Supporting data-enhanced hybrid ordinary differential equation model for phosphate dynamics in municipal wastewater...

A parallel hybrid ordinary differential equation (ODE) integrating the Activated Sludge Model No. 2d (ASM2d) and an artificial neural network (ANN) was developed to simulate biological phosphorus removal (BPR) with high accuracy and interpretability. Two novelties were introduced; first, the involved supporting data (i.e., phosphate-release activity) were incorporated as an input in the ANN. Second, the outputs of the ANN were selective. Three models were implemented using different ANN outputs, and all three outperformed ASM2d in phosphate estimation for anaerobic/aerobic sequencing batch reactor operation. In particular, the incorporation of four variables responsible for BPR into the ANN enabled the highest performance (R² = 0.93) owing to the capture of increasing phosphate-accumulating organisms (PAOs). The ANN with the supporting data worked satisfactorily to compensate for ASM2d by adding proper PAOs, resulting in improvement in phosphate estimation. The novel parallel hybrid ODE can simulate BPR while maintaining physical meaning.