Using physics informed neural networks, we construct numerical approximations to Ricci-flat Calabi–Yau metrics. This allows for the calculation of Yukawa couplings in the low-energy effective N=1 theories obtained upon heterotic compactification. In explicit examples, hierarchies arise from excursions away from symmetric points in complex structure moduli space. While numerical Ricci-flat metrics on Calabi–Yau manifolds are becoming increasingly accurate and useful, they lack the interpretability required to extract theoretical insights. From a variant of Donaldson's algorithm, we establish that the metric parameters obey novel power laws near the large complex structure limit.