  Simulating electronic behavior in materials and devices with realistic large
system sizes remains a formidable task within the $ab$ $initio$ framework. We
propose DeePTB, an efficient deep learning-based tight-binding (TB) approach
with $ab$ $initio$ accuracy to address this issue. By training with $ab$
$initio$ eigenvalues, our method can efficiently predict TB Hamiltonians for
unseen structures. This capability facilitates efficient simulation of
large-size systems under external perturbations like strain, which are vital
for semiconductor band gap engineering. Moreover, DeePTB, combined with
molecular dynamics, can be used to perform efficient and accurate finite
temperature simulations of both atomic and electronic behavior simultaneously.
This is demonstrated by computing the temperature-dependent properties of a GaP
system with $10^6$ atoms.
