cymyc -- Calabi-Yau Metrics, Yukawas, and Curvature

TL;DR

cymyc is a Python library that numerically models Calabi-Yau manifolds and their moduli spaces, integrating geometric ansatz and machine learning to solve complex tensor field equations.

Contribution

It introduces a novel geometric ansatz and machine learning approach for numerical investigation of Calabi-Yau manifolds and their tensor fields.

Findings

Efficient numerical modeling of Calabi-Yau metrics.

Incorporation of machine learning for PDE solutions on manifolds.

Enhanced understanding of moduli space geometry.

Abstract

We introduce \texttt{cymyc}, a high-performance Python library for numerical investigation of the geometry of a large class of string compactification manifolds and their associated moduli spaces. We develop a well-defined geometric ansatz to numerically model tensor fields of arbitrary degree on a large class of Calabi-Yau manifolds. \texttt{cymyc} includes a machine learning component which incorporates this ansatz to model tensor fields of interest on these spaces by finding an approximate solution to the system of partial differential equations they should satisfy.