We embed first-principles thermal dynamics constraints directly into Bayesian neural network priors, enabling calibrated uncertainty estimates that remain physically plausible even when data is scarce — a critical property for trustworthy building energy control and diagnostics.
Machine learning-based building energy models can achieve high predictive accuracy, but their uncertainty estimates are often poorly calibrated — they either overestimate confidence (making them unsafe for control) or underestimate it (making them useless for diagnostics). Standard Bayesian neural networks address this in principle, but their priors are agnostic to physical laws, allowing the model to learn thermodynamically implausible distributions, especially under sparse or irregular sensor data.
PG-BNNs solve this by encoding physics directly into the prior. We derive informative prior distributions over network weights from the thermal dynamics of buildings — energy balance equations, RC circuit analogies, heat transfer laws — so that the posterior always respects known physical constraints, even in extrapolation regimes far from the training data.
The PG-BNN framework has three components:
Calibrated uncertainty is a prerequisite for deploying ML-based building controls safely — a model that knows what it doesn't know can hand off to rule-based fallbacks rather than making dangerous predictions. PG-BNNs provide a practical path to that goal without sacrificing the flexibility of neural networks.
Future directions include extending the physics prior to multi-zone buildings with coupled thermal dynamics, integrating PG-BNNs into model predictive control loops with formal safety guarantees, and applying the framework to other physics-rich domains such as structural health monitoring and HVAC fault detection.