A physics-informed temporal convolutional network-temporal fusion transformer hybrid model for probabilistic wind speed predictions with quantile regression

Accurate wind speed prediction is crucial for mitigating the adverse effects of wind variability on power systems and facilitating the integration of wind energy into the grid. However, existing interval prediction studies often overlook the guidance from physics information and have not yet revealed the influence of physical constraints on interval prediction accuracy. This study presents two significant advances in probabilistic wind forecasting: First, we develop a novel physics-informed TCN-TFT hybrid model that uniquely integrates dilated causal convolutions (for multi-scale temporal feature extraction) with transformer-based attention mechanisms (for variable importance weighting), while enforcing physical consistency through Bernoulli's principle and the ideal gas law. Second, we introduce a joint optimization framework that minimizes quantile loss for uncertainty estimation and physics-based loss for meteorological consistency. Experimental results indicate that the proposed model outperforms comparative methods among four datasets, achieving lower PINAW and coverage width-based criterion (CWC) values while maintaining similar PICP values. For instance, in the two-step wind speed interval forecasting of dataset1, the PICP values achieve 0.986, 0.953, and 0.898, with corresponding PINAW values of 0.329, 0.247, and 0.214 for confidence levels of 0.95, 0.9, and 0.85, respectively. Furthermore, physical constraints enhance prediction interval reliability by boosting coverage (5.0 % PICP) with a modest width increase (27.1 % PINAW), outperforming unconstrained models that exhibit 320 % higher CWC due to coverage deficits. Overall, this novel approach effectively quantifies uncertainty in wind speed forecasts, demonstrating its potential for improved reliability in wind energy applications.