The study of topological properties by machine learning approaches has attracted considerable interest recently. Here we propose machine learning the topological invariants that are unique in non-Hermitian systems. Specifically, we train neural networks to predict the winding of eigenvalues of four prototypical non-Hermitian Hamiltonians on the complex energy plane with nearly $100\%$ accuracy. Our demonstrations in the non-Hermitian Hatano-Nelson model, Su-Schrieffer-Heeger model, and generalized Aubry-André-Harper model in one dimension and the two-dimensional Dirac fermion model with non-Hermitian terms show the capability of the neural networks to explore topological invariants and the associated topological phase transitions and topological phase diagrams in non-Hermitian systems. Moreover, the neural networks trained by a small data set in the phase diagram can successfully predict topological invariants in untouched phase regions. Thus, our work paves the way to revealing non-Hermitian topology with the machine learning toolbox.

• Received 31 August 2020
• Accepted 12 January 2021

DOI:https://doi.org/10.1103/PhysRevA.103.012419