  Motivated by the recent successful application of physics-informed neural
networks (PINNs) to solve Boltzmann-type equations [S. Jin, Z. Ma, and K. Wu,
J. Sci. Comput., 94 (2023), pp. 57], we provide a rigorous error analysis for
PINNs in approximating the solution of the Boltzmann equation near a global
Maxwellian. The challenge arises from the nonlocal quadratic interaction term
defined in the unbounded domain of velocity space. Analyzing this term on an
unbounded domain requires the inclusion of a truncation function, which demands
delicate analysis techniques. As a generalization of this analysis, we also
provide proof of the asymptotic preserving property when using micro-macro
decomposition-based neural networks.
