  Raman spectroscopy is a powerful and nondestructive method that is widely
used to study the vibrational properties of solids or molecules. Simulations of
finite-temperature Raman spectra rely on obtaining polarizabilities along
molecular dynamics trajectories, which is computationally highly demanding if
calculated from first principles. Machine learning force fields (MLFF) are
becoming widely used for accelerating molecular dynamics simulations, but
machine-learning models for polarizability are still rare. In this work, we
present and compare three polarizability models for obtaining Raman spectra in
conjunction with MLFF molecular dynamics trajectories: (i) model based on
projection to primitive cell eigenmodes, (ii) bond polarizability model, and
(iii) symmetry-adapted Gaussian process regression (SA-GPR) using smooth
overlap of atomic positions. In particular, we investigate the accuracy of
these models for different systems and how much training data is required.
Models are first applied to boron arsenide, where the first- and second-order
Raman spectra are studied as well as the effect of boron isotopes. With MoS$_2$
we study the applicability of the models for highly anisotropic systems and for
simulating resonant Raman spectra. Finally, inorganic halide perovskites
CsPbBr$_3$ and CsSnBr$_3$ are studied with a particular interest in simulating
the spectra across phase transitions and the evolution of the central peak. All
models can be used to efficiently predict polarizabilities and are applicable
to large systems and long simulation times, and while all three models were
found to perform similarly for BAs and MoS$_2$, only SA-GPR offers sufficient
flexibility to accurately describe complex anharmonic materials like the
perovskites.
