Fig. 25

Statistical assessment of the PINN model’s capability to simulate the concentrations of pH, TDS, EC, and Na\(^{+}\) across various Nile River regions. The model demonstrated strong predictive reliability, consistently maintaining high \(\textrm{R}^{2}\) values and low MSE during training, testing, and forecasting stages. Pollutant levels followed seasonal patterns, with peak concentrations observed during dry periods. These findings validate the model’s effectiveness in capturing WQI dynamics for accurate prediction.