where N is the number of UCNPs, Îvis-UV is the predicted UV emission intensity, and I vis-U V is the actual emission intensity. Data Augmentation During training of the hetero-GNN model, we utilize data augmentation as discussed in Section 5. We augment our training data on-the-fly by subdividing the input UCNPs with additional random subdivisions each time an UCNP is seen during training. Subdivided layers retain the dopant composition of their original parent layer. For each UCNP input, we randomly subdivide each parent layer into up to 3 child layers in the augmented UCNP. The subdivision is inserted between 5-90% of the parent layer radii. Optimization For a nanoparticle with N control volumes, we can define the following bounds.