A hybrid physics-informed neural network (PINN) for the electro-oxidation of 2-Chlorophenol on BDD electrodes in a flow-by reactor under batch recirculation

Abstract

The electro-oxidation of persistent organic pollutants such as 2-chlorophenol (2-CPh) using boron-doped diamond (BDD) electrodes offers a promising wastewater treatment route, yet conventional mechanistic models (e.g., CFD) suffer from prohibitive computational costs. This study develops a hybrid physics-informed neural network (PINN) to model the electro-oxidation of 2-CPh in a flow-by reactor coupled with a continuous stirred tank under batch recirculation mode. The PINN integrates a diffusion–convection partial differential equation with a lumped-parameter ordinary differential equation for the tank, embedding physical constraints directly into the loss function. The model was trained on simulated data generated from a previously validated parametric model and optimized using a systematic hyperparameter grid search. The PINN achieved excellent agreement with experimental data, yielding a coefficient of determination (R2) of 0.9927, a mean square error of 0.0009, and a root mean square error of 0.0294—outperforming both the CFD and parametric models in accuracy. Sensitivity analysis revealed that the apparent kinetic constant is the most influential parameter (normalized sensitivity of 14.20). While the CFD model required 42 days and the parametric model 8 s, the PINN achieved a balanced trade-off with a runtime of 7.36 h. We conclude that the PINN provides a highly accurate, computationally feasible surrogate model suitable for integration into digital twins and real-time control frameworks for electrochemical wastewater treatment.