Unveiling nonlinear descriptors via hierarchical learning for single-atom catalysts

Single-atom catalysts (SACs) hold great promise for CO-selective NO reduction (CO-SCR) due to their maximal metal atom utilization and the tunable adsorption of reactants and intermediates. However, optimizing SACs remains a major challenge because it requires a delicate balance of adsorption strengths, which are governed by complex atomic-scale interactions. Here, we combine first-principles calculations with interpretable AI to systematically investigate over 200 transition metal (TM)-doped metal oxides for CO-SCR using a hierarchical learning workflow, which delivers both higher training accuracy and better predictive performance than the conventional nonhierarchical approach. Through thermodynamic screening, we significantly reduce the candidate pool to 20 promising SACs and ultimately identify Mn-doped $\mathrm{Zr}{\mathrm{O}}_{2}(111)$ as the most effective catalyst based on both thermodynamic and kinetic criteria. While no single catalyst feature shows a direct correlation with activity, our hierarchical learning approach uncovers nonlinear combinations of features, such as $d$-band center, atomic radius, and charge state, that reliably predict performance. In addition, subgroup discovery data mining reveals physically meaningful strategies for optimizing catalytic properties. This work demonstrates the value of integrating first-principles theory with hierarchical learning to accelerate the discovery of efficient catalysts for environmentally important reactions.