Graph neural networks on ideal lattices. Highthroughput configurational sampling is often needed for thermodynamic property predictions in solid solution materials; therefore, a DFT surrogate model that can predict, for example, relaxed formation energies from a trivial-to-generate crystallographic representation is critical. In the case of the cubic FCC lattice (or BCC, HCP, etc.), the idealized crystal representation, X FCC , is defined by the elemental identify of each lattice site at its ideal fractional coordinate (Figure ). The energy of the DFT-relaxed crystal structure, X DFT , with respect to possible decomposition products yields the desired prediction target: the formation energy, E f,DFT . A useful model for ML-accelerated calculation of thermodynamic properties must utilize X FCC as input (if X DFT is known, then so is E f,DFT and the model is moot).