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 ℙ⁴.

我们使用机器学习来近似Calabi-Yau和SU（3）-结构度量，其中包括首次复杂的结构模量依赖性。我们的新方法在准确性和速度方面进一步改善了现有的数值近似。知道这些度量具有许多应用，从计算字符串压缩的有效场论的关键方面（例如汤川kawa合的规范化规范）到在沼泽猜想中起关键作用的庞大的字符串谱，到镜像对称和SYZ，一应俱全。推测。在SU（3）结构的情况下，我们的机器学习方法使我们能够设计具有某些扭转特性的度量。基于Cal中一参数五次超曲面族的Calabi-Yau和SU（3）-结构流形证明了我们的方法⁴。