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

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 R