Adaptive Physics-Informed Neural Networks with Learnable Seasonal Weights for Long-Horizon Building Temperature Prediction

Commercial buildings account for approximately 17% of U.S. carbon emissions, with HVAC systems consuming 40-60% of building energy. Accurate long-horizon temperature prediction is critical for intelligent HVAC control, yet existing models fail to capture seasonal physics variation — a key driver of prediction error at extended horizons. We present Seasonal-PINN V3, extending the hybrid XGBoost-PINN framework of [1] with three contributions on the Google Smart Building SB1 dataset (123 zones, 93,858 sq. ft., Mountain View, CA, 32.2M sensor readings). (1) Data-driven thermal regimes: k-means clustering (k=3, silhouette=0.515) identifies Cold (January–March, November–December), Transition (April–May), and Warm (June–October) regimes from annual inter-zone variance (σCold=3.09°F vs. σWarm=2.14°F), with regime-specific physics weights and imputation-aware sample weighting reducing Cold Stage-4 MAE by 75.7% (1.069→0.260°F). (2) Learnable physics weight: A per-timestep λ-MLP (2-layer, inputs: regime, season progress, setpoint gap, imputation flag), regularised toward the regime prior (μ=0.1), autonomously recovers the Cold > Transition > Warm weight ordering without supervision, preventing the collapse to λ≈0 observed under unregularised training. (3) Encoder ablation: Evaluating MLP, TCN, and LSTM encoders across a 9-stage scaling ladder, LSTM achieves best short-horizon MAE (Stage-4: 0.404°F) while adaptive-λ with MLP encoder achieves 0.138°F on 1-year cross-regime chaining — a 15.3% improvement over the V2 baseline (0.163°F) — demonstrating that learnable physics weighting with prior regularisation consistently outperforms fixed-λ approaches at long horizons.