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Quantum mechanics for many-body systems may be reduced to the evaluation of integrals in 3N dimensions using Monte-Carlo, providing the Quantum Monte Carlo ab initio methods. Here we limit ourselves to expectation values for trial…

Computational Physics · Physics 2010-11-22 John Robert Trail , Ryo Maezono

Diffusion Monte Carlo (DMC) is one of the most accurate techniques available for calculating the electronic properties of molecules and materials, yet it often remains a challenge to economically compute forces using this technique. As a…

Chemical Physics · Physics 2022-11-15 Cancan Huang , Brenda M. Rubenstein

Diffusion Monte Carlo (DMC) calculations typically yield highly accurate results in solid-state and quantum-chemical calculations. However, operators that do not commute with the Hamiltonian are at best sampled correctly up to second order…

Other Condensed Matter · Physics 2009-11-13 R. Gaudoin , J. M. Pitarke

For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties, without the sign problem. The list spans condensed matter, nuclear physics, and…

Computational Physics · Physics 2016-03-23 Hao Shi , Shiwei Zhang

We introduce a new class of Monte Carlo based approximations of expectations of random variables such that their laws are only available via certain discretizations. Sampling from the discretized versions of these laws can typically…

Computation · Statistics 2017-10-17 Dan Crisan , Pierre Del Moral , Jeremie Houssineau , Ajay Jasra

For many complex simulation tasks spanning areas such as healthcare, engineering, and finance, Monte Carlo (MC) methods are invaluable due to their unbiased estimates and precise error quantification. Nevertheless, Monte Carlo simulations…

We present high-accuracy correlated calculations of small Si$_x$H$_y$ molecular systems both in the ground and excited states. We employ quantum Monte Carlo (QMC) together with a variety of many-body wave function approaches based on basis…

Chemical Physics · Physics 2020-10-21 Guangming Wang , Abdulgani Annaberdiyev , Lubos Mitas

Many machine learning problems involve Monte Carlo gradient estimators. As a prominent example, we focus on Monte Carlo variational inference (MCVI) in this paper. The performance of MCVI crucially depends on the variance of its stochastic…

Machine Learning · Statistics 2018-07-05 Alexander Buchholz , Florian Wenzel , Stephan Mandt

We develop a formalism and present an algorithm for optimization of the trial wave-function used in fixed-node diffusion quantum Monte Carlo (DMC) methods. We take advantage of a basic property of the walker configuration distribution…

Strongly Correlated Electrons · Physics 2015-05-13 Fernando A. Reboredo , Randolph Q. Hood , Paul R. C. Kent

Diffusion Monte Carlo (DMC) based on fixed-node approximation has enjoyed significant developments in the past decades and become one of the go-to methods when accurate ground state energy of molecules and materials is needed. The remaining…

Chemical Physics · Physics 2023-08-07 Weiluo Ren , Weizhong Fu , Xiaojie Wu , Ji Chen

In statistical analysis, Monte Carlo (MC) stands as a classical numerical integration method. When encountering challenging sample problem, Markov chain Monte Carlo (MCMC) is a commonly employed method. However, the MCMC estimator is biased…

Numerical Analysis · Mathematics 2024-11-05 Jiarui Du , Zhijian He

Most applications of Bayesian Inference for parameter estimation and model selection in astrophysics involve the use of Monte Carlo techniques such as Markov Chain Monte Carlo (MCMC) and nested sampling. However, these techniques are time…

Instrumentation and Methods for Astrophysics · Physics 2022-01-26 Geetakrishnasai Gunapati , Anirudh Jain , P. K. Srijith , Shantanu Desai

Monte Carlo (MC) sampling algorithms are an extremely widely-used technique to estimate expectations of functions f(x), especially in high dimensions. Control variates are a very powerful technique to reduce the error of such estimates, but…

Machine Learning · Statistics 2016-06-08 Brendan D. Tracey , David H. Wolpert

Diffusion Monte Carlo (DMC) simulations for fermions are becoming the standard to provide high quality reference data in systems that are too large to be investigated via quantum chemical approaches. DMC with the fixed-node approximation…

Chemical Physics · Physics 2016-07-06 Andrea Zen , Sandro Sorella , Michael J. Gillan , Angelos Michaelides , Dario Alfè

Based on the central limit theorem, we discuss the problem of evaluation of the statistical error of Monte Carlo calculations using a time discretized diffusion process. We present a robust and practical method to determine the effective…

Computational Physics · Physics 2017-02-22 François Delyon , Bernard Bernu , Markus Holzmann

Properties that are necessarily formulated within pure (symmetric) expectation values are difficult to calculate for projector quantum Monte Carlo approaches, but are critical in order to compute many of the important observable properties…

Computational Physics · Physics 2015-06-23 Catherine Overy , George H. Booth , N. S. Blunt , James Shepherd , Deidre Cleland , Ali Alavi

Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo method that allows to sample high dimensional probability measures. It relies on the integration of the Hamiltonian dynamics to propose a move which is then accepted or rejected…

Numerical Analysis · Mathematics 2023-08-08 Tony Lelièvre , Régis Santet , Gabriel Stoltz

We introduce a variational algorithm to estimate the likelihood of a rare event within a nonequilibrium molecular dynamics simulation through the evaluation of an optimal control force. Optimization of a control force within a chosen basis…

Statistical Mechanics · Physics 2021-01-14 Avishek Das , David T. Limmer

Quantum Monte Carlo (QMC) methods can very accurately compute ground state properties of quantum systems. We applied these methods to a system of boson hard spheres to get exact, infinite system size results for the ground state at several…

Computational Physics · Physics 2016-09-08 Mark Dewing

Contemporary scientific studies often rely on the understanding of complex quantum systems via computer simulation. This paper initiates the statistical study of quantum simulation and proposes a Monte Carlo method for estimating…

Applications · Statistics 2011-08-04 Yazhen Wang