In addition to validating established domain knowledge, the extrapolated results from hetero-GNN optimization provide the opportunity to understand the behavior of complex UCNPs with a greater number of shells than can be readily synthesized or simulated. For example, a major unanswered question is the optimal number of layers for a UCNP, e.g., are more layers better? The optimization matrix in Figure suggests that for smaller particles (below 10 nm radius), moving beyond 2-3 layers does not substantially improve the brightness, most likely because the shell thicknesses would be thinner than characteristic energy transfer distances. However, larger UCNP heterostructures (r ¿10 nm) do see benefit from complex many-shell architectures, with the brightest 14-and 15-nm UCNPs having 7 and 10-shells, respectively. These manyshelled structures also suggest novel strategies to enhance upconversion efficiency. The most striking characteristic of the optimized 12-, 14-, and 15-nm UCNPs (Fig. .ii-iv) is their interleaving of multiple layers of Nd-and Er-rich shells. Rather than converging on one large layer of Nd sensitizer, the optimized 12-nm UCNP sandwiches a layer of Nd sensitizer between two layers of Er activator (with the appropriate Yb buffer layers, as in Figure .ii), while the brightest 15-nm UCNP exhibits the inverse arrangement (Figure .iv). This sandwich shell arrangement allows energy transfer to occur from two sizes, maximizing the number of donors or acceptors within a given distance while minimizing concentration quenching in those outer shells. Curiously, the 14-and 15nm-radius UCNPs also exhibit motifs in which two Nd-rich shells are separated by an intermediate shell of less concentrated Nd. It is unclear what advantage this motif provides. It is possible that UCNPs may be relatively insensitive to variations near their core (where this motif is observed) since the fraction of dopants is relatively small compared to those in outer shells. This argument may also explain the curious dearth of dopants in the core of the 15-nm UCNP. All of these intriguing structural design motif predictions must be verified and investigated more thoroughly through future experiments (preferably with the aid of precision automated synthesis ) and mechanistic analysis of energy transfer pathways from kMC simulations that the hetero-GNN cannot report on.