Publications [#347984] of Jian-Guo Liu

Papers Published

1. Jin, S; Li, L; Liu, JG, Random Batch Methods (RBM) for interacting particle systems, Journal of Computational Physics, vol. 400 (January, 2020) [doi] [high impact paper]
   (last updated on 2025/07/03)

   Author's Comments:
   We developed a general class of Random Batch Methods for interacting particle systems and has been successfully used molecular dynamics simulations and other important applications in many important science subjects. I expect our method will have a big impact in theoretical analysis and in these application areas.

   Abstract:
   We develop Random Batch Methods for interacting particle systems with large number of particles. These methods use small but random batches for particle interactions, thus the computational cost is reduced from O(N²) per time step to O(N), for a system with N particles with binary interactions. On one hand, these methods are efficient Asymptotic-Preserving schemes for the underlying particle systems, allowing N-independent time steps and also capture, in the N→∞ limit, the solution of the mean field limit which are nonlinear Fokker-Planck equations; on the other hand, the stochastic processes generated by the algorithms can also be regarded as new models for the underlying problems. For one of the methods, we give a particle number independent error estimate under some special interactions. Then, we apply these methods to some representative problems in mathematics, physics, social and data sciences, including the Dyson Brownian motion from random matrix theory, Thomson's problem, distribution of wealth, opinion dynamics and clustering. Numerical results show that the methods can capture both the transient solutions and the global equilibrium in these problems.