Modeling High-Resolution Spatio-Temporal Wind with Deep Echo State Networks and Stochastic Partial Differential Equations

TL;DR

This work tackles high-resolution spatio-temporal wind forecasting for Saudi Arabia by decoupling temporal dynamics and spatial structure: a deep, sparse Echo State Network models nonlinear temporal evolution at a reduced knot set, while a non-stationary SPDE reconstructs the full field with a Gaussian Markov random field representation. Spatial reduction is achieved via energy-distance–based support points, enabling scalable interpolation through SPDE; temporal dynamics are learned with a deep ESN whose outputs are ridge-estimated, and forecasts are batch-updated to balance accuracy and computation. The approach yields improved wind speed forecasts and, via hub-height extrapolation and turbine power curves, wind-power predictions with quantified uncertainty, delivering substantial potential cost savings over competing methods. The methodology demonstrates strong scalability to large domains and provides a framework for uncertainty-aware operational wind forecasting and grid planning.

Abstract

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. Modeling 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 behavior 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 and produce more accurate forecasts of both wind speed and energy in lead times of interest for energy grid management and save annually as much as one million dollar against the closest competitive model.

Figures (14)

• Figure 1: (a) Mean and (b) standard deviation of the WRF simulated hourly wind speed (m/s) over Saudi Arabia from 2013 to 2016. The N and S are the two sample locations (marked in black crosses) used to compute the diagnostics in Figure \ref{['FS2_acf']}.
• Figure 2: Computation time for inference and forecasting (three-hour ahead) of the ESN model \ref{['eqn:ESN']} as a function of the number of hidden state dimension $n_h$ for a small (panel (a)) and a large (b) number $n_{\text{red}}$ of knots. Panel (c) show the trade-off between prediction efficiency and computation complexity as a function of the batch size for forecasting; the order of the x-axis is reversed to show the increasing trend of computation time against the frequency of updates.
• Figure 3: Location-wise relative forecasting errors between ESN and B-ESN for up to three-hour lead ahead averaged across time. A positive number means that the B-ESN is better.
• Figure 4: (a): Histograms of the absolute differences between the predicted wind power and the true wind power obtained from our B-ESN against ESN, B-ESN-L and PER. (b): Forecast quantiles against annual sum of the absolute differences between the B-ESN wind power predictions and the true wind power.
• Figure S1: Auto-correlation function for $\hat{\mathbf{Y}}^{\text{trend}}_t(\mathbf{s}_i)$ (first row) and $\hat{\mathbf{Y}}^{\text{trend+time}}_t(\mathbf{s}_i)$ (second row), where the subscript refers to the N and S indicated as black crosses in Figure \ref{['fig:wind_data']}.