  The discovery of the first two macroscopic interstellar objects (ISOs)
passing through the Solar System has opened entirely new perspectives in
planetary science. The exploration of these objects offers a qualitatively new
insight into the processes related to the origin, structure and evolution of
planetary systems throughout the Galaxy. Knowledge about these phenomena will
greatly advance if current and future sky surveys discover more ISOs. On the
other hand, the surveys require better characterization of this population in
order to improve their discovery algorithms. However, despite their scientific
significance, there is still no comprehensive orbital model of ISOs in the
Solar System and computationally efficient algorithm for generating their
synthetic representations that would respond to these increasing needs.
Currently available method for generating synthetic populations cannot fully
take into account important phenomena, such as gravitational focusing and the
shielding effect of the Sun. On the other hand, this method is also
computationally far too demanding to be used for systematic exploration of the
ISO population. This paper presents an analytical method for determining the
distributions of the orbital elements of ISOs, as well as computationally
efficient algorithm for generating their synthetic populations, based on the
multivariate inverse transform sampling method. The developed method is several
orders of magnitudes more efficient than the available method, depending on the
size of the synthetic population. A Python implementation of the method is
freely available and can be used to generate synthetic populations of ISOs with
user-defined input parameters.
