Uncertainty-aware water-demand forecasting and leakage early warning with temporal fusion transformers and Bayesian model fusion

Abstract

Water distribution systems face persistent challenges from leakage, with approximately 20% of distributed water lost in the UK. This study presents a unified framework for 24h water-demand forecasting and early-leakage warning, integrating classification, regression and uncertainty quantification within a temporal fusion transformer (TFT) architecture. The framework evaluates three TFT variants: a recent-TFT (R-TFT) using one week of preceding flow, a lagged-TFT (L-TFT) using flow from two weeks prior and a combined-TFT (C-TFT) fusing both through Bayesian Markov chain Monte Carlo (MCMC) sensor fusion. It is trained and validated on approximately 18,600 flow groupings from ∼2,000 district metred areas in the UK, benchmarked against a vanilla long short-term memory (LSTM), the Informer transformer and the minimum night flow (MNF) industry standard, under both balanced and imbalanced class distributions. An operational decision framework translates the outputs into structured early warning protocols. The C-TFT achieves the strongest overall performance, with the highest central-prediction accuracy (median index of agreement 0.901) and tightest uncertainty bounds (median prediction interval normalised average width 0.696). The classification head achieves an area under the receiver operating characteristic curve (ROC-AUC) of 0.906, with recall stable above 80% under imbalanced conditions, substantially outperforming the minimum night flow baseline (AUC 0.738). TFT interpretability through variable selection and attention mechanisms aligns with physical consumption dynamics. No existing framework unifies flow forecasting, leakage classification, uncertainty quantification and interpretability within a single architecture. This work addresses that gap and demonstrates consistent performance across balanced and imbalanced evaluations, supporting deployment in operational environments where leakage events are rare.