A Random-Batch Monte Carlo Method for Many-Body Systems with Singular Kernels

DOI10.1137/19M1302077zbMath1439.82066arXiv2003.06554MaRDI QIDQ5112563

Zhenli Xu, Yue Zhao, Lei Li

Publication date: 29 May 2020

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.06554

zbMATH Keywords

Monte Carlostochastic differential equationsMarkov chainLangevin dynamicsrandom-batch method

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Monte Carlo methods applied to problems in statistical mechanics (82M31)

Related Items (11)

Asymptotic-preserving schemes for multiscale physical problems ⋮ Random Batch Methods for Classical and Quantum Interacting Particle Systems and Statistical Samplings ⋮ Random Batch Particle Methods for the Homogeneous Landau Equation ⋮ Some Random Batch Particle Methods for the Poisson-Nernst-Planck and Poisson-Boltzmann Equations ⋮ A framework for randomized time-splitting in linear-quadratic optimal control ⋮ On the Random Batch Method for Second Order Interacting Particle Systems ⋮ Ergodicity and long-time behavior of the Random Batch Method for interacting particle systems ⋮ Hybrid random batch idea and nonlinear conjugate gradient method for accelerating charged polymer dynamics simulation ⋮ Random Batch Algorithms for Quantum Monte Carlo Simulations ⋮ A Random Batch Ewald Method for Particle Systems with Coulomb Interactions ⋮ Numerical analysis for inchworm Monte Carlo method: Sign problem and error growth

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A stochastic version of Stein variational gradient descent for efficient sampling
• Mean field games
• Exponential convergence of Langevin distributions and their discrete approximations
• On the diffusion approximation of nonconvex stochastic gradient descent
• The Fokker-Planck equation. Methods of solutions and applications.
• Random batch methods (RBM) for interacting particle systems
• Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
• A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion
• On the mean field limit for Brownian particles with Coulomb interaction in 3D
• Equation of State Calculations by Fast Computing Machines
• A Dynamical Approach to Random Matrix Theory
• Monte Carlo sampling methods using Markov chains and their applications
• Theoretical Guarantees for Approximate Sampling from Smooth and Log-Concave Densities
• A Stochastic Approximation Method
• Stochastic differential equations. An introduction with applications.

This page was built for publication: A Random-Batch Monte Carlo Method for Many-Body Systems with Singular Kernels