Long Short-Term Memory and Bidirectional Long Short-Term Memory Modeling and Prediction of Hexavalent and Total Chromium Removal Capacity Kinetics of Cupressus lusitanica Bark

Hexavalent chromium Cr(VI) is a high-priority environmental pollutant because of its toxicity and potential to contaminate water sources. Biosorption, using low-cost biomaterials, is an emerging technology for removing pollutants from water. In this study, Long Short-Term Memory (LSTM) and bidirectional LSTM (Bi-LSTM) neural networks were used to model and predict the kinetics of the removal capacity of Cr(VI) and total chromium Cr(T) using Cupressus lusitanica bark (CLB) particles. The models were developed using 34 experimental kinetics datasets under various temperature, pH, particle size, and initial Cr(VI) concentration conditions. Data preprocessing via interpolation was implemented to augment the sparse time-series data. Early stopping regularization prevented overfitting, and dropout techniques enhanced model robustness. The Bi-LSTM models demonstrated a superior performance compared to the LSTM models. The inherent complexities of the process and data limitations resulted in a heavy-tailed and left-skewed residual distribution, indicating occasional deviations in the predictions of capacities obtained under extreme conditions. K-fold cross-validation demonstrated the stability of Bi-LSTM models 38 and 43, while response surfaces and validation with unseen datasets assessed their predictive accuracy and generalization capabilities. Shapley additive explanations analysis (SHAP) identified the initial Cr(VI) concentration and time as the most influential input features for the models. This study highlights the capabilities of deep recurrent neural networks in comprehending and predicting complex pollutant removal kinetic phenomena for environmental applications.