[Paper] Physics-Informed Neural Networks for Thermophysical Property Retrieval

Source: arXiv - 2511.23449v1

Overview

This paper introduces an iterative Physics‑Informed Neural Network (PINN) framework for retrieving the thermal conductivity of building walls directly from in‑situ temperature measurements. By coupling a forward heat‑diffusion PINN with a simple optimization loop, the authors demonstrate a fast, non‑invasive way to estimate a key energy‑efficiency parameter without the long‑duration, intrusive tests that are common today.

Key Contributions

• PINN‑based inverse solver: First application of PINNs to the inverse heat‑conduction problem for wall thermophysical property estimation.
• Iterative k‑estimation loop: Alternates between solving the forward heat equation (fixed k) and updating k by minimizing the mismatch between predicted and observed surface temperatures.
• Robustness to real‑world variability: Validated on both synthetic data from a high‑fidelity Finite‑Volume Method (FVM) simulator and on field data collected with a weather station, covering diverse environmental conditions.
• High accuracy with limited data: Achieves a maximum mean absolute error (MAE) of 4.09 % even when the steady‑state assumption is mildly violated.
• Open research pathway: Provides a baseline for future work on ML‑driven, non‑intrusive material property retrieval in civil and building engineering.

Methodology

1. Data Collection – Surface temperature maps (thermographs) are recorded over a day, together with ambient weather data (outside temperature, solar irradiance, wind).
2. Forward PINN – A neural network is trained to satisfy the 1‑D heat‑diffusion PDE (Fourier’s law) for a fixed thermal conductivity k while matching the observed boundary temperatures. The loss combines:
   • PDE residual (enforces physics)
   • Boundary/initial condition errors (fits measured data)
3. Inverse Loop – After the forward PINN converges, the predicted interior temperature field is compared to the measured thermographs. The discrepancy is used to update k via a simple gradient‑based optimizer (e.g., Adam).
4. Iteration – Steps 2–3 repeat until the change in k between iterations falls below a tolerance, indicating convergence.
5. Evaluation – The estimated k is benchmarked against ground‑truth values from the FVM simulator or laboratory measurements, using MAE and relative error metrics.

The whole pipeline runs on a standard GPU in minutes, making it practical for on‑site diagnostics.

Results & Findings

• Convergence typically occurs within 5–7 iterations.
• Sampling frequency as low as one measurement every 10 minutes still yields sub‑5 % error, highlighting data efficiency.
• The method is insensitive to moderate noise (added Gaussian noise up to 0.5 °C) thanks to the physics regularization in the PINN loss.

Practical Implications

• Rapid retrofit assessments – Energy auditors can estimate wall thermal transmittance on‑site in a single day, informing retrofit decisions without destructive sampling.
• Smart‑building monitoring – Integrated with IoT temperature sensors, the framework can continuously track material degradation (e.g., moisture ingress) by detecting drift in k.
• Reduced testing costs – Eliminates the need for expensive heat‑flow meters or long‑term calorimetric setups, lowering barriers for small‑scale developers and retrofit contractors.
• Scalable to other domains – The same PINN‑inverse loop can be adapted for soil thermal conductivity, composite material inspection, or any 1‑D diffusion‑type property where in‑situ data are available.

Limitations & Future Work

• Steady‑state assumption: Accuracy degrades when the wall temperature at dawn is far from equilibrium; future work could incorporate transient initial conditions or multi‑day data windows.
• 1‑D simplification: Real façades exhibit multi‑dimensional heat flows (e.g., thermal bridges); extending the PINN to 2‑D/3‑D geometries is a natural next step.
• Sensor placement: The current setup uses only surface thermographs; adding interior temperature probes could improve identifiability for heterogeneous walls.
• Generalization: The model was trained on a limited set of material types; broader material libraries and transfer‑learning strategies are needed for widespread deployment.

Overall, the paper showcases how physics‑aware deep learning can bridge the gap between laboratory‑grade material testing and practical, on‑site diagnostics—an exciting development for developers, building engineers, and the broader AI‑for‑physical‑systems community.

Authors

• Ali Waseem
• Malcolm Mielle

Paper Information

• arXiv ID: 2511.23449v1
• Categories: cs.LG, cs.AI, cs.CE, cs.CV
• Published: November 28, 2025
• PDF: Download PDF