Investigating the impact of model formulation on the accuracy andefficiency of a hybrid dynamical core with online training.

Data-driven algorithms provide an exciting opportunity to represent unresolved, and therefore parameterised, processes in a way that matches available data without the need to `hand-tune' the parameterisation. However, on their own they suffer from issues with accurate prediction of extreme events and long-term trends, at least in part due to their lack of any representation of physical constraints. Hybrid weather and climate prediction models address this issue by combining data-driven algorithms with more traditional algorithms based on solving the partial differential equations (PDEs) that govern atmospheric flow. However, training the data-driven component separately from the PDE solver can introduce issues with stability and still does not ensure that the combined model will not drift over long times. Online training addresses this issue by more tightly coupling the two model components during training. This requires that the PDE model is differentiable so that during training backpropagation can be performed on multiple timesteps of both the PDE solver and the data-driven component. In this work we introduce a compatible finite element dynamical core that is automatically differentiable since it is built using the Firedrake finite element library. Here we will show how this can be coupled to PyTorch to perform end-to-end training on idealised test cases.