Turbulent exchanges between sea ice and the atmosphere are known to influence the melting rate of sea ice, the development of atmospheric circulation anomalies and, potentially, teleconnections between polar and non-polar regions. Large model errors remain in the parametrization of turbulent heat fluxes over sea ice in climate models, resulting in significant uncertainties in projections of future climate. Fluxes are typically calculated using bulk formulae, based on Monin-Obukhov similarity theory, which have shown particular limitations in polar regions. Parametrizations developed specifically for polar conditions (e.g. representing form drag from ridges or melt ponds on sea ice) rely on sparse observations and thus may not be universally applicable. In this study, new data-driven parametrizations have been developed for surface turbulent fluxes of momentum, sensible heat and latent heat in the Arctic. Machine learning has already been used outside the polar regions to provide accurate and computationally inexpensive estimates of surface turbulent fluxes. To investigate the feasibility of this approach in the Arctic, we have fitted neural-network models to a reference dataset (SHEBA). Predictive performance has been tested using data from other observational campaigns. For momentum and sensible heat, performance of the neural networks is found to be comparable to, and in some cases substantially better than, that of a state-of-the-art bulk formulation. These results offer an efficient alternative to the traditional bulk approach in cases where the latter fails, and can serve to inform further physically based developments.