Physics-informed neural network-based serial hybrid model capturing the hidden kinetics for sulfur-driven autotrophic denitrification process

Sulfur-driven autotrophic denitrification (SdAD) is a biological process that can remove nitrate from low carbon/nitrogen (C/N) ratio wastewater. Although this process has been intensively researched, the mechanism whereby its intermediates (i.e., elemental sulfur and nitrite ions) are generated and accumulated remains elusive. Existing mathematical models developed for SdAD cannot accurately predict the intermediates in SdAD because of the incomplete knowledge of process kinetic resulting from changes in the environmental conditions and electron competition during SdAD. To address this limitation, we proposed a novel serial hybrid model structure based on a physics-informed neural network (PINN) to capture the dynamics of the process kinetics and predict the substrate concentrations in SdAD. In this study, we evaluated the model through numerical experiments and applied it to real case studies involving batch and continuous-flow reactor scenarios. By leveraging the PINN approach, the hybrid model yielded accurate predictions at both the state (i.e. substrate concentration) and kinetic levels in the numerical experiments and performed better than both mechanistic and purely data-driven models in the case studies. Furthermore, we used the trained hybrid model to design control strategies for SdAD and a novel integrated process involving SdAD and anammox for energy-efficient nitrogen removal. Finally, we discuss the advantages and application scope of the PINN-based hybrid model.