论文标题
Calabi-yau指标的神经网络近似
Neural Network Approximations for Calabi-Yau Metrics
论文作者
论文摘要
Calabi-yau三倍的RICCI平坦度量标准在分析上不知道。在这项工作中，我们采用机器学习的技术来推导费马特五重奏，dwork五句五个的数值平面度量，并为田野歧管推断出数值。这项调查采用了一个单个神经网络结构，该结构能够近似Ricci Flat Kaehler指标，以二维和三个尺寸的几个calabi-yau歧管。我们表明，在训练三个数量级后，评估几何降低的RICCI平坦度的衡量标准。这是在验证集中证实的，其中改进更为适中。最后，我们证明，在学习度量指标的过程中可以学习流形的离散对称性。
Ricci flat metrics for Calabi-Yau threefolds are not known analytically. In this work, we employ techniques from machine learning to deduce numerical flat metrics for the Fermat quintic, for the Dwork quintic, and for the Tian-Yau manifold. This investigation employs a single neural network architecture that is capable of approximating Ricci flat Kaehler metrics for several Calabi-Yau manifolds of dimensions two and three. We show that measures that assess the Ricci flatness of the geometry decrease after training by three orders of magnitude. This is corroborated on the validation set, where the improvement is more modest. Finally, we demonstrate that discrete symmetries of manifolds can be learned in the process of learning the metric.
