  We present new invariant machine learning models that approximate the
Ricci-flat metric on Calabi-Yau (CY) manifolds with discrete symmetries. We
accomplish this by combining the $\phi$-model of the cymetric package with
non-trainable, $G$-invariant, canonicalization layers that project the
$\phi$-model's input data (i.e. points sampled from the CY geometry) to the
fundamental domain of a given symmetry group $G$. These $G$-invariant layers
are easy to concatenate, provided one compatibility condition is fulfilled, and
combine well with spectral $\phi$-models. Through experiments on different CY
geometries, we find that, for fixed point sample size and training time,
canonicalized models give slightly more accurate metric approximations than the
standard $\phi$-model. The method may also be used to compute Ricci-flat metric
on smooth CY quotients. We demonstrate this aspect by experiments on a smooth
$\mathbb{Z}^2_5$ quotient of a 5-parameter quintic CY manifold.
