Predicting Precision: Equivariant Delta-learning and Uncertainty Quantification for High-Throughput DFT

Density Functional Theory (DFT) is a cornerstone of materials discovery, but running highly precise calculations requires expensive convergence testing for parameters like basis-set size and k-point density. To bypass this, we use $\Delta$-learning to predict the difference between fast, low-fidelity calculations and their converged, high-fidelity counterparts. Current machine learning models employed for similar tasks, however, are deterministic and often fail silently on out-of-distribution crystal structures. We introduce a framework that integrates Uncertainty Quantification directly into an $E(3)$-equivariant graph neural network to predict these $\Delta$-corrections. By conditioning the network on the low-fidelity DFT settings using Feature-wise Linear Modulation (FiLM), our model adapts to the specific physical approximations made. We evaluate our approach on a newly generated dataset of over 60,000 multi-fidelity relaxations for 4,220 binary semiconductors. The framework not only acts as a highly accurate error-corrector, outperforming heavily tuned Random Forests, but also functions as a zero-cost recommender system that predicts calculation errors and recommends what settings to use before the calculations are run. Finally, we show that Deep Ensembles and latent-space distance metrics provide explicit out-of-distribution detection, allowing the model to flag its own catastrophic errors and ensure out-of-distribution reliability for high-throughput screening.