用经济规律约束神经网络，提升商品需求预测的准确性与可解释性。

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 novel deep learning framework tailored for commodity demand forecasting. The model uniquely integrates a Gated Recurrent Unit (GRU) architecture with physics-informed neural network (PINN) principles by embedding a domain-specific economic constraint: the negative elasticity between price and demand. 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. To further enhance predictive performance and stability, PREIG incorporates a hybrid optimization strategy that couples NAdam and L-BFGS with Population-Based Training (POP). 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.