Using machine learning to improve simulations of a dynamical system

This project addresses the question of whether we can use machine learning to improve our ability to simulate and predict complex dynamical systems like the Earth's atmosphere and oceans. Lorenz96_and_neural_networks.ipynb is a Jupyter notebook illustrating a way to use machine learning algorithms to improve the simulation of complex dynamical systems. The basic idea is to train algorithms to correct the errors of existing models - reasons for doing it this way are that we get to keep the physical understanding embedded in our current models, and it will be much easier to train algorithms to give an error correction rather than simulating the entire system (although, a suitably well-funded programme may still be able to achieve the latter). Lorenz96_NN_preprint.pdf is a pre-print of a paper I have submitted describing this idea and the numerical experiments in more detail.