Extrapolating the properties of lattice polarons with Machine Learning

Predicting a phase transition for condensed matter systems can be a relatively easy task for Machine Learning methods if they are trained with data from both phases. On the contrary, predicting a phase transition with only training data from one of the phases is challenging.
We illustrate the use of Gaussian processes (GPs) to discover phase transitions only with data from only one of the phases.
GPs can also be used for extrapolation if a complex kernel function is used. We construct the kernel function by iteratively adding and multiplying simple kernels and selecting the kernel combination with the highest marginal likelihood.
As an example, we consider the change in the ground state momentum in the single polaron of the Su-Schrieffer-Heeger (SSH) model as a function of the electron-phonon coupling strength. We show that GPs trained in the weak coupling regime and before the phase transition are capable of discovering the change in the ground state momentum.