Load-as-a-sensor? Sensing indoor conditions at scale with system identification models of HVAC loads

The transition toward renewable-powered grids has intensified the need for building demand-side flexibility, yet unlocking building thermal flexibility potential requires accurate and scalable dynamic models. Current data-driven approaches face a critical scalability challenge: they predominantly rely on indoor temperature measurements and intrusive experiments for training, preventing massive deployment across heterogeneous building stocks. This paper proposes a physics-informed load-to-temperature transformation (LTT) framework to bridge this gap, enabling the identification of comprehensive thermal models using only ubiquitous HVAC load metering under regular operation conditions. We demonstrate that this inference methodology framework broadly allows integration of existing classical and differentiable system identification models. We selected, adapted, and developed four candidate models following two modeling paradigms: (1) State-Space models, considering both classical RC networks and an adapted differentiable Physics-Constrained Neural State-Space Model (PC-NSSM), and (2) Transfer Functions, comparing ARMAX with a newly developed differentiable Physics-Constrained ARX model (PC-ARX(1)). We validated our approach on real-world datasets covering both linear thermostatic control and non-linear weather-compensated radiator control. After LTT, our best candidate models achieve 2–5% MAPE in indoor temperature inference on unseen operating modes without "seeing" any explicit temperature data, approximating the accuracy of ideal baseline models trained with explicit temperature sensors. Beyond inference accuracy, we demonstrate that this transformation successfully identifies physical invariants—including time constants, steady-state heat loss factors, and non-linear radiator exponents—while providing robust uncertainty quantification. By resolving the scalability challenge broadly and advancing in the physics-informed differentiable learning for data-driven building thermal modeling, this work paves the way for credible, occupant-centric and energy-flexible building HVAC operation at scale.