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Ab initio quantum Monte Carlo (QMC) is a stochastic approach for solving the many-body Schr\"odinger equation without resorting to one-body approximations. QMC algorithms are readily parallelizable via ensembles of $N_w$ walkers, making…

Chemical Physics · Physics 2025-08-19 Kousuke Nakano , Sandro Sorella , Michele Casula

Simulating stochastic systems with feedback control is challenging due to the complex interplay between the system's dynamics and the feedback-dependent control protocols. We present a single-step-trajectory probability analysis to…

Statistical Mechanics · Physics 2024-12-19 Supraja S. Chittari , Zhiyue Lu

Markov Chain Monte Carlo (MCMC) algorithms are essential tools in computational statistics for sampling from unnormalised probability distributions, but can be fragile when targeting high-dimensional, multimodal, or complex target…

We propose a hierarchy of multi-level kinetic Monte Carlo methods for sampling high-dimensional, stochastic lattice particle dynamics with complex interactions. The method is based on the efficient coupling of different spatial resolution…

Numerical Analysis · Mathematics 2012-08-06 Evangelia Kalligiannaki , Markos A. Katsoulakis , Petr Plechac

The Direct Simulation Monte Carlo (DSMC) method is widely employed for simulating rarefied nonequilibrium gas flows. With advances in aerospace engineering and micro/nano-scale technologies, gas flows exhibit the coexistence of rarefied and…

Computational Physics · Physics 2025-07-01 Hao Jin , Sha Liu , Sirui Yang , Junzhe Cao , Congshan Zhuo , Chengwen Zhong

Traditionally, the field of computational Bayesian statistics has been divided into two main subfields: variational methods and Markov chain Monte Carlo (MCMC). In recent years, however, several methods have been proposed based on combining…

Computation · Statistics 2017-04-19 Cheng Zhang , Babak Shahbaba , Hongkai Zhao

In this paper, we design a novel algorithm based on Least-Squares Monte Carlo (LSMC) in order to approximate the solution of discrete time Backward Stochastic Differential Equations (BSDEs). Our algorithm allows massive parallelization of…

Numerical Analysis · Mathematics 2024-08-01 E. Gobet , J. G. López-Salas , P. Turkedjiev , C. Vázquez

We present Generative Monte Carlo (GMC), a novel paradigm for particle transport simulation that integrates generative artificial intelligence directly into the stochastic solution of the linear Boltzmann equation. By reformulating the…

Computational Physics · Physics 2025-12-17 Joseph A. Farmer , Aidan Murray , Johannes Krotz , Ryan G. McClarren

We present a highly scalable Monte Carlo (MC) three-dimensional photon transport simulation platform designed for heterogeneous computing systems. Through the development of a massively parallel MC algorithm using the Open Computing…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-02-06 Leiming Yu , Fanny Nina-Paravecino , David Kaeli , Qianqian Fang

In this paper we propose a new class of coupling methods for the sensitivity analysis of high dimensional stochastic systems and in particular for lattice Kinetic Monte Carlo. Sensitivity analysis for stochastic systems is typically based…

Numerical Analysis · Mathematics 2015-06-18 Georgios Arampatzis , Markos Katsoulakis

In dynamic Monte Carlo simulations, using for example the Metropolis dynamic, it is often required to simulate for long times and to simulate large systems. We present an overview of advanced algorithms to simulate for larger times and to…

Statistical Mechanics · Physics 2007-05-23 M. A. Novotny , Alice K. Kolakowska , G. Korniss

Markov chain Monte Carlo (MCMC) algorithms are based on the construction of a Markov chain with transition probabilities leaving invariant a probability distribution of interest. In this work, we look at these transition probabilities as…

Probability · Mathematics 2024-10-01 Rocco Caprio , Adam M. Johansen

Markov Chain Monte Carlo (MCMC) algorithms play an important role in statistical inference problems dealing with intractable probability distributions. Recently, many MCMC algorithms such as Hamiltonian Monte Carlo (HMC) and Riemannian…

Computation · Statistics 2017-04-19 Cheng Zhang , Babak Shahbaba , Hongkai Zhao

We introduce and analyze a parallel sequential Monte Carlo methodology for the numerical solution of optimization problems that involve the minimization of a cost function that consists of the sum of many individual components. The proposed…

Computation · Statistics 2022-01-04 Ömer Deniz Akyildiz , Dan Crisan , Joaquín Míguez

Quasi-Monte Carlo (QMC) methods for estimating integrals are attractive since the resulting estimators typically converge at a faster rate than pseudo-random Monte Carlo. However, they can be difficult to set up on arbitrary posterior…

Statistics Theory · Mathematics 2018-10-03 Tobias Schwedes , Ben Calderhead

In plasma edge simulations, the behavior of neutral particles is often described by a Boltzmann--BGK equation. Solving this kinetic equation and estimating the moments of its solution are essential tasks, typically carried out using Monte…

Numerical Analysis · Mathematics 2025-12-30 Zhirui Tang , Julian Koellermeier , Emil Løvbak , Giovanni Samaey

Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In order to foster…

Computation · Statistics 2016-09-27 L. Martino , V. Elvira , D. Luengo , J. Corander , F. Louzada

Markov chain Monte Carlo (MCMC) methods are foundational algorithms for Bayesian inference and probabilistic modeling. However, most MCMC algorithms are inherently sequential and their time complexity scales linearly with the sequence…

Computation · Statistics 2025-12-03 David M. Zoltowski , Skyler Wu , Xavier Gonzalez , Leo Kozachkov , Scott W. Linderman

Hamiltonian Monte Carlo (HMC) is a popular Markov chain Monte Carlo (MCMC) algorithm that generates proposals for a Metropolis-Hastings algorithm by simulating the dynamics of a Hamiltonian system. However, HMC is sensitive to large time…

Machine Learning · Statistics 2016-09-15 Xiaoyu Lu , Valerio Perrone , Leonard Hasenclever , Yee Whye Teh , Sebastian J. Vollmer

The variational quantum Monte Carlo (VQMC) method received significant attention in the recent past because of its ability to overcome the curse of dimensionality inherent in many-body quantum systems. Close parallels exist between VQMC and…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-07-01 Tianchen Zhao , Saibal De , Brian Chen , James Stokes , Shravan Veerapaneni