Approximation formula-embedded neural-network model incorporating operator expertise for flocculant-dosage estimation

Flocculant dosage-estimation model using neural network (NN) architectures has been developed to simulate the operation of skilled water treatment plant operators. While NN models can model operational data in a data-driven manner, they often lack interpretability and demonstrate low estimation accuracy under extrapolation conditions. To address these issues, we constructed an approximation formula-embedded NN model that incorporates domain knowledge of the flocculation process. A comparison between this model and a general fully connected NN model showed that the former achieved higher accuracy (mean absolute error, MAE: 3.8 mg/L) under extrapolated conditions compared with the latter (MAE: 20.7 mg/L). The effects of water quality and turbidity patterns on the approximation coefficients were also quantitatively analysed, demonstrating trends consistent with operator expertise. These results confirm the enhanced interpretability and estimating robustness of this model. In addition, we proposed a method for adding explanatory variables to the estimated flocculant dosage using mathematical equations.