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Learning Reduced-Order Stochastic Dynamics using Deep Learning to study Zonal Jets.

This PhD project is ongoing research and will extend my previous study which looked at encapsulating the dynamics of a simplified model of atmospheric circulation by using a neural network to find a reduced-order-model of the system.

Seasonal and longer-term prediction of mid-latitude weather and climate remains a major challenge due to the complexity of the mechanisms that drive the dynamics as well as their chaotic nature. While Machine Learning has emerged as a powerful tool for identifying patterns in datasets and increasingly has been applied to the field of fluid dynamics to either provide insight into or to attempt to model fluid flows. We look to provide both by using deep neural networks to provide a reduced-order model of the Beta-Plane approximation - a barotropic, stochastically forced turbulent flow on a Beta-plane - that provides an analogue for tropospheric mid-latitudinal dynamics, describing European weather, yeilding two key questions:

(i) Can ML be used to emulate improved stochastic parameterisation schemes

(ii) Can machine learning (ML) be used to better understand the variability exhibited in models of atmospheric circulation?

The system lies on a 2D plane, with the lack of baroclinicity due to the absence of stratification resulting in the requirement for small-scale eddies, that generate turbulence, to be parameterised by a stochastic forcing. The idealised model allows us to study the formation of zonal jets and their variability, with the formulation of a reduced-order model providing insight into the underlying dynamical mechanisms.

We utilise methods in manifold learning and adversarial training to learn the system dynamics using a stochastic neural network - accounting for the nature of the underlying system. The Neural Network is able to capture the formation of the zonal jets, as well as their variability, with the ensemble of predictions showing a similar spread of dynamics to that of the numerical integrations, with the neural network producing an emulation of the system ~50000 times faster than the numerical integration.

As the underlying system is non-deterministic, model verification is evaluated between an ensemble of predictions from the deep learning model, obtained by sampling in the latent space of the model, and an ensemble of numerical integrations with different realisations of noise - with information gained from both the size of the neural network’s latent space as well as the information within it, enabling for the exploration of this newly defined state-space, yielding insight into the dynamics of the system.

Jets

The above image shows Latitude-Time plots of Zonal wind showing an ensemble of numerical integrations, each with different realisations of the stochastic forcing, with identical intial condtions (up to the the dotted line) and an ensemble of 8 predictions made our Neural Network, with the same initial conditions (up to the dotted line), sampling noise differently in the systems's latent space.

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