Fig. 1. DEED for a disordered system.

a, DEED workflow. ⟨ΔH_hull⟩ and σ⁻¹ are calculated as the average distance of the POCC-tile energies to the convex hull and the spread (variance) of the POCC-tile energies, respectively. b, cPOCC workflow. The POCC expansion of a M₁₀C₅N₅ rock salt composition would require 17.5 million 20-atom tiles. This is overcome by a partition into M₅C₂N₃ and M₅C₃N₂ subsystems, each giving 490 unique ten-atom tiles and the subsequent energy convolutions. This cPOCC algorithm and its benchmarks are described in the Methods section.