Deep Graph Kernel Learning for Material & Atomic Level Uncertainty Quantification in Adsorption Energy Prediction

Abstract

Graph neural networks (GNNs) have emerged as powerful and efficient surrogates for computationally intensive density functional theory calculations and have greatly accelerated catalytic material discovery. However, their practical utility is often constrained by poor reliability and, critically, generalization to OOD chemical space. To address these challenges, we develop a deep graph kernel learning (DGKL) model, a scalable and versatile framework that integrates GNN backbones with the rigorous uncertainty quantification (UQ) of sparse variational Gaussian processes (SVGPs) for adsorption energy prediction. Compared to ensemble, evidential, and Monte Carlo dropout methods, DGKL consistently delivers better-calibrated uncertainties with competitive accuracy and fast inference. Across two benchmarks (CatHub and OC20) and two GNN backbones (SchNet and PaiNN), DGKL achieves superior calibration metrics (Expected Normalized Calibration Error: 0.06-0.10, Miscalibration Area: 0.04-0.07), strong error-uncertainty correlation (Spearman coefficient up to 0.51), and stable probabilistic fits. Furthermore, we present DGKL-Atomic, which provides atomic level UQ critical for controlling active learning sampling towards desired region of the chemical space. DGKL-Atomic shows excellent performance in detecting OOD samples (ROC-AUC: 0.84-0.88), and its atomic uncertainties correlate well with local structural novelty. Together, these methods enable calibrated, granular, and computationally efficient UQ to enhance active learning workflows and accelerating catalyst discovery.