Accurate refractive index modeling of surfactant-containing LiBr–water solutions via optimized machine learning techniques
Abstract
Accurate prediction of the refractive index of aqueous lithium bromide (LiBr) solutions is essential for optical diagnostics, interferometric measurements, and the design and monitoring of absorption systems. However, available correlations are generally limited in their ability to simultaneously account for variations in LiBr concentration, temperature, wavelength, and the presence of heat- and mass-transfer-enhancing surfactants. This study therefore develops and rigorously evaluates a machine-learning framework for predicting the refractive index of aqueous LiBr solutions under both surfactant-free and surfactant-containing conditions. A dataset comprising 3185 experimental refractive index measurements reported by Pérez de Luco et al. was employed, covering LiBr mass fraction, temperature, wavelength, and the presence or absence of 150 ppm 1-octanol as predictive variables. The principal modeling challenges arise from the need to simultaneously capture the nonlinear effects of concentration, temperature, and wavelength while resolving the comparatively subtle optical changes associated with ppm-level surfactant addition and maintaining reliable generalization to unseen data. To address these challenges, the proposed framework combines surfactant-aware machine learning, CSA-based hyperparameter optimization, independent test-set evaluation, and quantitative sensitivity analysis within a unified modeling strategy. Five machine-learning approaches, including CatBoost (CB), AdaBoost, heterogeneous Ensemble Learning (EL), Multi-Layer Perceptron Artificial Neural Network (MLP-ANN), and Random Forest (RF), were systematically developed and compared. Model hyperparameters were optimized using the Coupled Simulated Annealing (CSA) algorithm, with validation performed exclusively within the training subset, while the independent test dataset remained untouched during model development and optimization. Model performance was evaluated using R 2 , RMSE, and AARE%, together with complementary data-quality and diagnostic analyses. Among the evaluated approaches, CB achieved the best predictive performance, with R 2 values of 0.99989 and 0.99988, RMSE values of 0.00068 and 0.00069, and AARE values of 0.03666% and 0.03662% for the training and testing datasets, respectively. Monte Carlo-based sensitivity analysis further showed that wavelength was the most influential predictor, followed by temperature, surfactant presence, and LiBr mass fraction, with sensitivity indices of 6.97, 4.95, 3.67, and 1.52, respectively. The main contributions of this study are the explicit incorporation of surfactant presence into refractive-index prediction, the rigorous CSA-based optimization and comparative assessment of multiple machine-learning architectures under a common evaluation framework, and the quantitative interpretation of the relative influence of the governing physicochemical and optical variables. Overall, the proposed framework provides an accurate and computationally efficient approach for refractive-index estimation and offers a practical basis for reducing repetitive experimental measurements in LiBr-based optical monitoring and absorption-system applications.