For the GPR model trained on the Ni Olmsted et al. dataset, we observe that the path from Σ7 to Σ3 is strictly downhill in energy in Figure while the geodesic paths between Σ3 and Σ5, Σ9, Σ11 are separated by energy barriers (Figures and). This indicates that for grain growth systems governed by GBE, it is possible that a Σ7 GB may transform into a Σ3 GB, if the mechanisms required to traverse this trajectory in the GB energy landscape are available (e.g. if both grain rotation and plane reorientation are possible, such as during high-temperature plastic deformation, recrystallization, or in nanocrystalline materials). In contrast, for a Σ5, Σ9, or Σ11 GBs to transform into Σ3 coherent-twins, either an energy barrier must be overcome, or a different (perhaps more circuitous) trajectory through the 5DOF space must be taken.