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The Epoch of Reionization (EoR) refers to a period of the early Universe
when the first stars, galaxies, etc. formed and ionized the clouds of
neutral hydrogen that permeated the Universe. Observing the time
evolution of the distribution of neutral Hydrogen by looking at the
"21-cm signal" during EoR has been a goal that astrophysicists have been
chasing, using multiple radio interferometers like HERA, LOFAR, MWA,
PAPER, etc., and others like SKA in the future. Within the LOFAR EoR
Working Group, we have been using Gaussian Process Regression (GPR) for
removing other sources of photons to the observations in order to
isolate the 21-cm signal's power spectrum. However, recent work has
noted that there can be significant amounts of signal loss if the EoR
covariance (which is analogous to a "fitting function" for the 21-cm
signal) is misestimated. To have better covariance models, it has been
proposed to use Machine Learning trained models, by using training sets
from a large variety of simulations generated using the GRIZZLY code. In
this work, we have explored the limits of an ML-trained covariance model
used with GPR, by testing it against mock signals from a variety of
simulations, with different noise levels. Our work suggests the
possibility of successful extraction of the 21-cm signal from ~100
nights of observation using ML-GPR with better recovery of both shape
and power than previously used covariance models. However, in the case
of ~10 nights, it is only able to provide upper limits for some of the
mock signal cases. We also explore redshift dependence, to prepare for
future LOFAR observations at a range of redshifts as well as to compare
with current results from HERA.