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The Multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty Quantification (UQ) in Partial Differential Equation (PDE) models, combining model computations at different levels…

Mathematical Software · Computer Science 2023-05-24 Santiago Badia , Jerrad Hampton , Javier Principe

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

In this work we present an efficient implementation of Canonical Monte Carlo simulation for Coulomb many body systems on graphics processing units (GPU). Our method takes advantage of the GPU Single Instruction, Multiple Data (SIMD)…

Computational Physics · Physics 2017-03-13 Yihao Liang , Xiangjun Xing , Yaohang Li

Today, cheap numerical hardware offers huge amounts of parallel computing power, much of which is used for the task of fitting neural networks to data. Adoption of this hardware to accelerate statistical Markov chain Monte Carlo (MCMC)…

Computation · Statistics 2024-11-08 Pavel Sountsov , Colin Carroll , Matthew D. Hoffman

Processor design and verification require a synergistic approach that combines instruction-level functional simulations with precise hardware emulations. The trade-off between speed and accuracy in the instruction set simulation poses a…

Hardware Architecture · Computer Science 2025-04-08 Kun Qin , Xiaorang Guo , Martin Schulz , Carsten Trinitis

In view of the tremendous computing power jump of modern RISC processors the interest in parallel computing seems to be thinning out. Why use a complicated system of parallel processors, if the problem can be solved by a single powerful…

comp-gas · Physics 2008-02-03 G. Odor , F. Rohrbach , G. Vesztergombi , G. Varga , F. Tatrai

Standard MCMC methods can scale poorly to big data settings due to the need to evaluate the likelihood at each iteration. There have been a number of approximate MCMC algorithms that use sub-sampling ideas to reduce this computational…

Computation · Statistics 2020-09-29 Joris Bierkens , Paul Fearnhead , Gareth Roberts

While recent work towards the development of tight-binding and ab-initio algorithms has focused on molecular dynamics, Monte Carlo methods can often lead to better results with relatively little effort. We present here a multi-step Monte…

Statistical Mechanics · Physics 2009-10-31 Parthapratim Biswas , G. T. Barkema , Normand Mousseau , W. F. van der Weg

In the quantum Monte Carlo (QMC) method, the Pseudo-Random Number Generator (PRNG) plays a crucial role in determining the computation time. However, the hidden structure of the PRNG may lead to serious issues such as the breakdown of the…

Strongly Correlated Electrons · Physics 2024-03-12 Dong-Xu Liu , Wei Xu , Xue-Feng Zhang

We propose a new framework for how to use sequential Monte Carlo (SMC) algorithms for inference in probabilistic graphical models (PGM). Via a sequential decomposition of the PGM we find a sequence of auxiliary distributions defined on a…

Methodology · Statistics 2014-10-07 Christian A. Naesseth , Fredrik Lindsten , Thomas B. Schön

It has always been difficult to balance the accuracy and performance of ISSs. RTL simulators or systems such as gem5 are used to execute programs in a cycle-accurate manner but are often prohibitively slow. In contrast, functional…

Hardware Architecture · Computer Science 2020-05-26 Xuan Guo , Robert Mullins

We propose a parallel version of the cross interpolation algorithm and apply it to calculate high-dimensional integrals motivated by Ising model in quantum physics. In contrast to mainstream approaches, such as Monte Carlo and quasi Monte…

Numerical Analysis · Mathematics 2019-08-27 Sergey Dolgov , Dmitry Savostyanov

High-performance streams of (pseudo) random numbers are crucial for the efficient implementation for countless stochastic algorithms, most importantly, Monte Carlo simulations and molecular dynamics simulations with stochastic thermostats.…

Computational Physics · Physics 2012-08-30 Markus Manssen , Martin Weigel , Alexander K. Hartmann

Being the most classical generative model for serial data, state-space models (SSM) are fundamental in AI and statistical machine learning. In SSM, any form of parameter learning or latent state inference typically involves the computation…

Machine Learning · Statistics 2024-07-04 Alessandro Mastrototaro , Jimmy Olsson

This paper presents a parallel Monte Carlo simulation based performance quantification method for nonlinear model predictive control (NMPC) in closed-loop. The method provides distributions for the controller performance in stochastic…

Systems and Control · Electrical Eng. & Systems 2023-06-22 Morten Wahlgreen Kaysfeld , Mario Zanon , John Bagterp Jørgensen

We present a cross-language C++/Python program for simulations of quantum mechanical systems with the use of Quantum Monte Carlo (QMC) methods. We describe a system for which to apply QMC, the algorithms of variational Monte Carlo and…

Computational Physics · Physics 2009-11-13 J. K. Nilsen

Possibilities for performing stochastic simulations on the analog and fully parallelized Cellular Neural Network Universal Machine (CNN-UM) are investigated. By using a chaotic cellular automaton perturbed with the natural noise of the…

Computational Physics · Physics 2009-11-11 M. Ercsey-Ravasz , T. Roska , Z. Neda

The generation of pseudo-random numbers is one of the interesting problems in Monte Carlo simulations, mostly because the common computer generators produce periodic numbers. We used simple pseudo-random numbers generated with the simplest…

Other Condensed Matter · Physics 2009-11-13 Gaston E. Barberis

We introduce an algorithm to systematically improve the efficiency of parallel tempering Monte Carlo simulations by optimizing the simulated temperature set. Our approach is closely related to a recently introduced adaptive algorithm that…

Other Condensed Matter · Physics 2007-05-23 Helmut G. Katzgraber , Simon Trebst , David A. Huse , Matthias Troyer

We introduce a GPU-accelerated Monte Carlo framework for nonconvex, free-final-time trajectory optimization problems. This framework makes use of the prox-linear method, which belongs to the larger family of sequential convex programming…

Optimization and Control · Mathematics 2024-04-30 Govind M. Chari , Abhinav G. Kamath , Purnanand Elango , Behçet Açıkmeşe