Physics-Informed Vector LSTM for Multi-Horizon Hub-Height Wind Speed Forecasting Across Multiple Sites

Accurate hub-height wind-speed forecasting is a prerequisite for the safe and economical integration of wind power into the electricity grid, because forecasting errors propagate directly into imbalance penalties, reserve sizing, and turbine wear, and short-term predictions (one to twenty-four hours ahead) are of direct operational value. The literature on wind-speed and, more broadly, multivariate time-series forecasting has advanced through three overlapping waves, namely classical statistical and physical models, shallow machine-learning regression, and deep sequence models, which share a common trajectory of replacing hand-crafted meteorological relationships by data-driven estimators. Four shared limits recur across this work: deep architectures treat covariates as exchangeable tokens and under-use the physically grounded relationships among synchronous variables; they optimize pure accuracy without a mechanism that keeps the forecast physically consistent with the atmosphere; evaluations concentrate on generic benchmarks where the short-term optimum is often a linear or persistence baseline, so the benefit of complex inductive biases at operational horizons is unclear; and wind-speed studies seldom isolate an explicit physical prior from the recurrent or attention backbone. This work contributes (a) a reproducible multi-site benchmark of eight forecasting strategies, namely persistence, ARIMA, gradient-boosted trees, a plain LSTM, and four further deep architectures including PatchTST, DLinear, iTransformer, and the proposed physics-informed PIV-LSTM, evaluated at five horizons on four real sites; (b) a physics-informed vector (PIV) that augments the network input with an ordinary-least-squares linear reconstruction of the target from its known covariates, and regularizes training with a decaying consistency loss, implemented on an LSTM backbone (PIV-LSTM); and (c) an ablation that quantifies where the physical prior helps and where it does not, together with an honest assessment of the results, including where a classical model remains competitive and the long-horizon regime in which every model loses skill.