Metaheuristic-enhanced extreme learning machine for ammonia nitrogen modeling in coastal waters

Nutrient enrichment intensifies eutrophication in coastal waters, where ammonia nitrogen (NH₃-N) promotes algal blooms and ecosystem degradation. This study developed an interpretable hybrid machine learning model for predicting NH₃-N concentrations in coastal waters. The feature selection was done based on Mutual Information and Recursive Feature Elimination (RFE), with artificial neural network, support vector machine and extreme learning machine (ELM) models were used. To increase accuracy ELM was optimized by three metaheuristics algorithms, such as grey wolf optimization (GWO), whale optimization algorithm, and cockroach swarm optimization. The ELM-GWO showed the best performance using the features based on RFE, with a coefficient of determination (R² = 0.96). The results of pairwise Wilcoxon and Diebold-Mariano tests showed statistically significant improvement of baseline models (p < 0.05). The interpretability was evaluated using Shapley Additive explanations (SHAP), partial dependence plots (PDP), and Local Interpretable Model-agnostic Explanations (LIME). SHAP, PDP, and LIME analyses revealed complex nonlinear feature interactions and provided improved interpretability of NH₃-N predictions.