  We propose a data-driven learning framework for the analytic continuation
problem in numerical quantum many-body physics. Designing an accurate and
efficient framework for the analytic continuation of imaginary time using
computational data is a grand challenge that has hindered meaningful links with
experimental data. The standard Maximum Entropy (MaxEnt)-based method is
limited by the quality of the computational data and the availability of prior
information. Also, the MaxEnt is not able to solve the inversion problem under
high level of noise in the data. Here we introduce a novel learning model for
the analytic continuation problem using a Adams-Bashforth residual neural
network (AB-ResNet). The advantage of this deep learning network is that it is
model independent and, therefore, does not require prior information concerning
the quantity of interest given by the spectral function. More importantly, the
ResNet-based model achieves higher accuracy than MaxEnt for data with higher
level of noise. Finally, numerical examples show that the developed AB-ResNet
is able to recover the spectral function with accuracy comparable to MaxEnt
where the noise level is relatively small.
