Modeling the dynamics of Greenland and Antarctic ice sheets is critical for computing projections of sea-level rise. In this talk, I will provide a brief overview of ice-sheet modeling. I will then focus on approaches to accelerate the quantification of the uncertainty in projections of ice-sheets mass loss, which is a proxy for sea-level rise. Specifically,  I will describe a multi-fidelity strategy for uncertainty quantification. Given a hierarchy of computational models with different fidelities and costs, the multi-fidelity strategy allows to optimally sample the models of different fidelities to minimize the cost  of the analysis for a target accuracy. Our lower fidelity models are obtained by solving the high-fidelity model on coarser meshes or by simplifying the physics described by the models. An alternative approach is to build a surrogate (e.g., neural network based) of the high-fidelity model. In this context, we developed a hybrid ice-sheet model where momentum equations, the most expensive part of an ice-sheet model, are approximated with Deep Operator Networks. In order to demonstrate these approaches, I will show results targeting the evolution of the Humboldt Glacier in Greenland.