  We investigate applying 3D deep convolutional neural networks as fast
surrogate models of the formation and feedback effects of primordial stars in
hydrodynamic cosmological simulations of the first galaxies. Here, we present
the surrogate model to predict localized primordial star formation; the
feedback model will be presented in a subsequent paper. The star formation
prediction model consists of two sub-models: the first is a 3D volume
classifier that predicts which (10 comoving kpc)$^3$ volumes will host star
formation, followed by a 3D Inception-based U-net voxel segmentation model that
predicts which voxels will form primordial stars. We find that the combined
model predicts primordial star forming volumes with high skill, with $F_1
>0.995$ and true skill score $>0.994$. The star formation is localized within
the volume to $\lesssim5^3$~voxels ($\sim1.6$~comoving kpc$^3$) with
$F_1>0.399$ and true skill score $>0.857$. Applied to simulations with low
spatial resolution, the model predicts star forming regions in the same
locations and at similar redshifts as sites in resolved full-physics
simulations that explicitly model primordial star formation and feedback. When
applied to simulations with lower mass resolution, we find that the model
predicts star forming regions at later redshift due to delayed structure
formation resulting from lower mass resolution. Our model predicts primordial
star formation without halo finding, so will be useful in spatially
under-resolved simulations that cannot resolve primordial star forming halos.
To our knowledge, this is the first model that can predict primordial star
forming regions that match highly-resolved cosmological simulations.
