Convergence of the Random Batch Method for Interacting Particles with Disparate Species and Weights

DOI10.1137/20M1327641zbMath1466.65011arXiv2003.11257OpenAlexW3136945732MaRDI QIDQ5855640

Jian-Guo Liu, Lei Li, Shih Jin

Publication date: 19 March 2021

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.11257

zbMATH Keywords

interacting particle systemsempirical measure\(N\)-body Liouville equationrandom batchmultispecies problem

Mathematics Subject Classification ID

Probabilistic models, generic numerical methods in probability and statistics (65C20) Simulation of dynamical systems (37M05)

Related Items (13)

Random Batch Methods for Classical and Quantum Interacting Particle Systems and Statistical Samplings ⋮ 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 ⋮ Random-batch method for multi-species stochastic interacting particle systems ⋮ On the Random Batch Method for Second Order Interacting Particle Systems ⋮ Random Batch Sum-of-Gaussians Method for Molecular Dynamics Simulations of 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 ⋮ Convergence toward equilibrium of the first-order consensus model with random batch interactions ⋮ Random Batch Algorithms for Quantum Monte Carlo Simulations ⋮ Uniform-in-time error estimate of the random batch method for the Cucker–Smale model ⋮ On the mean field limit of the random batch method for interacting particle systems ⋮ A Random Batch Ewald Method for Particle Systems with Coulomb Interactions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A weak trapezoidal method for a class of stochastic differential equations
• Coagulation-fragmentation model for animal group-size statistics
• A stochastic version of Stein variational gradient descent for efficient sampling
• Mean field games
• Rapid solution of integral equations of classical potential theory
• From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I
• Semigroups of stochastic gradient descent and online principal component analysis: properties and diffusion approximations
• Random batch methods (RBM) for interacting particle systems
• A simple proof of the Cucker-Smale flocking dynamics and mean-field limit
• Hamiltonian-preserving schemes for the Liouville equation with discontinuous potentials
• Convergence of the point vortex method for 2-D vortex sheet
• A blob method for the aggregation equation
• KINETIC LIMITS FOR PAIR-INTERACTION DRIVEN MASTER EQUATIONS AND BIOLOGICAL SWARM MODELS
• Characterization of Radially Symmetric Finite Time Blowup in Multidimensional Aggregation Equations
• Heterophilious Dynamics Enhances Consensus
• A random particle blob method for the Keller-Segel equation and convergence analysis
• COOPERATIVE STRATEGIES IN FORMATION OF COMPLEX BACTERIAL PATTERNS
• Markov Chains and Stochastic Stability
• Weak Approximation of Solutions of Systems of Stochastic Differential Equations
• A Convergence Proof for Nanbu’s Simulation Method for the Full Boltzmann Equation
• Asymptotic analysis of the Poisson–Boltzmann equation describing electrokinetics in porous media
• The Random Batch Method for N-Body Quantum Dynamics
• Large time behaviors of upwind schemes and $B$-schemes for Fokker-Planck equations on $\mathbb {R}$ by jump processes
• Particle Based gPC Methods for Mean-Field Models of Swarming with Uncertainty
• Emergent Behavior in Flocks
• Binary Interaction Algorithms for the Simulation of Flocking and Swarming Dynamics
• A Stochastic Approximation Method
• Probability
• Stochastic differential equations. An introduction with applications.

This page was built for publication: Convergence of the Random Batch Method for Interacting Particles with Disparate Species and Weights