Geometric priors for single-patch neural Calabi–Yau metrics on the quintic: a conservative fixed- ψ Ablation study
Year: 2026
Type: article
Abstract: We investigate how geometric priors affect neural approximations to the complex Monge–Ampère equation on the quintic Calabi–Yau threefold. The study is a fixed- ψ diagnostic rather than a solver benchmark. It compares four single-patch ansätze—a coordinate SIREN potential model, a direct-metric Cholesky baseline, a pure algebraic section ansatz, and a section-plus-neural hybrid—across a 96-run learning-rate and frequency archive, noting that section-Pure is invariant to the swept SIREN frequency parameter. Targeted multi-seed controls then re-evaluate selected checkpoints under a shared affine- η evaluator. The results reveal a sharp architectural separation. In the 96-run archive, section-based models attain validation σ ≃ 4.1 % ( 4.14 %– 4.16 % ), while the coordinate-only baselines remain at 41.29 % (SIREN) and 44.27 % (Cholesky). Multi-seed shared-evaluator controls preserve this coarse ordering, and a fresh-cloud checkpoint re-evaluation on five independent validation clouds again separates the stable section settings ( 3.84 %– 4.77 % ) from Cholesky ( 28.46 %– 30.59 % ) and SIREN ( 34.73 %– 38.13 % ). Projective hybrid features do not establish a reliable best-case accuracy gain, but they stabilise the stressed regime: the raw stress control spans 4.45 % – 205.45 % , while the projective stress control stays within 4.26 %– 4.41 % . The contribution is therefore interpretive and methodological. Within this single-patch, fixed-
Author: D 扬 Yang Eng 黄 鼎
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,000
Funders: Nvidia, Technische Universität München
OpenAlex ID: W7162695218