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

2025-07-29

AI Summary

To address strong market volatility, complex nonlinear dependencies, and insufficient economic interpretability in commodity demand forecasting, this paper proposes an interpretable time-series modeling framework integrated with economic priors. Methodologically, it embeds the price–demand negative elasticity principle—grounded in microeconomic theory—as a physics-informed constraint into a GRU architecture and designs a corresponding negative elasticity regularization loss. Furthermore, it introduces a hybrid optimization strategy combining NAdam and L-BFGS, augmented by population-based training to enhance generalization. Empirically evaluated on a multi-commodity dataset, the model achieves statistically significant improvements in RMSE and MAPE over ARIMA, GARCH, BPNN, and standard RNN baselines. Crucially, all predictions strictly adhere to fundamental microeconomic principles—ensuring both high predictive accuracy and rigorous economic interpretability.

Technology Category

• Search and Optimization: Learning to Search
• Natural Language Processing: Learning & Optimization for NLP
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

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.

Problem

• Forecasting commodity demand with volatile market dynamics
• Ensuring economically consistent predictions via physics-informed constraints
• Improving interpretability and accuracy in nonlinear time series

Innovation

• GRU with physics-informed economic constraints
• Hybrid NAdam and L-BFGS optimization
• Interpretable commodity demand forecasting