  Feasibility of accurate quantum calculations is often restricted by the
dimensionality of the truncated Hilbert space required for the numerical
computations. The present work demonstrates Bayesian machine learning (ML)
models that use quantum properties in an effectively lower-dimensional Hilbert
space to make predictions for the Hamiltonian parameters that require a larger
basis set as applied to a classical problem in quantum statistical mechanics,
the polaron problem. We consider two polaron models: the Su-Schrieffer-Heeger
(SSH) model and the mixed SSH-Holstein model. We demonstrate ML models that can
extrapolate polaron properties in the phonon frequency. We consider the sharp
transition in the ground-state momentum of the SSH polaron and examine the
evolution of this transition from the anti-adiabatic regime to the adiabatic
regime. We also demonstrate Bayesian models that use the posterior
distributions of highly approximate quantum calculations as the prior
distribution for models of more accurate quantum results. This drastically
reduces the number of fully converged quantum calculations required to map out
the polaron dispersion relations for the full range of Hamiltonian parameters
of interest.
