  We used a convolutional neural network to infer stellar rotation periods from
a set of synthetic light curves simulated with realistic spot evolution
patterns. We convolved these simulated light curves with real TESS light curves
containing minimal intrinsic astrophysical variability to allow the network to
learn TESS systematics and estimate rotation periods despite them. In addition
to periods, we predict uncertainties via heteroskedastic regression to estimate
the credibility of the period predictions. In the most credible half of the
test data, we recover 10%-accurate periods for 46% of the targets, and
20%-accurate periods for 69% of the targets. Using our trained network, we
successfully recover periods of real stars with literature rotation
measurements, even past the 13.7-day limit generally encountered by TESS
rotation searches using conventional period-finding techniques. Our method also
demonstrates resistance to half-period aliases. We present the neural network
and simulated training data, and introduce the software butterpy used to
synthesize the light curves using realistic star spot evolution.
