Reasoning that the poor performance of homogeneous GNNs was related to inadequate representation of the physical interactions between dopants, we developed a UCNP representation based on a directed heterogeneous graph (Figure ). Unlike the homogeneous graphs, dopant-dopant interactions in our heterogeneous graphs are represented by interaction nodes that connect dopant nodes (via edges), allowing the encoding of additional physical features of the interactions. Two different types of interaction nodes are used, intra-layer and trans-layer, to delineate interactions between dopants within the same geometric region (i.e., core or shell domain) and those in different regions, respectively. It is important to note that dopant nodes are never connected to other dopant nodes, and every interaction node connects exactly two dopant nodes. A self-interaction node, describing interactions between different dopant ions of the same type in the same region, has edges both from and to the same dopant node. The use of a directed graph introduces asymmetry in energy transfer between two dopants (e.g. Yb → Er as compared to Er → Yb). This is important for energy transfer processes that are not reversible, such as non-resonant, phonon-assisted energy transfer that results in irreversible heat dissipation. When establishing features encoded in the nodes, we chose a minimal set of descriptors that are most relevant for UCNPs. Dopant node features include dopant type, dopant concentration (within the respective region), and geometric bounds (inner and outer radii of the core/shell domain they reside in). The interaction nodes contain the interaction type (e.g., Yb-Er, Er-Yb, Er-Er, . . . ) and features derived from the pair of connected dopant nodes -dopant concentrations and geometric bounds. Since we explore only spherical nanoparticles with multiple concentric shells, layer radii fully specify heterostructure geometry.