Neural-network-assisted Boltzmann approach for dilute microswimmer suspensions

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.