The Greenland ice sheet is a key contributor to global sea-level rise and ex- hibits strong seasonal and long-term melt dynamics. Understanding its be- haviour is crucial for climate predictions. This proposal outlines a research plan to model Greenland ice sheet melt using Physics-Informed Neural Net- works (PINNs). By integrating high-resolution observational datasets (ERA5, NSIDC, PROMICE, ICESat-2) with physical constraints, the project aims to pro- duce a predictive model that respects both data-driven patterns and govern- ing physical laws. The expected outcome is a validated framework capable of informing climate modelling and extrapolating the dynamics of ice sheets and glaciers.