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.

翻译：逆热问题指的是在已知或观测到热扩散行为的情况下，估计材料的热物理性质。逆热问题具有广泛的应用，其中一个关键应用在于量化建筑立面改造如何降低热传递系数，这是建筑能效的关键决定因素。然而，利用现场非侵入式采集的数据解决逆热问题容易因环境变化或与理论假设条件的偏差而产生误差。因此，当前测量导热系数的方法要么具有侵入性，要么需要较长的观测周期，要么对环境及实验条件敏感。本文提出了一种基于PINN的迭代框架，用于从一组热成像图中估计墙体的导热系数k；该框架交替进行以下步骤：在固定k的情况下使用PINN估计正向热问题，并通过比较热成像图与PINN预测的表面温度来优化k，重复此过程直至估计的k收敛。利用气象站采集的环境数据以及有限体积法软件模拟生成的数据，在墙体黎明时温度分布接近稳态的条件下，我们准确预测了不同环境条件和数据采集采样时间下的k。尽管违反稳态假设会影响k估计的准确性，但我们提出的框架仍仅表现出最大平均绝对误差为4.0851。我们的工作展示了基于PINN的方法在现场及实际条件下可靠估计材料性质的潜力，无需进行长时间的测量活动。鉴于目前缺乏利用机器学习，特别是PINN解决现场逆问题的研究，我们期望本工作能成为该领域更多研究的起点。