Synthetic-to-Real Transfer with a Causal Temporal Convolutional Network for Site-Calibrated Virtual Heat-Flux Sensing

Accurate in-situ estimation of building envelope thermal transmittance (U-value) is essential for reliable building energy assessment and retrofit analysis. However, conventional heat flux meter (HFM) methods based on ISO 9869 require long measurement periods and quasi-steady-state conditions, limiting their applicability under dynamic environmental conditions. This paper proposes a physics-informed transformer framework for rapid and robust U-value estimation using short-duration transient measurements. The proposed approach combines a transformer-based temporal encoder with physics-based regularization derived from transient heat-transfer principles to improve prediction accuracy and physical consistency. Unlike recurrent neural network approaches, the transformer architecture captures long-range temporal dependencies and dynamic thermal storage effects occurring in multilayer wall assemblies under varying climatic conditions.
A hybrid loss function incorporating both data-driven error and heat-equation residual constraints is introduced to reduce physically inconsistent predictions and improve generalization capability. The model is trained and evaluated using a combination of experimentally acquired HFM datasets and synthetic thermal simulations generated under diverse boundary conditions, including varying outdoor temperatures, solar radiation, and sensor noise levels. Model performance is compared against conventional ISO 9869 averaging procedures and LSTM-based approaches. Results indicate that the proposed framework significantly reduces the required measurement duration while maintaining high estimation accuracy and improved robustness under nonstationary conditions. In addition, uncertainty-aware prediction intervals are incorporated to quantify confidence in estimated U-values. The proposed method demonstrates the potential of physics-informed transformer architectures for intelligent and scalable building envelope thermal diagnostics.