A physics-informed neural network framework for ice-water two-phase temperature reconstruction and interface inversion in Arctic sea ice

Accurate characterization of temperature fields and ice thickness evolution is critical for the rapidly changing Arctic sea ice system, when field-based buoy observations remain limited. Building on weak solution theory and solvability analysis for the coupled ice-water two-phase system, a physics-informed neural network (PINN) framework was developed for forward simulation and interface inversion of a Stefan free-boundary problem. The proposed approach enabled the simultaneous reconstruction of temperature fields in phases and identification of the interface trajectory. Methodologically, the framework combined rigorous theoretical analysis, a PINN implementation consistent with physical constraints, and observation-driven validation, thereby providing a systematic procedure for temperature field reconstruction and physically consistent inversion in ice-water two-phase Stefan free-boundary inverse problems. Validation proceeded from equivalent-flux benchmarks to fully coupled two-phase simulations. In the equivalent-flux stage, the water-phase impact on the ice was parameterized by a time-varying equivalent oceanic heat flux. With a three-stage training strategy and a multiplicative correction factor for the conductive flux, the ice temperature error was below 0.5 ℃, and the absolute thickness error was under 2.5 cm. In the coupled stage, hard enforcement of the boundary conditions further stabilized convergence, keeping temperature errors below 0.3 ℃ in both phases and limiting the absolute thickness error to at most 4 cm. These results demonstrated that a physics-constrained PINN can deliver stable and accurate two-phase thermodynamic inversion from limited observations, and they motivate extensions toward a unified atmosphere-snow-ice-ocean inversion framework.