In recent years, deep learning models have rapidly emerged as a standalone alternative to physics-based numerical models for medium-range weather forecasting. Several independent research groups claim to have developed deep-learning weather forecasts which outperform those from state-of-the-art physics-basics models. Thus, operational implementation of data-driven forecasts appears to be drawing near. However, some questions remain on the capabilities of deep learning models to provide robust forecasts of extreme weather. The predictions generated by leading deep learning models appear to be oversmooth, tending to underestimate the magnitude of extreme weather events such as windstorms and cold spells. The aim of this project is to i) evaluate the performance of state-of-the-art deep learning models in relation to weather extremes ii) Propose and test meaningful improvements to existing models, to improve performance in relation to near-surface weather extremes.