When the hetero-GNN is trained using on-the-fly-augmentation, its performance improves by 23% on the ID test set (with error falling from 13.8 cps to 10.6 cps) and by 25% on the OOD test set (with error falling from 22.1 cps (2.3%) to 16.5 cps (1.7%)). Additionally, we validated that this augmentation scheme actually trains the model to learn subdivision invariance by evaluating the vector distance between the representation of nanoparticles and their subdivided analogs, observing that the augmented hetero-GNN model more closely represented the subdivided UCNPs in the ID and OOD test sets in embedding space than the nonaugmented model across a range of subdivisions (Figure ). These results underscore the importance of considering subdivision invariance in model training.