论文标题
机器学习calabi-yau四倍
Machine Learning Calabi-Yau Four-folds
论文作者
论文摘要
卡拉比（Calabi-Yau）歧管的杂货数非依赖基础流形数据，它们对机器学习提出了一个有趣的挑战。在这封信中，我们考虑了四倍的完整交点Calabi-yau的数据集，大约900,000个拓扑类型，并研究了对这些流形的Hodge数字H^1,1和H^3,1的监督学习。我们发现，通过完全连接的分类器和回归器网络可以成功地学习H^1,1（精度为96％）。尽管这两种类型的网络都失败了H^3,1，但我们表明，至少在数据子集中，一个更复杂的两分支网络（结合特征增强）可以作为H^3,1的有效回归器（至98％的精度）。这暗示了Hodge数字的AN（尚不清楚）公式的存在。
Hodge numbers of Calabi-Yau manifolds depend non-trivially on the underlying manifold data and they present an interesting challenge for machine learning. In this letter we consider the data set of complete intersection Calabi-Yau four-folds, a set of about 900,000 topological types, and study supervised learning of the Hodge numbers h^1,1 and h^3,1 for these manifolds. We find that h^1,1 can be successfully learned (to 96% precision) by fully connected classifier and regressor networks. While both types of networks fail for h^3,1, we show that a more complicated two-branch network, combined with feature enhancement, can act as an efficient regressor (to 98% precision) for h^3,1, at least for a subset of the data. This hints at the existence of an, as yet unknown, formula for Hodge numbers.
