2018/05/31 by Ning Sun, Jinmin Yi, Pengfei Zhang +2 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Artificial intelligence #Artificial neural network #Berry connection and curvature #Combinatorics #Computer science #Curvature #Deep neural networks #Geometry #Invariant (physics) #Mathematical analysis #Mathematics #Physics #Pure mathematics #Quantum #Quantum many-body systems #Quantum mechanics #Topological Materials and Phenomena #Topological and Geometric Data Analysis #Topological complexity #Topology (electrical circuits) #Winding number #cond-mat.str-el #cs.AI #cs.LG #physics.comp-ph
paper · pdf · doi:10.1103/physrevb.98.085402
published as Phys. Rev. B 98, 085402 (2018) · 8 pages, 5 figures
arxiv created 2018/06/09 · openalex publication_date 2018/08/02 · arxiv updated 2018/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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%, even for Hamiltonians whose invariants are beyond the training data set. 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.