Physics-Informed Neural Networks for Thermophysical Property Retrieval

TL;DR

This work introduces PINN-it, a physics-informed neural network framework for noninvasively estimating thermophysical properties from in situ thermographs. By alternately training a forward heat-diffusion PINN at fixed k and then updating k to minimize thermograph prediction error, the method retrieves the wall's thermal conductivity under realistic environmental conditions. Results show accurate k recovery under steady-state assumptions and reasonable robustness when the steady-state condition is relaxed, with forward-model predictions achieving sub-K temperature errors across seasons for higher conductivities. The approach demonstrates the viability of PINNs for in situ inverse problems in building envelopes, potentially reducing measurement time and enabling scalable, noninvasive retrofit assessments. It lays a foundation for extending PINN-based inverse analyses to multi-material walls and more complex boundary conditions in real-world settings.

Abstract

Inverse heat problems refer to the estimation of material thermophysical properties given observed or known heat diffusion behaviour. Inverse heat problems have wide-ranging uses, but a critical application lies in quantifying how building facade renovation reduces thermal transmittance, a key determinant of building energy efficiency. However, solving inverse heat problems with non-invasive data collected in situ is error-prone due to environmental variability or deviations from theoretically assumed conditions. Hence, current methods for measuring thermal conductivity are either invasive, require lengthy observation periods, or are sensitive to environmental and experimental conditions. Here, we present a PINN-based iterative framework to estimate the thermal conductivity k of a wall from a set of thermographs; our framework alternates between estimating the forward heat problem with a PINN for a fixed k, and optimizing k by comparing the thermographs and surface temperatures predicted by the PINN, repeating until the estimated k's convergence. Using both environmental data captured by a weather station and data generated from Finite-Volume-Method software simulations, we accurately predict k across different environmental conditions and data collection sampling times, given the temperature profile of the wall at dawn is close to steady state. Although violating the steady-state assumption impacts the accuracy of k's estimation, we show that our proposed framework still only exhibits a maximum MAE of 4.0851. Our work demonstrates the potential of PINN-based methods for reliable estimation of material properties in situ and under realistic conditions, without lengthy measurement campaigns. Given the lack of research on using machine learning, and more specifically on PINNs, for solving in-situ inverse problems, we expect our work to be a starting point for more research on the topic.

Figures (4)

• Figure 1: PINN-it iteratively optimizes both a PINN and the estimation of the thermal conductivity $k$ in a 2-step process. In dashed lines are the optimized elements and losses at each step. First (\ref{['fig:first']}), a PINN is optimized to estimate the reverse heat problem given a fixed estimated $k$ value, i.e. $\hat{k}$. Then (\ref{['fig:second']}), $\hat{k}$ is optimized using a fixed PINN, using the difference between the estimated thermographs and measured ones as the loss. Steps 1 and 2 are iteratively repeated until convergence of $\hat{k}$.
• Figure 2: Boxplot distribution of the estimation of $k$ for all simulations with enforced steady-state condition at $t=0$.
• Figure 3: Boxplot distribution of the estimation of $k$ for all simulations without steady-state condition. While the estimation of $k$ is less stable than with guaranteed steady-state condition, PINN-it mostly converges toward the correct value of $k$.
• Figure 4: Initial temperature profile MAE vs log absolute $k$ error for both T$_{4-18}$ and T$_{1-5}$. The initial temperature profile MAE is calculated as the MAE between the temperature profile at $t=0$ from the openFOAM simulations and the temperature profile if the wall were in steady state at $t=0$. Log $k$ error compares the error in the predicted value of $k$ from PINN-it and the value of $k$ used to run the openFOAM simulation. While higher errors in predictions are associated with higher MAE values, PINN-it is still able to estimate $k$ with a large initial temperature profile's MAE.