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Random Batch Methods for Classical and Quantum Interacting Particle Systems and Statistical Samplings

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Active Particles, Volume 3

Abstract

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 \(\mathcal {O}(N^2)\), which is prohibitively expensive. The RBM methods use small but random batches so the computational cost is reduced, per time step, to \(\mathcal {O}(N)\). In this article we discuss these methods for both classical and quantum systems, the corresponding theory, and applications from molecular dynamics, statistical samplings, to agent-based models for collective behavior, and quantum Monte Carlo methods.

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Notes

  1. 1.

    By “chaotic configuration,” we mean that there exists a one-particle distribution f such that for any j, the j-marginal distribution is given by μ (j) = f ⊗j. Such independence in a configuration is then loosely called “chaos.” If the j-marginal distribution is more close to f ⊗j for some f, we loosely say “there is more chaos.”

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Acknowledgements

S. Jin was partially supported by the NSFC grant No.12031013. The work of L. Li was partially sponsored by NSFC 11901389, 11971314, and Shanghai Sailing Program 19YF1421300. Both authors were also supported by Shanghai Science and Technology Commission Grant No. 20JC144100.

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  1. School of Mathematical Sciences, Institute of Natural Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai, P. R. China

    Shi Jin & Lei Li

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  1. Shi Jin
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  1. Department of Mathematical Sciences, Politecnico di Torino, Turin, Italy

    Nicola Bellomo

  2. Mathematical Institute, University of Oxford, Oxford, UK

    José Antonio Carrillo

  3. Department of Mathematics and Institute for Physical Science & Technology, University of Maryland, College Park, MD, USA

    Eitan Tadmor

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Jin, S., Li, L. (2022). Random Batch Methods for Classical and Quantum Interacting Particle Systems and Statistical Samplings. In: Bellomo, N., Carrillo, J.A., Tadmor, E. (eds) Active Particles, Volume 3. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-93302-9_5

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