Reduced-Order Modelling of Stochastically Forced Zonal Jets using a 'Stochastic Latent Transformer'

We present the 'Stochastic Latent Transformer', a probabilistic Deep Learning approach for producing reduced-order models for stochastic nonlinear PDEs. It captures stochastic dynamics by considering temporal correlations and forced noise - producing a state-dependent adaptive weighting of the contribution of the noise. Applied to model zonal jets, using a quasi-geostrophic model with stochastically parameterised turbulent eddies, it achieves a speed-up of several orders of magnitude over numerical integration. This allows for the cost-effective generation of large ensembles, allowing the study of properties of the physical system, such as characterising spontaneous transition events, in a manner prohibitively expensive with conventional methods.