From Correlation to Causation: A Hybrid Physics-Data Approach with Double Machine Learning for Interpretable Phosphorus Regulation in Water Systems

Abstract Artificial intelligence (AI) offers transformative potential for wastewater treatment plant (WWTP) optimization, yet black-box models often suffer from physical inconsistency and poor interpretability, causing overprediction and operational risks. This study develops a hybrid physics-data-driven framework (Phys-VMD-BiTCN-iTransformer) to enhance reliability of effluent total phosphorus (TP) prediction and control. By leveraging Variational Mode Decomposition (VMD) and Bidirectional Temporal Convolutional Network (BiTCN) for spatiotemporal feature extraction, and improved Transformer (iTransformer) for long-term dependency modeling, the framework integrates operational data with seven mechanistic features derived from ASM2d and physical laws. To transition from correlation to causality, a Double Machine Learning (DML) framework was implemented. Causal inference identified Aeration Tank 1 Dissolved Oxygen (AT1 DO) and Hydrolysis Tank 1 Oxidation–Reduction Potential (HT1 ORP) as primary drivers of effluent TP fluctuations. Based on these insights, an 8-tier staged DO adjustment strategy was developed; scenario analysis showed the effluent TP compliance rate increased from 36.1% to 58.7%, while reducing exceedance risk and unnecessary energy and chemical costs. The framework bridges deep-learning architectures with practical engineering logic. By providing interpretable causal pathways and a reliable control coefficient (K = 0.15), this research offers a scalable solution for intelligent, sustainable water systems.