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The energetics of hydrogen absorption in C15 cubic and C14 hexagonal TiCr2Hx Laves phases is investigated for 0 x 6 with density functional theory (DFT) and machine learning interatomic potentials (MLIPs). The MLIPs are trained with configurations generated through a series of active-learning schemes. Basin-hopping Monte Carlo (BHMC) simulations based on the MLIPs predict minimum-energy hydrogen configurations, along with enthalpies of formation and hydrogen orderings. The obtained phase transformations at 0 K agree well with the experiments at low temperatures. The hydrogen solubility limits in the low-concentration phases at 0 K are predicted to be x = 1.0 and x = 1.5 for the C15 and the C14 phases, respectively. At these concentrations, C15 TiCr2H shows the monoclinic symmetry, while C14 TiCr2H1.5 shows the orthorhombic symmetry, both of which have not been reported for this system. The first and the second hydride phases, i.e., and , at 0 K are found around x = 3 and x = 4, respectively, for both the C15 and the C14 phases. In the second-hydride phases, C15 TiCr2H4 shows the tetragonal symmetry, while C14 TiCr2H4 shows the rhombohedral symmetry. Hydrogen repulsions are found to extend to edge-sharing interstices, affecting the hydrogen ordering. Furthermore, the 6h2 A2B2 interstices are found to be energetically substantially more preferable for C14 TiCr2Hx than the other A2B2 interstices at low hydrogen concentrations, influencing the hydrogen-occupation trend.