Papers › Learning Group Invariant Calabi-Yau Metrics by Fundamental Domain Projections
Learning Group Invariant Calabi-Yau Metrics by Fundamental Domain Projections
Yacoub Hendi, Magdalena Larfors, Moritz Walden
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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.
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