In this work, we employed MACE, an equivariant message-passing graph tensor network with two message-passing layers, each featuring a 6 Å cutoff radius. This effectively results in a 12 Å cutoff in MACE, corresponding to the number of layers multiplied by the cutoff distance in each layer . The initial MACE model was trained and further refined through an active-learning (AL) protocol, which integrates data generation with the sampling process, as illustrated in Figure . The initial training set consisted of DFT-calculated structures, including dimers with varying bond lengths, and rutile and anatase TiO2 bulk configurations. This set included both fully optimized unit cells and supercells with fixed lattice constants, where the internal coordinates were either optimized or purposefully displaced. Additionally, bulk supercells with random oxygen vacancies and 40 inequivalent low-index surface configurations (20 rutile and 20 anatase) derived from bulk truncations were included.