  Machine learning is a promising tool to reconstruct time-series phenomena,
such as variability of active galactic nuclei (AGN), from sparsely-sampled
data. Here we use three Continuous Auto-Regressive Moving Average (CARMA)
representations of AGN variability -- the Damped Random Walk (DRW) and
(over/under-)Damped Harmonic Oscillator (DHO) -- to simulate 10-year AGN light
curves as they would appear in the upcoming Vera Rubin Observatory Legacy
Survey of Space and Time (LSST), and provide a public tool to generate these
for any survey cadence. We investigate the impact on AGN science of five
proposed cadence strategies for LSST's primary Wide-Fast-Deep (WFD) survey. We
apply for the first time in astronomy a novel Stochastic Recurrent Neural
Network (SRNN) algorithm to reconstruct input light curves from the simulated
LSST data, and provide a metric to evaluate how well SRNN can help recover the
underlying CARMA parameters. We find that the light curve reconstruction is
most sensitive to the duration of gaps between observing season, and that of
the proposed cadences, those that change the balance between filters, or avoid
having long gaps in the {g}-band perform better. Overall, SRNN is a promising
means to reconstruct densely sampled AGN light curves and recover the long-term
Structure Function of the DRW process (SF$_\infty$) reasonably well. However,
we find that for all cadences, CARMA/SRNN models struggle to recover the
decorrelation timescale ($\tau$) due to the long gaps in survey observations.
This may indicate a major limitation in using LSST WFD data for AGN variability
science.
