Machine Learning Calabi–Yau Metrics
Copyright policy )Machine Learning Calabi–Yau Metrics
AbstractWe 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.
- University of Oxford United Kingdom
- University of Pennsylvania United States
- University of London United Kingdom
- UNIVERSITY OF LONDON United Kingdom
- City, University of London United Kingdom
High Energy Physics - Theory, FOS: Computer and information sciences, Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills), Learning and adaptive systems in artificial intelligence, FOS: Physical sciences, Machine Learning (stat.ML), Calabi-Yau manifolds (algebro-geometric aspects), Mathematics - Algebraic Geometry, Computational methods for problems pertaining to differential geometry, High Energy Physics - Theory (hep-th), Statistics - Machine Learning, generalized geometry, FOS: Mathematics, Calabi-Yau theory (complex-analytic aspects), Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.), Generalized geometries (à la Hitchin), Algebraic Geometry (math.AG), Artificial neural networks and deep learning, supergravity backgrounds
High Energy Physics - Theory, FOS: Computer and information sciences, Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills), Learning and adaptive systems in artificial intelligence, FOS: Physical sciences, Machine Learning (stat.ML), Calabi-Yau manifolds (algebro-geometric aspects), Mathematics - Algebraic Geometry, Computational methods for problems pertaining to differential geometry, High Energy Physics - Theory (hep-th), Statistics - Machine Learning, generalized geometry, FOS: Mathematics, Calabi-Yau theory (complex-analytic aspects), Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.), Generalized geometries (à la Hitchin), Algebraic Geometry (math.AG), Artificial neural networks and deep learning, supergravity backgrounds
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).51 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 1% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!