All of the runs mentioned in the preceding sections used uncorrelated uncertainties for all of the mechanisms analyzed. This is not reflective of the true system, especially for the case of linear scaling relations, where species share a very clear linear correlation with other species bound through the same atom. The covariance matrices for the DFT and LSR mechanisms were constructed using the BEEF-vdW ensembles mentioned previously. As described in Section 2.4.3, each of the equations in Section 2.2.1 were applied for all 2000 rows of the ensemble calculations, and then the covariance was calculated for each species from the resulting 2000 heats of formation. The resulting prior and posterior covariance matrices can be found in the supplementary data. The ML model could not be supplied with a covariance matrix.