Data-Driven Parameterisations for the Multiscale Lorenz 96 System

Data-driven parameterisations offer a promising route to improving the representation of unresolved processes in geophysical models. In this work, the two-timescale Lorenz 96 system is used as a controlled testbed to systematically compare deterministic, stochastic, and memory-aware machine-learning closures. A range of architectures are implemented, including multilayer perceptrons, convolutional networks, recurrent models, and conditional generative approaches, and are evaluated in both offline and online settings using weather-style forecast metrics and long-term climatological diagnostics. The results show that models incorporating physically motivated inductive biases, such as stochasticity, spatial structure, or temporal memory, outperform simpler deterministic and memoryless closures. In particular, stochastic generative models and recurrent networks better reproduce regime behaviour, spatio-temporal correlations, and long-term statistics, highlighting the importance of representing intrinsic variability and non-Markovian effects. Ongoing and future work will extend this framework to more realistic dynamical systems, including quasi-geostrophic and primitive-equation models, with a focus on enforcing physical consistency, incorporating explicit memory effects, and developing hydrid physics-machine learning closures.