  The single particle Green's function provides valuable information on the
momentum and energy-resolved spectral properties for a strongly correlated
system. In large-scale numerical calculations using quantum Monte Carlo (QMC),
dynamical mean field theory (DMFT), including cluster-DMFT, one usually obtains
the Green's function in imaginary-time $G(\tau)$. The process of inverting a
Laplace transform to obtain the spectral function $A(\omega)$ in real-frequency
is an ill-posed problem and forms the core of the analytic continuation
problem. In this Letter, we propose to use a completely unsupervised
autoencoder-type neural network to solve the analytic continuation problem. We
introduce an encoder-decoder approach that, together with only minor physical
assumptions, can extract a high-quality frequency response from the imaginary
time domain. With a deeply tunable architecture, this method can, in principle,
locate sharp features of spectral functions that might normally be lost using
already well-established methods, such as maximum entropy (MaxEnt) methods. We
demonstrate the strength of the autoencoder approach by applying it to QMC
results of $G(\tau)$ for a single-band Hubbard model. The proposed method is
general and can also be applied to other ill-posed inverse problems.
