  Calculating polarizabilities of large clusters with first-principles
techniques is challenging because of the unfavorable scaling of computational
cost with cluster size. To address this challenge, we demonstrate that
polarizabilities of large hydrogenated silicon clusters containing thousands of
atoms can be efficiently calculated with machine learning methods.
Specifically, we construct machine learning models based on the smooth overlap
of atomic positions (SOAP) descriptor and train the models using a database of
calculated random-phase approximation polarizabilities for clusters containing
up to 110 silicon atoms. We first demonstrate the ability of the machine
learning models to fit the data and then assess their ability to predict
cluster polarizabilities using k-fold cross validation. Finally, we study the
machine learning predictions for clusters that are too large for explicit
first-principles calculations and find that they accurately describe the
dependence of the polarizabilities on the ratio of hydrogen to silicon atoms
and also predict a bulk limit that is in good agreement with previous studies.
