  Calculating perturbation response properties of materials from first
principles provides a vital link between theory and experiment, but is
bottlenecked by the high computational cost. Here a general framework is
proposed to perform density functional perturbation theory (DFPT) calculations
by neural networks, greatly improving the computational efficiency. Automatic
differentiation is applied on neural networks, facilitating accurate
computation of derivatives. High efficiency and good accuracy of the approach
are demonstrated by studying electron-phonon coupling and related physical
quantities. This work brings deep-learning density functional theory and DFPT
into a unified framework, creating opportunities for developing ab initio
artificial intelligence.
