  Interacting defect systems are ubiquitous in materials under realistic
scenarios, yet gaining an atomic-level understanding of these systems from a
computational perspective is challenging - it often demands substantial
resources due to the necessity of employing supercell calculations. While
machine learning techniques have shown potential in accelerating materials
simulations, their application to systems involving interacting defects remains
relatively rare. In this work, we present a comparative study of three
different methods to predict the free energy change of systems with interacting
defects. We leveraging a limited dataset from Density Functional Theory(DFT)
calculations to assess the performance models using materials descriptors,
graph neural networks and cluster expansion. Our findings indicate that the
cluster expansion model can achieve precise energetics predictions even with
this limited dataset. Furthermore, with synthetic data generate from cluster
expansion model at near-DFT levels, we obtained enlarged dataset to assess the
demands on data for training accurate prediction models using graph neural
networks for systems featuring interacting defects. A brief discussion of the
computational cost for each method is provided at the end. This research
provide a preliminary evaluation of applying machine learning techniques in
imperfect surface systems.
