  This study explores the use of neural network-based analytic continuation to
extract spectra from Monte Carlo data. We apply this technique to both
synthetic and Monte Carlo-generated data. The training sets for neural networks
are carefully synthesized without ``data leakage". We found that the training
set should match the input correlation functions in terms of statistical error
properties, such as noise level, noise dependence on imaginary time, and
imaginary time-displaced correlations. We have developed a systematic method to
synthesize such training datasets. Our improved algorithm outperform the widely
used maximum entropy method in highly noisy situations. As an example, our
method successfully extracted the dynamic structure factor of the spin-1/2
Heisenberg chain from quantum Monte Carlo simulations.
