Reliable boundary-layer turbulence parametrizations for polar conditions are needed to reduce uncertainty in projections of Arctic sea ice melting rate and its potential global repercussions. Surface turbulent fluxes of sensible and latent heat are typically represented in climate models using bulk formulae based on the Monin-Obukhov Similarity Theory (MOST), sometimes finely tuned to high stability conditions and the potential presence of sea ice. In this study, we test the performance of new, machine-learning (ML) flux parametrizations, using an advanced polar-specific bulk algorithm as a baseline. Neural networks, trained on observations from previous Arctic campaigns, are used to predict surface turbulent fluxes measured over sea ice as part of the recent MOSAiC expedition. The ML parametrizations outperform the bulk at the MOSAiC sites, with RMSE reductions of up to 70 percent. We provide a plug-in Fortran implementation of the neural networks for use in climate models.