High-throughput screening. As shown in Figure for one example material, we first enumerate all possible inequivalent O-O paths in the crystal structure (up to 5 Å), then use d 2 GNN to predict {∆H pi } for all p, and finally assign the predicted activation energies to each possible symmetrically equivalent path in the migration path network. A critical aspect of our screening is the bootstrapped uncertainty metric, σ pi , which we use to eliminate materials with uncertainty above a chosen threshold. From hereon we only show materials predictions where the average uncertainty across all paths in a given material, {p}, is below a threshold, ⟨σ pi ⟩ {p} < 0.75 eV. Figure shows the distribution of all computed activation energies and vacancy formation enthalpies (∆H V = ∆H p {0,4} ) across these screened compounds, both of which are highly skewed. The raw screening data, including the high uncertainty predictions, also reveals anomaly/outlier predictions that can be readily identified as out-of-distribution materials with respect to our training data; these are therefore discarded on the basis of uncertainty (Supplementary Section 4). Our goal is then to predict the temperature-dependent oxygen vacancy diffusivity tensor, D, in a highthroughput manner to identify materials with useful (i.e., fast, slow, aniostropic) diffusivities and to elucidate relevant correlations between vacancy defect thermodynamics, kinetics, host stability, and chemistry. Given the va-cancy sites, their energies, the connectivity of sites, and transition state energies, the master equation for the diffusivity is solved directly at each temperature T . The direct solution, implemented in the open source Onsager software (), is more computationally efficient than a Monte Carlo approach, and accuracy is limited only by roundoff error. Using the d 2 GNN predictions, we can therefore obtain the temperature dependent oxygen vacancy diffusivity tensors, D T , for each screened material. Units for all reported diffusivity values are in cm 2 /s.