Physics-Guided Residual Correction for Temperature Prediction in Water Distribution Networks

📋 Type MA thesis
⚡ Status running
📅 Duration Apr 1, 2026 – Oct 1, 2026
👤 Primary supervisor Andreas Maier
👥 Co-supervisors Siming Bayer Mohammad Moataz Tolba, M. Sc.
🎓 Student Ahmed Mohamed Ahmed Aly Master Artificial Intelligence

Background and Motivation

Modern water distribution networks rely on smart meters and SCADA systems that provide hourly demand and temperature measurements. These temperature signals encode thermohydraulic information that supports tasks such as pipe characterization and leak detection [1, 2].

Physics-based thermal solvers simulate temperature propagation using hydraulic flow and heat transfer dynamics. While they capture global physical behavior, their accuracy is limited by uncertain parameters and simplified boundary conditions. This leads to systematic meter-specific bias and temporally correlated residual errors.

Recent work on physics-informed learning [3] suggests combining physical simulations with data-driven correction. Instead of replacing physics with purely black-box models, we learn a residual:

Tmeasured = Tphysics + r

where a neural model predicts the residual r. This hybrid approach preserves physical consistency while capturing local effects not modeled by simulation.

Problem Definition

Given hourly smart meter temperature and demand measurements, along with SCADA inlet flow and temperature, the objective is to improve temperature prediction at each consumer node. The physics solver provides a baseline estimate

Tphysics,i(t)

and the model learns a correction term

r̂i(t) = Tmeasured,i(t) – Tphysics,i(t)

The final prediction becomes

T̂i(t) = Tphysics,i(t) + r̂i(t)

Physics Thermal Solver
(WNTR Simulation)

↓

Smart Meter Data
(Temp & Demand)

→

Residual Learning Model
LSTM / TCN / Transformer

→

Corrected Temperature
Predictions

Figure 1: Hybrid physics-guided residual correction framework for temperature prediction.

Research Questions

  1. How much does residual correction improve accuracy over physics-only and pure ML models?
  2. Which temporal architectures best capture residual dynamics?
  3. What systematic physics-model errors are revealed by learned residuals?
  4. Does improved temperature prediction enhance downstream leak detection?

Methodology

Data and Baseline

The study uses a real-world network with 85 smart meters providing hourly temperature and demand, combined with SCADA inlet measurements and weather data. A WNTR-based thermal solver generates baseline temperature predictions using network topology, inlet conditions, and shared soil temperature.

Residual Learning Models

For each meter and timestep, the model predicts the residual using:

  • Global features: inlet flow/temperature, weather, time encodings
  • Local features: demand history, temperature history, physics prediction
  • Meter embedding capturing consumer-specific characteristics

The following architectures will be compared:

  • LSTM for temporal dependencies,
  • Temporal Convolutional Networks (TCN),
  • Transformer encoder with attention [5],
  • Denoising autoencoder refining physics outputs.

Evaluation

Baselines include physics-only simulation and standalone ML prediction. Metrics include MAE, RMSE, and correlation per meter. Interpretability analysis will examine residual patterns and attention weights. Improved baseline accuracy is expected to increase leak detection sensitivity.

Expected Contributions

  • A hybrid physics-guided residual correction framework for temperature prediction.
  • Systematic comparison of temporal neural architectures for residual modeling.
  • Interpretability insights revealing systematic deficiencies in physics simulations.
  • Quantitative accuracy improvements on real smart meter data.
  • Demonstration that improved temperature baselines enhance leak detection sensitivity.

References

[1] M. Tolba, Data-Driven Thermohydraulic Estimation of Service Pipe Lengths in Water Distribution Networks, Friedrich-Alexander University Erlangen–Nürnberg, 2026.

[2] M. Tolba, Leak Localization in Intermittent-Flow Pipes Using Thermal Modeling, Friedrich-Alexander University Erlangen–Nürnberg, 2026.

[3] X. Cheng, Physics-informed neural networks with trust-region sequential quadratic programming, arXiv preprint arXiv:2409.10777, 2024.

[4] A. Antunes, Short-term water demand forecasting using machine learning techniques, Journal of Hydroinformatics, vol. 20, no. 6, pp. 1343–1366, 2018.

[5] A. Vaswani, Attention Is All You Need, Advances in Neural Information Processing Systems (NeurIPS), vol. 30, 2017.