论文标题
完整交叉点的机器学习卡拉比（Calabi-Yau）歧管：一种方法学研究
Machine learning for complete intersection Calabi-Yau manifolds: a methodological study
论文作者
论文摘要
我们重新讨论了使用机器学习（ML）的完整相交的Calabi-Yau（Cicy）的完整交点的$ H^{1,1} $和$ H^{1,1} $的问题，并考虑了Candelas-dale-dale-dale-lutken-schimmrigk / greensersers的旧数据和新数据集，分别考虑了新旧数据。在现实世界应用中，实施ML系统很少会减少以将蛮数据馈送到算法中。相反，典型的工作流程始于探索性数据分析（EDA），该分析旨在更好地理解输入数据并找到最佳表示。随后是验证过程和基线模型的设计。最后，比较和组合了几种ML模型，通常涉及与物理中通常使用的顺序模型更复杂的神经网络。通过遵循此过程，我们提高了相对于现有文献的ML计算的准确性。首先，我们使用受旧数据集的启动模型启发的神经网络获得$ h^{1,1} $的97％（分别为99％），仅使用30％（分别为70％）进行培训。对于新的，简单的线性回归导致了几乎100％的精度，其中30％用于培训。 $ h^{2,1} $的计算仅能达到两个数据集的准确性50％，但这仍然比使用简单的神经网络获得的16％（具有高斯内核的SVM和功能工程和Sequeential Network网络，最佳36％）。这是一种概念证明，即神经网络对于研究字符串理论中出现的几何形状的特性可能是有价值的。
We revisit the question of predicting both Hodge numbers $h^{1,1}$ and $h^{2,1}$ of complete intersection Calabi-Yau (CICY) 3-folds using machine learning (ML), considering both the old and new datasets built respectively by Candelas-Dale-Lutken-Schimmrigk / Green-Hübsch-Lutken and by Anderson-Gao-Gray-Lee. In real world applications, implementing a ML system rarely reduces to feed the brute data to the algorithm. Instead, the typical workflow starts with an exploratory data analysis (EDA) which aims at understanding better the input data and finding an optimal representation. It is followed by the design of a validation procedure and a baseline model. Finally, several ML models are compared and combined, often involving neural networks with a topology more complicated than the sequential models typically used in physics. By following this procedure, we improve the accuracy of ML computations for Hodge numbers with respect to the existing literature. First, we obtain 97% (resp. 99%) accuracy for $h^{1,1}$ using a neural network inspired by the Inception model for the old dataset, using only 30% (resp. 70%) of the data for training. For the new one, a simple linear regression leads to almost 100% accuracy with 30% of the data for training. The computation of $h^{2,1}$ is less successful as we manage to reach only 50% accuracy for both datasets, but this is still better than the 16% obtained with a simple neural network (SVM with Gaussian kernel and feature engineering and sequential convolutional network reach at best 36%). This serves as a proof of concept that neural networks can be valuable to study the properties of geometries appearing in string theory.
