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In this work we design and train deep neural networks to predict topologicalinvariants for one-dimensional four-band insulators in AIII class whosetopological invariant is the winding number, and two-dimensional two-bandinsulators in A class whose topological invariant is the Chern number. GivenHamiltonians in the momentum space as the input, neural networks can predicttopological invariants for both classes with accuracy close to or higher than90%, even for Hamiltonians whose invariants are beyond the training data set.Despite the complexity of the neural network, we find that the output ofcertain intermediate hidden layers resembles either the winding angle formodels in AIII class or the solid angle (Berry curvature) for models in Aclass, indicating that neural networks essentially capture the mathematicalformula of topological invariants. Our work demonstrates the ability of neuralnetworks to predict topological invariants for complicated models with localHamiltonians as the only input, and offers an example that even a deep neuralnetwork is understandable.

Deep Learning Topological Invariants of Band Insulators