Identifying Temporal Drivers for Microbial Community Assembly in Wastewater Treatment by Stochastic Physics-Informed Deep Learning Based on Limited-View and Sparsely Sampled Data

Microbial community assembly (MCA) is the key to biological wastewater treatment by dynamically shaping the functional populations responsible for pollutant removal through deterministic selection and stochastic ecological processes, but identifying temporal drivers for the MCA remains a challenge. This study reported a stochastic physics-informed deep learning (SPI-DL) framework that embedded generalized Lotka–Volterra (gLV) models, stochastic differential equations (SDEs), and SDE integrators to identify deterministic and stochastic dynamics for MCA based on limited-view and sparsely sampled data. The effectiveness was verified by MCA for nitrifying groups of ammonia-oxidizing bacteria (AOB) and nitrite-oxidizing bacteria (NOB) as a representative case. The log-likelihood decoupling (LLD) method coupled with SHAP analysis was proposed to unravel the time-resolved relative contribution of the deterministic and stochastic factors. As indicated by driver decomposition based on LLD/SHAP analysis, stochastic variability was mainly linked to flow rate and hydraulic retention time, whereas deterministic succession was associated with selective covariates (e.g., DO for NOB; NH4–N/TN for AOB). The SPI-DL+LLD framework demonstrates satisfactory representability, predictability, and generalizability in explaining and identifying temporal drivers for MCA in WWTPs, which has important implications for precise process control and optimization of smart wastewater treatment systems.