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  • Letter
  • Open Access

Neural-network-assisted Boltzmann approach for dilute microswimmer suspensions

Haruki Hayano* and Akira Furukawa†

Kang Kim‡

  • Division of Chemical Engineering, Department of Materials Engineering Science, Graduate School of Engineering Science, The University of Osaka, Toyonaka, Osaka 560-8531, Japan

  • *Contact author: hayano@iis.u-tokyo.ac.jp
  • †Contact author: furu@iis.u-tokyo.ac.jp
  • ‡Contact author: kk@cheng.es.osaka-u.ac.jp
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Phys. Rev. Research 8, L032029 – Published 21 August, 2026

DOI: https://doi.org/10.1103/7565-51x2

Abstract

We introduce a neural-network-assisted Boltzmann framework that learns the binary-collision map of microswimmers from two-body scattering data and uses it as microscopic input to evaluate Boltzmann collision integrals. For a representative swimmer model, the learned map provides quantitative predictions for rotational and translational diffusivities, in close agreement with direct many-body hydrodynamic simulations, and it also enables a linear-stability analysis of the isotropic state against polar ordering within the same dilute, binary-collision-dominated regime. The key advance is not merely that a neural network approximates collision outcomes, but that it provides a compact and continuous representation of the full collision-geometry manifold, thereby making the Boltzmann collision integrals directly accessible and revealing which collisions dominate the overall transport and alignment/disalignment. Because the framework relies only on two-body collision statistics, it provides a transferable, data-driven route from microscopic scattering data to transport properties and ordering tendencies in dilute active suspensions.

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Outline

Information

Phys. Rev. Research 8, L032029– Published 21 August, 2026
  • Received 28 October 2025
  • Accepted 31 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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