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In this study, supervised machine learning (ML) regression models are employed to predict water uptake during the sorption process in a sorption reactor for thermal energy storage applications. Two main methods are used to study sorption storage systems: experimental studies and numerical simulations. Experimental studies involve physical testing and measurements but are often costly and time-consuming. Numerical simulations are more flexible and cost-effective, though they can require significant computational resources for large or complex systems. To address these challenges, researchers are increasingly employing various machine learning techniques, which offer strong potential for data analysis and predictive modeling. In this study, CFD-based sorption simulations are integrated with machine learning models to predict the spatiotemporal evolution of water uptake. Several ML techniques including support vector regression (SVR), Random Forest, XGBoost, CatBoost (gradient boosting decision trees), and multilayer perceptron neural networks (MLPs) are evaluated and compared. A fixed-bed reactor equipped with fins and tubes is considered within a closed adsorption thermal storage system. Numerical simulations are conducted for three different fin lengths (10 mm, 25 mm, and 35 mm) to generate a comprehensive dataset for training the ML models and capturing the complex temporal evolution of water uptake, thereby enabling predictions for unseen fin geometries. The results indicate that neural network-based models achieve superior predictive performance compared to the other methods. For water uptake training, the mean absolute error (MAE), root mean squared error (RMSE), and coefficient of determination R2 are approximately 2.83, 4.37, and 0.91, respectively. The predicted water uptake shows close agreement with the numerical simulation results. For the prediction cases, the MAE, MSE, and R2 values are approximately 1.13, 1.2, and 0.8, respectively. Overall, the study demonstrates that machine learning models can accurately predict water uptake beyond the training dataset, indicating strong generalization capability and significant potential for improving thermal management system design. Additionally, the proposed approach reduces simulation time and computational cost while providing an efficient and reliable framework for modeling complex sorption processes in thermal energy storage systems.