In this Letter we supervisedly train neural networks to distinguish different
topological phases in the context of topological band insulators. After
training with Hamiltonians of one-dimensional insulators with chiral symmetry,
the neural network can predict their topological winding numbers with nearly
100% accuracy, even for Hamiltonians with larger winding numbers that are not
included in the training data. These results show a remarkable success that the
neural network can capture the global and nonlinear topological features of
quantum phases from local inputs. By opening up the neural network, we confirm
that the network does learn the discrete version of the winding number formula.
We also make a couple of remarks regarding the role of the symmetry and the
opposite effect of regularization techniques when applying machine learning to
physical systems.

本文研究如何使用神经网络在拓扑绝缘体中区分不同的拓扑相，经过训练，即使是大于训练数据的的 Hamiltonians winding number，神经网络也能够预测其拓扑缠绕数，证明了神经网络能够从局部输入中捕捉到量子相的全局和非线性拓扑特征。同时，本文确认了神经网络学到了离散版本的缠绕数公式，在运用机器学习到物理系统时，研究了对称性的作用和正则化技术的相反影响。