Physics-Informed Stochastic Modeling of Temperature Dynamics and Product Degradation in Cold Chains

The integrity of cold chains is critical for preserving the quality, safety, and efficacy of temperature-sensitive products, including pharmaceuticals, vaccines, and perishable goods. However, real-world cold-chain operations are subject to environmental variability, operational disturbances, and transport-related uncertainties that are often inadequately captured by deterministic models. This study presents a stochastic modeling methodology that integrates a physics-based heat-transfer model with a machine-learning residual correction to predict temperature dynamics and product degradation under uncertainty. Temperature evolution is represented through a stochastic heat-transfer model incorporating random perturbations, while product degradation is quantified using Arrhenius-based kinetics that link thermal exposure to quality loss. A machine-learning-based residual correction is subsequently incorporated to improve predictive accuracy while preserving the physical structure of the governing model. The proposed methodology is evaluated through computational experiments using a representative pharmaceutical cold-chain transportation scenario. Numerical experiments based on the Euler–Maruyama method and Monte Carlo analysis are performed to assess the proposed methodology under representative operating conditions. Results indicate that stochastic variability can produce transient temperature excursions even when average operating conditions remain acceptable, leading to increased degradation and higher failure probabilities. The computational results demonstrate the feasibility of the proposed methodology for the probabilistic estimation of thermal risk and product quality deterioration by integrating physics-based modeling, uncertainty analysis, and data-driven residual correction within a unified computational methodology. The proposed methodology provides a computational basis for the future development of intelligent cold-chain monitoring and decision-support systems. Overall, it offers practical capabilities for uncertainty quantification, reliability assessment, and informed decision making in temperature-sensitive supply chains.