Adaptive Stochastic Physics Weighting for Long-Horizon Building Temperature Prediction under Sensor Uncertainty

Building temperature dynamics involve stochastic thermal processes driven by HVAC actuation, weather, and occupancy. Physics-informed neural networks (PINNs) Raissi et al. [2019] embed smoothness constraints via a fixed global weight λ - assuming homoscedastic physics across seasons. We show this assumption is violated: inter-zone variance shifts from σCold=3.09°F to σWarm=2.14°F, motivating a seasonally adaptive λ. We present Seasonal-PINN V3, a hybrid XGBoost-PINN Chen and Guestrin [2016] that replaces fixed λ with a per-timestep λ-MLP conditioned on regime identity, season progress, setpoint gap, and imputation flag, regularised toward regime-specific priors (λCold=0.35 > λTrans=0.20 > λWarm=0.12) via µ·(λ(t)−λfixed)². Sensor dropout (28.6% missing in Google SB1 dataset Goldfeder et al. [2024]) introduces measurement uncertainty; we propagate this into the physics constraint via imputation-aware sample weighting (w=0.3 imputed, w=1.0 real). On SB1 (123 zones, 93,858 sq. ft., 32.2M readings), the λ-MLP autonomously recovers Cold > Transition > Warm without supervision. Imputation-aware weighting reduces Stage-4 MAE by 66.5% (0.451→0.151°F). XGB-based cross-regime chaining reduces 2-year MAE by 76.6% over the unweighted XGB-only chain (0.338 vs. 1.444°F) - demonstrating that propagating sensor uncertainty into the physics constraint is the dominant design decision for long-horizon building temperature prediction.