Modelling high-resolution spatio-temporal wind with deep echo state networks and stochastic partial differential equations

In the past decades, clean and renewable energy has gained increasing attention due to a global effort on carbon footprint reduction. In particular, Saudi Arabia is gradually shifting its energy portfolio from an exclusive use of oil to a reliance on renewable energy, and, in particular, wind. Modelling wind for assessing potential energy output in a country as large, geographically diverse and understudied as Saudi Arabia is a challenge which implies highly non-linear dynamic structures in both space and time. To address this, we propose a spatio-temporal model whose spatial information is first reduced via an energy distance-based approach and then its dynamical behaviour is informed by a sparse and stochastic recurrent neural network (Echo State Network). Finally, the full spatial data is reconstructed by means of a non-stationary stochastic partial differential equation-based approach. Our model can capture the fine scale wind structure from a high-resolution simulation and produce more accurate forecasts of both wind speed and energy in lead times of interest for energy grid management.