  A large fraction of Type Ia supernova (SN Ia) observations over the next
decade will be in the near-infrared (NIR), at wavelengths beyond the reach of
the current standard light-curve model for SN Ia cosmology, SALT3 ($\sim
2800$--8700$A$ central filter wavelength). To harness this new SN Ia sample and
reduce future light-curve standardization systematic uncertainties, we train
SALT3 at NIR wavelengths (SALT3-NIR) up to 2 $\mu$m with the open-source
model-training software SALTShaker, which can easily accommodate future
observations. Using simulated data we show that the training process constrains
the NIR model to $\sim 2$--3% across the phase range ($-20$ to $50$ days). We
find that Hubble residual (HR) scatter is smaller using the NIR alone or
optical+NIR compared to optical alone, by up to $\sim 30$% depending on filter
choice (95% confidence). There is significant correlation between NIR
light-curve stretch measurements and luminosity, with stretch and color
corrections often improving HR scatter by up to $\sim20%$. For SN Ia
observations expected from the \textit{Roman Space Telescope}, SALT3-NIR
increases the amount of usable data in the SALT framework by $\sim 20$% at
redshift $z\lesssim0.4$ and by $\sim 50$% at $z\lesssim0.15$. The SALT3-NIR
model is part of the open-source {\tt SNCosmo} and {\tt SNANA} SN Ia cosmology
packages.
