Predicting Osmotic Coefficients in Aqueous Inorganic Systems: A Hybrid Gazelle Optimization Algorithm (GOA)–Machine Learning Framework for Sustainable Water Treatment

Efficient design of desalination and brine management systems, which are central to a water circular economy, requires accurate thermodynamic data such as the osmotic coefficient. This property is key to understanding salt behavior in aqueous solutions, directly impacting the energy efficiency and sustainability of treatment processes. This study presents a predictive framework that combines machine learning with the Gazelle Optimization Algorithm (GOA) to accurately estimate osmotic coefficients for various inorganic salt solutions. The GOA was employed to automatically tune the hyperparameters of two models: Decision Tree (DT) and Gradient Boosting Machine (GBM). Using a comprehensive dataset of 893 samples with 27 salt-specific parameters, the GOA-GBM hybrid model delivered the highest predictive accuracy, achieving an R 2 of 0.9734 on test data. The GOA-DT model also performed robustly (R 2 = 0.9260), providing a more interpretable alternative. By creating a reliable tool for predicting osmotic coefficients, this methodology enables more precise process simulation and optimization. This directly supports the development of energy-efficient desalination technologies and informed decision-making for water reuse and resource recovery. The integration of advanced digital tools like GOA with machine learning offers a powerful approach to enhancing process efficiency and environmental safety, contributing directly to the design of sustainable, circular economy-based water treatment solutions for industrial and municipal applications.