## 1 Introduction
For physical methods, to attain effective forecasting results, information on a range of physical factors is needed, rather than information on just a single factor such as the wind speed time series; thus, these meteorological models cannot generate forecasts simply [15]. In addition, physical models are not proficient in dealing with short-term series and involve a complex calculation process and high expansion costs, which all contribute to significant forecasting errors [16]. Physical models necessitate the gathering of numerical physical variables, such as the horizontal pressure gradient, geostrophic force, and fractionate to undergo wind speed forecasting [17]. However, the complex calculation and polytrophic processes involved are not only time consuming but create the risk of forecasting error [18]. 2. With sufficient accessible spatial and temporal information from multiple wind farms, a few spatio-temporal prediction methodologies have been able to be investigated in recent studies. The spatio-temporal characteristics of wind speed are extracted by an undirected graph of wind farms [19]. A hybrid support vector machine forecasting model is proposed, which is based on the spatio-temporal and grey wolf optimization, to forecast wind power for multiple wind farms [20]. Ref. [21] uses copula theory and Bayesian theory to simulate spatio-temporal correlations between wind farms and deduce a conditional distribution of aggregated wind power. A probabilistic wind speed prediction approach was presented in Ref. [22] based on a spatio-temporal neural network (STNN) and variational Bayesian inference. With feeding of both the spatial and temporal information into the forecasting model, these methods have achieved a better forecasting performance. Nevertheless, most of these forecasting models often collected the wind speed information from different wind farms indiscriminately, and to some extent, the implicit spatial correlations cannot be fully exploited in the original wind speed data. Also, the thorny multi-dimensional computing problem caused by the large amount of wind speed data from multiple wind farms needs to be solved in an effective way. 3. Typical statistical methods can yield excellent forecasting results under the assumption that the input series was recorded under normal conditions [23]; however, nonlinearity, noise, instability, fluctuations, and other features within the raw time series are always difficult to control, resulting in a lack of modeling information. Therefore, such methods often result in bad short-term wind speed forecasting performance, especially in multistep-ahead forecasting [24]. In addition, historical data are utilized for statistical modeling methods, and only potential linear correlations between the variables and future forecasts are revealed; such models are unable to obtain a good forecasting performance within the required limits [25]. Statistical models, including typical autoregressive moving average family models (e.g., AR [26], MA, ARMA [27], autoregressive integrated moving average models (ARIMA) [28], SARIMA, etc. ), exponential smoothing [29], Kalman filtering [30], vector autoregression structures for very short-term wind power forecasting [31], and autoregressive conditional heteroskedastic family models (e.g., ARCH, GARCH, and EARCH) [32] utilize significant amounts of historical data for wind speed forecasting with no consideration of other potential influencing factors to support the stochastic process. Meanwhile, a spatial-temporal forecasting method based on the vector autoregression framework has been proposed for renewable forecasting [33]. Generally, statistical methods work well for approaching linear features; however, they tend to fail when it comes to nonlinear problems due to the linear assumptions of the models [34]. 4.