Finally, It should be noted that Monte Carlo methods are a taxing way to optimize a model and quantify error. While this study does show the computational e ciency of using a ML calculator to replace DFT, exploring the uncertainty space of the resulting model was costly. Specifically, the chain length required for convergence on each model (approximately one million points) took 52 CPU cores approximately 3 days of computing time. In light of this, it would be impractical to run BPE for every point within a screening study. It is more important to apply it to experimental data that are well known, and then using the error bars obtained to extrapolate to di↵erent systems.