Related papers: Mean field error estimate of the random batch meth…
The Random Batch Method proposed in our previous work [Jin et al., J. Comput. Phys., 400(1), 2020] is not only a numerical method for interacting particle systems and its mean-field limit, but also can be viewed as a model of particle…
The random batch method provides an efficient algorithm for computing statistical properties of a canonical ensemble of interacting particles. In this work, we study the error estimates of the fully discrete random batch method, especially…
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 $O(N^2)$ per time step to…
In this work, we focus on the mean-field limit of the Random Batch Method (RBM) for the Cucker-Smale model. Different from the classical mean-field limit analysis, the chaos in this model is imposed at discrete time and is propagated to…
The Random Batch Method (RBM) proposed in [Jin et al. J Comput Phys, 2020] is an efficient algorithm for simulating interacting particle systems (IPS). In this paper, we investigate the Random Batch Method with replacement (RBM-r), which is…
The Random Batch Method (RBM) [S. Jin, L. Li and J.-G. Liu, Random Batch Methods (RBM) for interacting particle systems, J. Comput. Phys. 400 (2020) 108877] is not only an efficient algorithm for simulating interacting particle systems, but…
Random Batch Methods (RBM) for mean-field interacting particle systems enable the reduction of the quadratic computational cost associated with particle interactions to a near-linear cost. The essence of these algorithms lies in the random…
We review the Random Batch Methods (RBM) for interacting particle systems consisting of $N$-particles, with $N$ being large. The computational cost of such systems is of $O(N^2)$, which is prohibitively expensive. The RBM methods use small…
The Random Batch Method (RBM) is an effective technique to reduce the computational complexity when solving certain stochastic differential problems (SDEs) involving interacting particles. It can transform the computational complexity from…
In this article, we focus on two toy models : the Curie-Weiss model and the system of $N$ particles in linear interactions in a double well confining potential. Both models, which have been extensively studied, describe a large system of…
An efficient sampling method, the pmmLang+RBM, is proposed to compute the quantum thermal average in the interacting quantum particle system. Benefiting from the random batch method (RBM), the pmmLang+RBM reduces the complexity due to the…
In many real-world scenarios, the underlying random fluctuations are non-Gaussian, particularly in contexts where heavy-tailed data distributions arise. A typical example of such non-Gaussian phenomena calls for L\'evy noise, which…
This paper discusses a numerical method for computing the evolution of large interacting system of quantum particles. The idea of the random batch method is to replace the total interaction of each particle with the $N-1$ other particles by…
A random-batch method for multi-species interacting particle systems is proposed, extending the method of S. Jin, L. Li, and J.-G. Liu [J. Comput. Phys. 400 (2020), 108877]. The idea of the algorithmus is to randomly divide, at each time…
In this paper, we present an innovative particle system characterized by moderate interactions, designed to accurately approximate kinetic flocking models that incorporate singular interaction forces and local alignment mechanisms. We…
We investigate several important issues regarding the Random Batch Method (RBM) for second order interacting particle systems. We first show the uniform-in-time strong convergence for second order systems under suitable contraction…
We consider in this work the convergence of Random Batch Method proposed in our previous work [Jin et al., J. Comput. Phys., 400(1), 2020] for interacting particles to the case of disparate species and weights. We show that the strong error…
We consider in this paper random batch interacting particle methods for solving the Poisson-Nernst-Planck (PNP) equations, and thus the Poisson-Boltzmann (PB) equation as the equilibrium, in the external unbounded domain. To justify the…
For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…
This article introduces a novel approach to the mean-field limit of stochastic systems of interacting particles, leading to the first ever derivation of the mean-field limit to the Vlasov-Poisson-Fokker-Planck system for plasmas in…