A Trajectory-Regularized Physics-Informed Hybrid Framework for Specialty Fresh Food Commodity Price Forecasting and...

Price volatility in fresh food commodities can weaken supply-chain coordination, disturb market expectations, and increase short-term risks to food availability and affordability. This issue is more pronounced for specialty crops with seasonal production, concentrated supply, limited storability, and high sensitivity to climate, trade, energy, and online-attention shocks. This study develops a trajectory-regularized physics-informed multi-source forecasting framework for daily wholesale prices of garlic, scallion, and ginger in China from 2014 to 2024. The framework, denoted as STL-ETO-EMA-PILSTM, integrates Seasonal-Trend decomposition using LOESS (STL), Efficient Multi-scale Attention (EMA), Long Short-Term Memory (LSTM), an economically motivated physics-informed trajectory residual constraint, and Exponential-Trigonometric Optimization (ETO), using production, climate, macroeconomic, trade, crude-oil, and online-attention indicators. In this framework, the physics-informed component is implemented as a trajectory residual constraint inspired by price-adjustment inertia and local continuity, rather than as a conventional PINN based on strict governing physical equations. In one-step-ahead forecasting, the model outperformed conventional machine learning baselines and additional time-series baselines, including naive persistence, Transformer Encoder, and PatchTST, with MAE values of 0.0853, 0.0581, and 0.1409 for garlic, scallion, and ginger, respectively, and R² values above 0.996. Leakage-prevention procedures, walk-forward validation, multi-horizon forecasting, and Diebold-Mariano tests were used to strengthen result credibility. Multi-step forecasting showed clear performance degradation as the horizon increased, supporting the positioning of the framework as a short-term market-monitoring tool rather than a long-horizon structural projection model. Permutation-based feature-importance and interaction analyses revealed crop-specific price drivers. The framework provides an interpretable tool for fresh food price forecasting, market stability monitoring, and short-term operational risk monitoring in fresh food supply chains.