From Numerical Models to Physics Informed Neural Networks: Advancing Water Quality Predictions in Distribution Systems

<p dir="ltr">Accurate prediction of chlorine concentrations in drinking water distribution systems (WDSs) is essential for public health protection and regulatory compliance. Traditional solvers such as EPANET‐MSX provide high fidelity numerical solutions to the advection reaction partial differential equations (PDEs) governing solute transport and decay, yet can be challenged by fine scale resolution and rapidly varying boundary conditions. Physics Informed Neural Networks (PINNs) have recently emerged as a complementary methodology, embedding the governing PDE directly into a neural network loss function to yield continuous, differentiable approximations in space and time. This paper establishes a reactive transport baseline in a canonical single pipe network with bulk decay coefficient kb=10 day-1 and zero wall decay. Two inlet concentration scenarios are investigated: (1) a constant input of 1 mg/L, benchmarked against EPANET‐MSX; and (2) a linear ramp from 0 mg/L at t=0 to 2 mg/L at t=1h, compared to a high-resolution finite difference solver. Both the pure physics PINN and a hybrid PINN augmented with data‐mismatch terms drawn from EPANET or the numerical solver are evaluated. Predictive accuracy is quantified by root mean square error (RMSE) and coefficient of determination (R2). For the constant inlet, the PINN achieves RMSE < 3.7×10⁻³ mg/L (R2>0.9998), while the hybrid version attains RMSE ≈ 1.3×10⁻² mg/L (R2≈0.9967). Under the ramped inlet conditions, both models reach R2=1.00, with RMSE of 4.6×10⁻³ mg/L and 2.1×10⁻³ mg/L for the pure physics and hybrid PINNs, respectively. These results demonstrate PINNs’ capability to capture both steady and dynamic boundary conditions in decay dominated transport and indicate that data augmented training can enhance performance during abrupt transients.</p><p dir="ltr">This paper was presented at the 21st Computing and Control in the Water Industry Conference (CCWI 2025) at the University of Sheffield (1st - 3rd September 2025).</p>