Adaptive multi-domain uncertainty quantification for digital twin water forecasting

Machine learning (ML) models are often used to predict demand in digital twins (DTs) of water distribution systems (WDS). However, most models do not provide uncertainty estimation, and this makes risk evaluation limited. In this work, we introduce the first systematic framework for hierarchical uncertainty transfer in regional water networks, because until now no method existed for DT of regional water systems. We propose Adaptive Multi-Village Conformal Prediction (AMV-CP), a method that keeps theoretical guarantees and also allows transfer of uncertainty information between villages that are similar in structure but different in operation. The main ideas are: (i) village-adaptive conformity scores that capture local patterns, (ii) a meta-learning algorithm that reduces calibration cost by 88.6%, and (iii) regime-aware calibration that keeps 94.2% coverage when seasons change. We use eight years of data from six villages with 6174 users in one regional network. The results show a theoretical basis for cross-village transfer and 95.1% empirical coverage (target was 95%), with real-time speed of 120 predictions per second. Early multi-step tests also show 93.7% coverage for 24-hour horizons, with controlled trade-offs. This framework is the first systematic method for controlled uncertainty transfer in infrastructure DTs, with theoretical guarantees under 𝜙-mixing and practical deployment. Our multi-village tests demonstrate the value of meta-learning for uncertainty estimation and make a base method that can be used in other hierarchical infrastructure systems. The system is validated in a Mediterranean rural network, but generalization to other climates, urban settings, and cascading systems needs further empirical study.