  We use machine learning to approximate Calabi-Yau and SU(3)-structure
metrics, including for the first time complex structure moduli dependence. Our
new methods furthermore improve existing numerical approximations in terms of
accuracy and speed. Knowing these metrics has numerous applications, ranging
from computations of crucial aspects of the effective field theory of string
compactifications such as the canonical normalizations for Yukawa couplings,
and the massive string spectrum which plays a crucial role in swampland
conjectures, to mirror symmetry and the SYZ conjecture. In the case of SU(3)
structure, our machine learning approach allows us to engineer metrics with
certain torsion properties. Our methods are demonstrated for Calabi-Yau and
SU(3)-structure manifolds based on a one-parameter family of quintic
hypersurfaces in $\mathbb{P}^4.$
