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• Combined DFT+machine learning analysis was carried out for Pd-Zr-substituted ceria. • Relevant descriptors governing the vacancy formation energy were identified. • Palladium-vacancy distance was identified to be the most crucial factor. • Rationale behing Zr substitution was established. [Display omitted] Solid solutions of ceria are important catalytic materials with the reversible oxygen exchange as a key property governing their redox catalytic activities. Considering this important class of catalytic materials with an aim of developing insights and establishing the key variables governing the oxygen vacancy formation energy in Pd-Zr-substituted ceria solid solutions, machine learning-assisted DFT calculations were implemented in this study. A set of descriptors influencing the vacancy formation energy, including metal-vacancy and metal-metal distances, and partial charges on the ions in the system were identified. Theoretically generated oxygen vacancy formation energetics along with features of atomic distances, and charges on ionic species were chosen to train the random forest algorithm and make deductions on the influence of key variables on the vacancy formation energies. Our results from machine learning conclusively inferred the partial charge on Pd to be the most important factor influencing the vacancy formation energy in such solid solutions with the partial charge on Zr to play a supportive role. [ABSTRACT FROM AUTHOR]