  $\beta$ phase gallium oxide ($\beta$-$\rm Ga_2O_3$) demonstrates tremendous
potential for electronics applications and offers promising prospects for
integration into future space systems with the necessity of high radiation
resistance. Therefore, a comprehensive understanding of the threshold
displacement energy (TDE) and the radiation-induced formation of Frenkel pairs
(FPs) in this material is vital but has not yet been thoroughly studied. In
this work, we performed over 5,000 molecular dynamics simulations using our
machine-learning potentials to determine the TDE and investigate the formation
of FPs. The average TDEs for the two Ga sites, Ga1 (tetrahedral site) and Ga2
(octahedral site), are 22.9 and 20.0 eV, respectively. While the average TDEs
for the three O sites are nearly uniform, ranging from 17.0 to 17.4 eV. The
generated TDE maps reveal significant differences in displacement behavior
between these five atomic sites. Our developed defect identification methods
successfully categorize various types of FPs in this material, with more than
ten types of Ga FPs being produced during our simulations. O atoms are found to
form two main types of FPs and the O split interstitial site on O1 site is most
common. Finally, the recombination behavior and barriers of Ga and O FPs
indicate that the O FP has a higher possibility of recovery upon annealing. Our
findings provide important insights into the studies of radiation damage and
defects in $\rm Ga_2O_3$ and can contribute to the design and development of
$\rm Ga_2O_3$-based devices
