Machine Learning Topological Invariants with Neural Networks

TL;DR

This paper demonstrates that neural networks can accurately classify topological phases and predict winding numbers in topological insulators, capturing complex quantum features from local data.

Contribution

It introduces a supervised learning approach to identify topological invariants, showing neural networks can learn and generalize topological properties beyond training data.

Findings

Neural networks predict winding numbers with nearly 100% accuracy.

Networks learn the discrete winding number formula.

Symmetry and regularization impact learning of topological features.

Abstract

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.