Calabi-Yau Metrics, Energy Functionals and Machine-Learning

Anthony Ashmore (1) , Lucille Calmon , Yang-Hui He , Burt A. Ovrut

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

We apply machine learning to the problem of finding numerical Calabi-Yau metrics. We extend previous work on learning approximate Ricci-flat metrics calculated using Donaldson's algorithm to the much more accurate "optimal" metrics of Headrick and Nassar. We show that machine learning is able to predict the Kähler potential of a Calabi-Yau metric having seen only a small sample of training data.

Mots clés: metric; Calabi-Yau; machine learning

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Physique mathématique [math-ph]

Anthony Ashmore, Lucille Calmon, Yang-Hui He, Burt A. Ovrut. Calabi-Yau Metrics, Energy Functionals and Machine-Learning. International Journal of Data Science in the Mathematical Sciences, 2023, 1 (1), pp.49-61. ⟨10.1142/S2810939222500034⟩. ⟨hal-03514436⟩