Accurate modeling of high-temperature creep in zirconium alloys is critical for nuclear applications, yet existing models often oversimplify dislocation-mediated mechanisms, particularly the role of jogs in screw dislocation motion—a key factor observed experimentally in transient and steady-state creep regimes. This work presents a physics-informed machine learning framework to calibrate a multi-mechanism creep model for zirconium, explicitly incorporating jogged screw dislocation dynamics. The model integrates: Multi-Mechanism Creep Model: The model encompasses various creep mechanisms in zirconium, including dislocation climb, dislocation glide, and Coble creep. A dominant creep map is provided to elucidate the contributions of each mechanism. Mechanistic formulation: A dislocation velocity law, derived from line tension theory, accounts for the effects of jog dragging and jog bypass. The mechanisms involving jogs are systematically evaluated across different temperatures and stress conditions. Data-driven optimization: A hybrid approach that combines global optimization techniques (utilizing neural networks and genetic algorithms) with experimental datasets. These datasets include steady-state creep rates and transient creep responses measured across a range of temperatures (623-923 K) and stresses (8-70 MPa). The framework establishes a quantitative relationship between external conditions (temperature and stress), jog height and length, stress dependence, and creep rate. Simultaneous alignment with both steady-state and transient data ensures the model's generalizability. This framework bridges microstructure-aware physical models with data efficiency of machine learning, offering a transferable paradigm for computationally robust material behavior prediction in extreme environments.