  A crucial yet challenging task in galaxy evolution studies is the
identification of distant merging galaxies, a task which suffers from a variety
of issues ranging from telescope sensitivities and limitations to the
inherently chaotic morphologies of young galaxies. In this paper, we use random
forests and convolutional neural networks to identify high-redshift JWST CEERS
galaxy mergers. We train these algorithms on simulated $3<z<5$ CEERS galaxies
created from the IllustrisTNG subhalo morphologies and the Santa Cruz SAM
lightcone. We apply our models to observed CEERS galaxies at $3<z<5$. We find
that our models correctly classify $\sim60-70\%$ of simulated merging and
non-merging galaxies; better performance on the merger class comes at the
expense of misclassifying more non-mergers. We could achieve more accurate
classifications, as well as test for the dependency on physical parameters such
as gas fraction, mass ratio, and relative orbits, by curating larger training
sets. When applied to real CEERS galaxies using visual classifications as
ground truth, the random forests correctly classified $40-60\%$ of mergers and
non-mergers at $3<z<4$, but tended to classify most objects as non-mergers at
$4<z<5$ (misclassifying $\sim70\%$ of visually-classified mergers). On the
other hand, the CNNs tended to classify most objects as mergers across all
redshifts (misclassifying $80-90\%$ of visually-classified non-mergers). We
investigate what features the models find most useful, as well as
characteristics of false positives and false negatives, and also calculate
merger rates derived from the identifications made by the models.
