accelerated dynamics techniques. Special attention is given to the force bias Monte Carlo technique and its combination with molecular dynamics, in view of promising recent developments, including a definable timescale. Various examples of the application of combined molecular dynamics / Monte Carlo simulations are given, in order to demonstrate the enhanced simulation efficiency with respect to either pure molecular dynamics or Monte Carlo.

Dynamic Monte Carlo Method for Nuclear Reactor Kinetics Calculations

Abstract: In nuclear reactor physics, deterministic and hybrid calculation methods dominate the field of transient analysis. This implies that important safety assessments are subject to many approximations, which are needed by these methods. This paper proposes the Dynamic Monte Carlo method (Dynamic MC), which solves the coupled Boltzmann and kinetic equations with exact geometry and continuous energy, using only Monte Carlo techniques.For Dynamic MC a number of new techniques are developed, e.g., precursor tracking, forced decay for precursors, and the branchless method. Also, the particle source of the simulation has to be determined differently from what is current standard Monte Carlo practice, and the simulation scheme is adapted.A few example cases are simulated, demonstrating the effectiveness of Dynamic MC. The sample cases vary from simple homogeneous systems to full fuel assemblies with an asymmetric flux profile during the transient. Since Dynamic MC is implemented in the general-purpose Monte ...

Monte Carlo Simulations Applied to Uncertainty in Measurement

Abstract: Metrology is the science that covers all theoretical and practical concepts involved in a measurement, which when applied are able to provide results with appropriate accuracy and metrological reliability to a given measurement process. In any area in which a decision is made from a measurement result, all attention is critical to the metrological concepts in‐ volved. For example, the control panels of an aircraft are composed by several instruments that must be calibrated to perform measurements with metrological traceability and reliabil‐ ity, influencing the decisions that the pilot will make during the flight. In this way, it is clear that concepts involving metrology and reliability of measurements must be well established and harmonized to provide reliability and quality for products and services.

Nonlinear intrinsic variables and state reconstruction in multiscale simulations

Abstract: Finding informative low-dimensional descriptions of high-dimensional simulation data (like the ones arising in molecular dynamics or kinetic Monte Carlo simulations of physical and chemical processes) is crucial to understanding physical phenomena, and can also dramatically assist in accelerating the simulations themselves. In this paper, we discuss and illustrate the use of nonlinear intrinsic variables (NIV) in the mining of high-dimensional multiscale simulation data. In particular, we focus on the way NIV allows us to functionally merge different simulation ensembles, and different partial observations of these ensembles, as well as to infer variables not explicitly measured. The approach relies on certain simple features of the underlying process variability to filter out measurement noise and systematically recover a unique reference coordinate frame. We illustrate the approach through two distinct sets of atomistic simulations: a stochastic simulation of an enzyme reaction network exhibiting both fast and slow time scales, and a molecular dynamics simulation of alanine dipeptide in explicit water.

A local superbasin kinetic Monte Carlo method

Abstract: We present a local superbasin kinetic Monte Carlo (LSKMC) method that efficiently treats multiple-time-scale problems in kinetic Monte Carlo (KMC). The method is designed to solve the small-barrier problem created by groups of recurrent free-energy minima connected by low free-energy barriers and separated from the full phase space of the system by high barriers. We propose an algorithm to detect, on the fly, groups of recurrent free-energy minima connected by low free-energy barriers and to consolidate them into “superbasins,” which we treat with rate equations and/or absorbing Markov chains. We discuss various issues involved with implementing LSKMC simulations that contain local superbasins and non-superbasin events concurrently. These issues include the time distribution of superbasin escapes and interactions between superbasin and non-superbasin states. The LSKMC method is exact, as it introduces no new approximations into conventional KMC simulations. We demonstrate various aspects of LSKMC in several examples, which indicate that significant increases in computational efficiency can be achieved using this method.

The practice of recent radiative transfer Monte Carlo advances and its contribution to the field of microorganisms cultivation in photobioreactors

Abstract: The present text illustrates the practice of integral formulation, zero-variance approaches and sensitivity evaluations in the field of radiative transfer Monte Carlo simulation, as well as the practical implementation of the corresponding algorithms, for such realistic systems as photobioreactors involving spectral integration, multiple scattering and complex geometries. We try to argue that even in such non-academic contexts, strong benefits can be expected from the effort of translating the considered Monte Carlo algorithm into a rigorously equivalent integral formulation. Modifying the initial algorithm to simultaneously compute sensitivities is then straightforward (except for domain deformation sensitivities) and the question of enhancing convergence is turned into that of modeling a set of well identified physical quantities.

Strongly correlated systems : numerical methods

Abstract: 1. Ground State and Finite Temperature Lanczos Method.- 2. The Density Matrix Renormalization Group.- 3. Matrix Product State Algorithms: DMRG, TEBD and Relatives.- 4. Quantum Criticality with the Multi-scale Entanglement Renormalization Ansatz.- 5. The Time-Dependent Density Matrix Renormalization Groupd.- 6. Loop Algorithm.- 7. Stochastic Series Expansion Quantum Monte Carlo.- 8. Variatonal Monte Carlo and Markov Chanis for Computational Physics.- 9. Coupled Cluster Theories for Strongly Correlated Molecular Systems.- 10. Diagrammatic Monte Carlo and Worm Algorithm Techniques.- 11. Fermionic and Continuous Time Quantum Monte Carlo.