Deep Learning for Topological Invariants

05/26/2018
by   Ning Sun, et al.
0

In this work we design and train deep neural networks to predict topological invariants for one-dimensional four-band insulators in AIII class whose topological invariant is the winding number, and two-dimensional two-band insulators in A class whose topological invariant is the Chern number. Given Hamiltonians in the momentum space as the input, neural networks can predict topological invariants for both classes with accuracy close to or higher than 90 Despite the complexity of the neural network, we find that the output of certain intermediate hidden layers resembles either the winding angle for models in AIII class or the solid angle (Berry curvature) for models in A class, indicating that neural networks essentially capture the mathematical formula of topological invariants. Our work demonstrates the ability of neural networks to predict topological invariants for complicated models with local Hamiltonians as the only input, and offers an example that even a deep neural network is understandable.

READ FULL TEXT

page 2

page 5

research
05/26/2018

Deep Learning Topological Invariants of Band Insulators

In this work we design and train deep neural networks to predict topolog...
research
04/29/2019

Finding Invariants in Deep Neural Networks

We present techniques for automatically inferring invariant properties o...
research
05/09/2023

Metric Space Magnitude and Generalisation in Neural Networks

Deep learning models have seen significant successes in numerous applica...
research
01/07/2019

Machine learning topological phases in real space

We develop a supervised machine learning algorithm that is able to learn...
research
11/30/2021

Learning knot invariants across dimensions

We use deep neural networks to machine learn correlations between knot i...
research
11/27/2021

Nonparametric Topological Layers in Neural Networks

Various topological techniques and tools have been applied to neural net...
research
12/31/2020

Topological obstructions in neural networks learning

We apply methods of topological data analysis to loss functions to gain ...

Please sign up or login with your details

Forgot password? Click here to reset