  Understanding charge motion in a background of interacting quantum spins is a
fundamental problem in quantum many-body physics. The most extensively studied
model for this problem is the so-called $t$-$t'$-$t''$-$J$ model, where the
determination of the parameter $t'$ in the context of cuprate superconductors
is challenging. Here we present a theoretical study of the spectral functions
of a mobile hole in the $t$-$t'$-$t''$-$J$ model using two machine learning
techniques: K-nearest Neighbors regression (KNN) and a feed-forward neural
network (FFNN). We employ the self-consistent Born approximation to generate a
dataset of about $1.3 \times 10^5$ spectral functions. We show that for the
forward problem, both methods allow for the accurate and efficient prediction
of spectral functions, allowing for e.g. rapid searches through parameter
space. Furthermore, we find that for the inverse problem (inferring Hamiltonian
parameters from spectra), the FFNN can, but the KNN cannot, accurately predict
the model parameters using merely the density-of-state. Our results suggest
that it may be possible to use deep learning methods to predict materials
parameters from experimentally measured spectral functions.
