Machine learning Calabi-Yau hypersurfaces
Machine learning Calabi-Yau hypersurfaces
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DOI：
10.1103/physrevd.105.066002
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发表时间：
2021-12
影响因子：
5
通讯作者：
D. Berman;Yang-Hui He;Edward Hirst
中科院分区：
文献类型：
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作者：
D. Berman;Yang-Hui He;Edward Hirst
我们回顾了经典的加权P4数据库，该数据库承认Calabi-Yau三重超曲面配备了来自机器学习工具箱的各种工具集。无监督技术识别出乎意料的拓扑数据与权重的近乎线性的相关性。这使我们能够在Calabi-Yau数据中识别出以前未被注意到的星团。有监督的方法成功地从超曲面的权值预测超曲面的拓扑参数，准确率为R^2>；95%。监督学习还允许我们通过利用由聚类行为支持的划分来识别允许Calabi-Yau超曲面达到100%准确率的加权P4。
We revisit the classic database of weighted-P4s which admit Calabi-Yau 3-fold hypersurfaces equipped with a diverse set of tools from the machine-learning toolbox. Unsupervised techniques identify an unanticipated almost linear dependence of the topological data on the weights. This then allows us to identify a previously unnoticed clustering in the Calabi-Yau data. Supervised techniques are successful in predicting the topological parameters of the hypersurface from its weights with an accuracy of R^2>95%. Supervised learning also allows us to identify weighted-P4s which admit Calabi-Yau hypersurfaces to 100% accuracy by making use of partitioning supported by the clustering behaviour.