Adaptive Ensemble Weight Optimization for Natural Gas Consumption Forecasting: A Hybrid Stochastic–Deep Learning Framework Applied to the Czech Market

The transition towards data-driven energy management requires predictive frameworks capable of handling the nonlinear and non-stationary nature of natural gas consumption. Traditional static models often struggle to adapt to rapid regime shifts in liberalized markets. To address this forecasting problem, this study proposes a convex ensemble weight optimization framework. Moving beyond simple model averaging, we formulate the ensemble weighting problem as a constrained convex optimization task on the unit simplex. We utilize the Frank–Wolfe algorithm (Conditional Gradient) to dynamically optimize the weights of a heterogeneous set of base learners, including SARIMAX, XGBoost, N-HiTS, and Temporal Fusion Transformers (TFTs). Our results on the Czech gas market dataset demonstrate that this mathematically grounded approach achieves a Mean Absolute Percentage Error (MAPE) of 4.25%, which compares favorably to individual models such as N-HiTS (5.31%) and static averaging (6.74%). While the accuracy gain over greedy ensemble selection is marginal, the proposed convex formulation offers improved stability and interpretability, which are practical advantages for operational deployment.