CYJAX: A package for Calabi-Yau metrics with JAX

TL;DR

CYJAX is a new software package that leverages JAX to machine learn Calabi-Yau metrics, focusing on algebraic ansatz for Kähler potentials, with plans for broader generalizations.

Contribution

Introduces CYJAX, a modular, accessible tool for computing Calabi-Yau metrics using machine learning and algebraic ansatz within the JAX framework.

Findings

First implementation of machine learning Calabi-Yau metrics with JAX.

Automates satisfaction of Kählerity and patch compatibility.

Currently limited to single-equation varieties in projective space.

Abstract

We present the first version of CYJAX, a package for machine learning Calabi-Yau metrics using JAX. It is meant to be accessible both as a top-level tool and as a library of modular functions. CYJAX is currently centered around the algebraic ansatz for the K\"ahler potential which automatically satisfies K\"ahlerity and compatibility on patch overlaps. As of now, this implementation is limited to varieties defined by a single defining equation on one complex projective space. We comment on some planned generalizations.