Parallel hybrid ordinary differential equation for modeling biological phosphorus removal modified for enhanced...

Area of Science:

• Environmental Engineering
• Computational Chemistry
• Biotechnology

Background:

• Wastewater treatment plants (WWTPs) require advanced operational support for environmental goals.
• Hybrid ordinary differential equations (ODEs) combine mechanistic and data-driven models for WWTPs.
• Existing hybrid ODEs face challenges in balancing predictive accuracy and physical interpretability.

Purpose of the Study:

• To enhance the physical consistency of a previously developed supporting data-enhanced hybrid ODE (SH-ODE).
• To improve predictive performance and physical interpretability for biological phosphorus removal modeling in WWTPs.

Main Methods:

• Embedded ASM2d stoichiometry into the ANN component of the hybrid ODE to enforce mass conservation.
• Incorporated a serialized ANN with mass conservation for automatic calibration of five parameters.
• Utilized operational data from sequencing batch reactors and anaerobic batch experiments for supporting data.

Main Results:

• The modified SH-ODE achieved a coefficient of determination (R²) of 0.90 for phosphate prediction.
• Further improvements led to an R² value of 0.93 with automatic calibration and mass conservation.
• A novel index demonstrated enhanced physical interpretability of the model.

Conclusions:

• The modified SH-ODE significantly improves predictive performance for phosphate removal.
• The integration of mass conservation and automatic calibration enhances the physical consistency of the hybrid model.
• This approach offers a robust framework for operational management in WWTPs aiming for environmental sustainability.