DeepMIDE: A Multi-Output Spatio-Temporal Method for Ultra-Scale Offshore Wind Energy Forecasting

TL;DR

This work tackles ultra-scale offshore wind forecasting by introducing DeepMIDE, a multi-output integro-difference equation framework that models wind speeds across space, time, and height. It embeds a transformer-based physics extractor to learn advection vectors from high-dimensional exogenous weather maps, feeding a nonstationary kernel k^{(pq)} that captures height- and time-varying dependencies. Inference is performed with a Kalman filter to yield probabilistic forecasts, and extensive experiments on NY/NJ Bight data show consistent improvements in both wind speed and wind power forecasts over a range of horizons and heights. The approach enables robust, physics-informed short-horizon forecasts essential for operation and planning of ultra-scale offshore wind farms, while maintaining probabilistic quantification and computational practicality for online use.

Abstract

To unlock access to stronger winds, the offshore wind industry is advancing towards significantly larger and taller wind turbines. This massive upscaling motivates a departure from wind forecasting methods that traditionally focused on a single representative height. To fill this gap, we propose DeepMIDE--a statistical deep learning method which jointly models the offshore wind speeds across space, time, and height. DeepMIDE is formulated as a multi-output integro-difference equation model with a multivariate nonstationary kernel characterized by a set of advection vectors that encode the physics of wind field formation and propagation. Embedded within DeepMIDE, an advanced deep learning architecture learns these advection vectors from high-dimensional streams of exogenous weather information, which, along with other parameters, are plugged back into the statistical model for probabilistic multi-height space-time forecasting. Tested on real-world data from offshore wind energy areas in the Northeastern United States, the wind speed and power forecasts from DeepMIDE are shown to outperform those from prevalent time series, spatio-temporal, and deep learning methods.

Figures (9)

• Figure 1: (a) Locations of the three sites, E05N, E06, and ASOW6, on top of the offshore wind energy areas in the NY/NJ Bight. The background map is generated using the Northeast Ocean Data Portal map; (b) Wind rose plot for the wind speeds, averaged over space and height; (c) The empirical temporal covariogram of wind speeds at multiple heights (different colors) and locations (different markers); (d) Time series of wind speeds at all locations (different colors) and heights (different markers), showing strong spatial, temporal, and vertical dependencies.
• Figure 2: Spatial weather maps from RU-WRF (wind speed at 100/140/180m, sea-surface temperature, humidity, and pressure) on June 11th, 2021 at 8:00 GMT on top of the planned offshore wind energy areas (denoted by dashed polygons) in the NY/NJ Bight. Red stars denote the spatial locations where local measurements are available.
• Figure 3: Asymmetry in space-time dependencies, versus the time lag in hours, for different heights (different columns). The top and bottom rows represent weak and strong wind regimes, respectively. Different colors denote different pairs of locations.
• Figure 4: Illustration of the DeepMIDE framework. During both offline and online training, the inputs to the network are the exogenous image streams $\mathbf{X}_t$ (e.g., Pressure, Temperature, etc) (offline $t \in 1, \hdots \tau$; online $t \in {\tau + 1, \hdots, T+h}$). In the offline phase, the network parameters $\boldsymbol{\Phi}$ are learned jointly with other statistical parameters $\boldsymbol{\Omega}$ by maximizing the likelihood $\mathcal{L}(\mathcal{Z}|\boldsymbol{\Omega}, \boldsymbol{\Phi})$. For the online phase, the deep learning model will be frozen, the network parameters $\boldsymbol{\Phi}$ are fixed and the statistical parameters $\boldsymbol{\Omega}$ will be continuously updated in light of new data. The structure of the deep CNN-based AlexNet is shown to the right. The transformer model architecture, along with more details about the deep learning model, are deferred to the supplementary material document appended to this manuscript.
• Figure 5: (a) MAE versus the forecast horizon for all models. (b) CRPS versus the forecast horizon for all models (excluding PER due to poor performance for probabilistic forecasts).