2024/07/09 by Yacoub Hendi, Hendi, Yacoub, Magdalena Larfors +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2407.06914
openalex publication_date 2024/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We present new invariant machine learning models that approximate the Ricci-flat metric on Calabi-Yau (CY) manifolds with discrete symmetries. We accomplish this by combining the ϕ-model of the cymetric package with non-trainable, G-invariant, canonicalization layers that project the ϕ-model's input data (i.e. points sampled from the CY geometry) to the fundamental domain of a given symmetry group G. These G-invariant layers are easy to concatenate, provided one compatibility condition is fulfilled, and combine well with spectral ϕ-models. Through experiments on different CY geometries, we find that, for fixed point sample size and training time, canonicalized models give slightly more accurate metric approximations than the standard ϕ-model. The method may also be used to compute Ricci-flat metric on smooth CY quotients. We demonstrate this aspect by experiments on a smooth ℤ25 quotient of a 5-parameter quintic CY manifold.