  We have developed a neural network model to perform event reconstruction of
Compton telescopes. This model reconstructs events that consist of three or
more interactions in a detector. It is essential for Compton telescopes to
determine the time order of the gamma-ray interactions and whether the incident
photon deposits all energy in a detector or it escapes from the detector. Our
model simultaneously predicts these two essential factors using a multi-task
neural network with three hidden layers of fully connected nodes. For
verification, we have conducted numerical experiments using Monte Carlo
simulation, assuming a large-area Compton telescope using liquid argon to
measure gamma rays with energies up to $3.0\,\mathrm{MeV}$. The reconstruction
model shows excellent performance of event reconstruction for multiple
scattering events that consist of up to eight hits. The accuracies of hit order
prediction are around $60\%$ while those of escape flags are higher than $70\%$
for up to eight-hit events of $4\pi$ isotropic photons. Compared with two other
algorithms, a classical model and a physics-based probabilistic one, the
present neural network method shows high performance in estimation accuracy
particularly when the number of scattering is small, 3 or 4. Since simulation
data easily optimize the network model, the model can be flexibly applied to a
wide variety of Compton telescopes.
