Calibrated Thermal Twins for Localizing and Quantifying Thermal-Bridge Heat Loss

We introduce a calibrated thermal twin that localizes thermal bridges and quantifies heat loss from as-built geometry, material information, and exterior infrared measurements. The central challenge is that distinct interior conductivity fields can produce the same surface temperature, making full-field reconstruction an ambiguous target for learned inversion. Our approach exploits the distinction between this hidden field and the surface transmittance that remains identifiable under known steady-state boundary conditions. The twin combines a geometry-conditioned neural surrogate for surface-temperature prediction with an amortized network for bridge localization. Its diagnostic stage recovers surface transmittance (U-value) through a physical surface-flux identity and localizes the lateral footprint of thermal bridges without reconstructing the interior. Split-conformal calibration provides U-value intervals with distribution-free, finite-sample marginal coverage under exchangeability. On the synthetic junction benchmark generated with a solver validated against ISO 10211 reference cases, direct surface readout achieves a U-value mean absolute error of $0.039\mathrm{W}{\mathrm{m}}^{-2}{\mathrm{K}}^{-1}$, compared with $0.046\mathrm{W}{\mathrm{m}}^{-2}{\mathrm{K}}^{-1}$ when the same quantity is read from an optimized conductivity field. The surface-anomaly localizer achieves a bridge-footprint IoU of $0.35$, compared with $0.15$ for optimization and at most $0.08$ for the learned field inverses. Across increasing measurement noise, U-value error remains substantially more stable than field-based optimization, while empirical conformal coverage remains at or above the nominal $90\%$ level. Experiments in heat conduction, Darcy flow, and electrical-impedance tomography further show that useful physical quantities can remain recoverable despite inaccurate field reconstruction. Experiments on real building geometry and measured infrared data further assess localization plausibility, while differentiable retrofit optimization demonstrates the downstream use of the thermal twin. These results support designing inverse methods around quantities that boundary observations actually identify.