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Conformal Prediction-Driven Adaptive Sampling for Digital Twins of Water Distribution Networks

Mohammadhossein Homaei, Oscar Mogollon Gutierrez, Ruben Molano, Andres Caro, Mar Avila

TL;DR

This work addresses the challenge of accurate state estimation in water distribution network digital twins under limited sensing. It proposes an adaptive framework that combines per-node LSTM demand forecasting with marginal conformal prediction to quantify uncertainty and guide sensor allocation to the most uncertain nodes. The approach yields substantial improvements, achieving roughly 33–34% lower demand RMSE at a 40% sensing budget across three benchmark networks, while maintaining about 90% empirical coverage and only modest computational overhead. The results demonstrate the practicality of uncertainty-aware adaptive sensing for real-time DTs, with implications for improved reliability, safety, and efficiency in large-scale water networks.

Abstract

Digital Twins (DTs) for Water Distribution Networks (WDNs) require accurate state estimation with limited sensors. Uniform sampling often wastes resources across nodes with different uncertainty. We propose an adaptive framework combining LSTM forecasting and Conformal Prediction (CP) to estimate node-wise uncertainty and focus sensing on the most uncertain points. Marginal CP is used for its low computational cost, suitable for real-time DTs. Experiments on Hanoi, Net3, and CTOWN show 33-34% lower demand error than uniform sampling at 40% coverage and maintain 89.4-90.2% empirical coverage with only 5-10% extra computation.

Conformal Prediction-Driven Adaptive Sampling for Digital Twins of Water Distribution Networks

TL;DR

This work addresses the challenge of accurate state estimation in water distribution network digital twins under limited sensing. It proposes an adaptive framework that combines per-node LSTM demand forecasting with marginal conformal prediction to quantify uncertainty and guide sensor allocation to the most uncertain nodes. The approach yields substantial improvements, achieving roughly 33–34% lower demand RMSE at a 40% sensing budget across three benchmark networks, while maintaining about 90% empirical coverage and only modest computational overhead. The results demonstrate the practicality of uncertainty-aware adaptive sensing for real-time DTs, with implications for improved reliability, safety, and efficiency in large-scale water networks.

Abstract

Digital Twins (DTs) for Water Distribution Networks (WDNs) require accurate state estimation with limited sensors. Uniform sampling often wastes resources across nodes with different uncertainty. We propose an adaptive framework combining LSTM forecasting and Conformal Prediction (CP) to estimate node-wise uncertainty and focus sensing on the most uncertain points. Marginal CP is used for its low computational cost, suitable for real-time DTs. Experiments on Hanoi, Net3, and CTOWN show 33-34% lower demand error than uniform sampling at 40% coverage and maintain 89.4-90.2% empirical coverage with only 5-10% extra computation.

Paper Structure

This paper contains 26 sections, 16 equations, 1 figure, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. DTs for WDNs
  4. Sensor Placement Optimization
  5. Data-Driven Forecasting and Uncertainty
  6. Research Gap and Contributions
  7. Methodology
  8. Problem Formulation
  9. Demand Prediction with LSTM
  10. Uncertainty Quantification via Conformal Prediction
  11. Adaptive Sampling Strategy
  12. Experimental Evaluation
  13. Experimental Setup
  14. Demand Estimation Performance
  15. Pressure Estimation and Safety Implications
  16. ...and 11 more sections

Figures (1)

  • Figure 1: Closed-loop architecture of the Conformal Prediction-Driven Adaptive Sampling framework, where uncertainty scores ($U$) guide node selection for real-time measurement, fused with predictions ($\hat{q}$) for hydraulic state reconstruction.