Using the composition information for each of the 12,178 data points, we have computed the pairwise EMD matrix of compositional distances; table gives the statistical results of models trained using composition alone as well as combined with GRID. Combining compositional and structural information gives the optimum bulk modulus prediction, achieving a minimum MAE of 18 GPa (Fig. ). This approaches the state-of-the-art literature value (~10 GPa), but using a much simpler nearest neighbour model. Using EMD as a metric gives better predictions than cosine distance, particularly for composition comparisons. The predicted and DFT-calculated values using combined GRID and composition distances are shown in Fig. . From this and the results in table 1, it is apparent that while most predictions are close to the ground truth value, a few significant outliers give the resulting large MAEs; indeed, the median absolute error is only 9 GPa, comparable to the state-of-theart model. Similar plots when fitting GRID or compositional similarity alone give a much broader spread around x = y (Fig. ). It might be assumed that these most erroneous points arise due to the small number of points with high bulk modulus, however, there seems to be little correlation between the prediction error for a material and the distance to its nearest neighbour (Fig. ). Interrogating this further, the maximum prediction error occurs for two anti-perovskite materials: BiAsSr3 (KDFT = 575 GPa, Fig. ) and BiPSr3 (KDFT = 30 GPa, Fig. ). These two structures are near-identical, and As and P are chemically very similar; it is unclear why these two (theoretical) materials should give such different bulk moduli, especially as the shear moduli are equivalent at 17 GPa and 22 GPa, respectively. This may point to irregularities within the bulk modulus data used to train the models, or alternatively suggest that accurate bulk modulus prediction requires information beyond structure and composition, such as detailed knowledge of the electron distribution.