PREIG: Physics-informed and Reinforcement-driven Interpretable GRU for Commodity Demand Forecasting

--Accurately forecasting commodity demand remains a critical challenge due to volatile market dynamics, nonlinear dependencies, and the need for economically consistent predictions. This paper introduces PREIG--a Physics-informed and Reinforcement-driven Interpretable model with GRU--a novel deep learning framework tailored for commodity demand forecasting. This constraint is enforced through a customized loss function that penalizes violations of the physical rule, ensuring that model predictions remain interpretable and aligned with economic theory. T o further enhance predictive performance and stability, PREIG incorporates a hybrid optimization strategy that couples NAdam and L-BFGS with Population-Based Training (POP)--a reinforcement-learning inspired mechanism that dynamically tunes hyperparameters via evolutionary exploration and exploitation. Experiments across multiple commodities datasets demonstrate that PREIG significantly outperforms traditional econometric models (ARIMA, GARCH) and deep learning baselines (BPNN,RNN) in both RMSE and MAPE. When compared with GRU, PREIG maintains good explainability while still performing well in prediction. By bridging domain knowledge, optimization theory and deep learning, PREIG provides a robust, interpretable, and scalable solution for high-dimensional nonlinear time series forecasting in economy.