Machine Learning Calabi–Yau Metrics

• Published in: Fortschritte der Physik Vol. 68; no. 9
• Main Authors: Ashmore, Anthony, He, Yang‐Hui, Ovrut, Burt A.
• Format: Journal Article
• Language: English
• Published: Weinheim Wiley Subscription Services, Inc 01.09.2020; Wiley Blackwell (John Wiley & Sons)
• Subjects: Algorithms; Curve fitting; generalized geometry; Machine learning; supergravity backgrounds
• ISSN: 0015-8208; 1521-3978
• DOI: 10.1002/prop.202000068

We apply machine learning to the problem of finding numerical Calabi–Yau metrics. Building on Donaldson's algorithm for calculating balanced metrics on Kähler 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. The concept of machine‐learning is applied to the problem of finding numerical Calabi–Yau metrics. Building on Donaldson's algorithm for calculating balanced metrics on Kähler manifolds, conventional curve fitting and machine‐learning techniques are combined to numerically approximate Ricci‐flat metrics. It is shown 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, the authors demonstrate that it is possible to find highly accurate numerical metrics much more quickly than by using Donaldson's algorithm alone, with the new machine‐learning algorithm decreasing the time required by between one and two orders of magnitude.