Machine learning Calabi-Yau metrics

TL;DR

This paper introduces a machine learning approach to efficiently approximate Ricci-flat Calabi-Yau metrics, significantly reducing computation time compared to traditional algorithms by combining neural predictions with curve fitting.

Contribution

It presents a novel hybrid method that leverages machine learning to predict Calabi-Yau metrics, improving speed and accuracy over existing techniques.

Findings

Machine learning accurately predicts Calabi-Yau metrics from limited data.

The new method reduces computation time by 10 to 100 times.

It achieves high-precision metrics faster than Donaldson's algorithm.

Abstract

We apply machine learning to the problem of finding numerical Calabi-Yau metrics. Building on Donaldson's algorithm for calculating balanced metrics on K\"ahler manifolds, we combine conventional curve fitting and machine-learning techniques to numerically approximate Ricci-flat metrics. We show that machine learning is able to predict the Calabi-Yau metric and quantities associated with it, such as its determinant, having seen only a small sample of training data. Using this in conjunction with a straightforward curve fitting routine, we demonstrate that it is possible to find highly accurate numerical metrics much more quickly than by using Donaldson's algorithm alone, with our new machine-learning algorithm decreasing the time required by between one and two orders of magnitude.