Novel insights into refractive index in LiBr/H2O solutions
Abstract
In the study of LiBr/H₂O systems, developing highly reliable predictive tools is crucial for accurately determining the refractive index of solutions a property strongly governed by factors such as lithium bromide concentration, operating temperature, and incident wavelength. To achieve this, a tailored Gradient Boosting Decision Tree (GBDT) model is employed, whose performance is enhanced through four advanced hyperparameter optimization schemes: Bayesian Probability Improvement (BPI), Batch Bayesian Optimization (BBO), Evolution Strategies (ES), and Gaussian Processes Optimization (GPO). The analysis utilizes an extensive dataset of 2240 experimentally measured samples, reserving the majority for model training while allocating the remainder for independent testing. To prevent overfitting and promote model generalizability, k-fold cross-validation is incorporated throughout the training pipeline. Comparative assessments of the optimization strategies consider both computational burden and predictive precision based on standard error metrics, including MSE, R², and AARE%. The correlation study reveals that refractive index exhibits a strong positive association with LiBr mass fraction (0.99), while wavelength (-0.11) and temperature (-0.02) display slight negative relationships. Across the optimization techniques, the GBDT model tuned via BPI produces the most accurate predictions, achieving R² values of 0.99997 for training and 0.99995 for testing, surpassing the performance of the remaining strategies. In contrast, GPO proves to be the most time-efficient method, completing optimization in 269.6 seconds compared with BBO’s longer runtime of 459.3 seconds. SHAP analysis further highlights the dominant role of LiBr concentration in shaping refractive index variations, followed by wavelength and temperature. Collectively, these findings underscore the capability of optimized GBDT models to provide highly dependable refractive index predictions, offering rapid and accurate estimation within the studied parameter range.