  Calabi--Yau compactifications of the $E_8\times E_8$ heterotic string provide
a promising route to recovering the four-dimensional particle physics described
by the Standard Model. While the topology of the Calabi--Yau space determines
the overall matter content in the low-energy effective field theory, further
details of the compactification geometry are needed to calculate the normalized
physical couplings and masses of elementary particles. In this work, we present
numerical computations of physical Yukawa couplings in a number of heterotic
models in the standard embedding and demonstrate the existence of natural
hierarchies, a coveted feature in string model building.
