A machine learning surrogate for finite element modelling of vacuum cooling in leafy vegetables: Real-Time prediction of heat and mass transfer

Vacuum cooling (VC) is an efficient cooling technique for high-moisture porous foods, but its practical application is limited by water loss, spatial nonuniformity, and the poor real-time performance of high-fidelity physical models. In this study, spinach petiole bundles were selected as a representative leafy vegetable, and a machine learning (ML) surrogate was developed for finite element modelling (FEM) of VC. A transient FEM was established based on porous medium theory by imposing the fitted experimental chamber pressure as the boundary condition, and the model was validated against experimental measurements of sample temperature and weight loss. Based on the validated FEM, a parametric sweep was performed over 2000 operating cases designed using a maximin Latin hypercube sampling (LHS) strategy, covering six input parameters: end pressure, depressurisation rate, porosity, radius, initial temperature, and initial water concentration. Temperature and water concentration responses at 15 spatial locations and 21 time points were extracted to train six ML models, namely KNN, RF, XGBoost, MLP, GRU, and LSTM. Among them, LSTM achieved the best overall performance, with weighted MAE, MSE, RMSE, and R 2 values of 1.104, 4.098, 2.024, and 0.9999 on the test set, respectively, while accurately reproducing the temporal evolution and spatial distribution under representative conditions. Moreover, the surrogate reduced single-case prediction time from minutes for FEM to milliseconds. These results demonstrate the potential of the surrogate model for real-time prediction, accurate assessment, and practical deployment of VC systems. • A validated FEM described heat and moisture transfer in petiole bundles during VC. • A spatiotemporal dataset was constructed from 2000 maximin LHS-sampled conditions. • LSTM showed the best generalisation under unseen operating conditions. • The surrogate cut single-case prediction time from minutes to milliseconds. • The surrogate advances high-fidelity VC modelling toward practical deployment.