In recent years we have seen an explosion of interest in the use of machine learning to tackle problems arising in environmental applications. Such environmental models involve complex PDE models that are partly known, multiple length scales (many of which are unresolvable), with huge size of the data and various uncertainties. To address these challenges, we employ the extraordinary modelling capability of DL techniques to both complement, and be informed by, physical models.

In particular (physics inspired) deep learning generative models can be used to emulate physical processes at a sub-grid scale level in order to provide parametrisations of these which can be fed into the dynamical simulations. Maths4DL will be studying ways of making such DL based parametrisations faster, more accurate and robust. One area of application will be the modelling of clouds in the sky. Another application is in down scaling, which can provide more detailed forecasts at a sub grid level by using data from dynamical simulations as input. Examples might be the forecasting of local rainfall or wind, with applications (for example) to the energy industry.

A more ambitious project is to use data driven DL to replace the dynamical models themselves. This has been shown to work well for short (2 hours) now casts, and for longer seasonal forecasts. The question remains whether data driven methods will replace model based methods for ‘traditional’ weather forecasts over one to five days.