Building-MoE: A closed-loop routing sparse mixture-of-experts time-series foundation model for building short-term load forecasting

Short-term load forecasting (STLF) is crucial to building energy optimization. Among existing approaches, forecasting methods face challenges in improving predictive accuracy, achieving cross-building transferability, and meeting engineering compliance requirements, among others. To address these challenges, we propose Building-MoE, a sparse Transformer-based Time-series Foundation Model (TSFM) for building STLF that integrates a Mixture-of-Experts (MoE) into an encoder–decoder framework to enhance cross-building transferability under heterogeneous and non-stationary building loads. At inference, only about 98M active parameters are engaged (compared with Time-MoE ≈198M and Chronos-Bolt ≈ 203M), delivering higher parameter and compute efficiency. However, sparse MoE training is prone to expert imbalance or collapse, which reduces effective capacity and generalization. Therefore, we design a Closed-Loop Routing Scheduler (CLRS) that continuously monitors routing entropy and the maximum expert share, combines stagewise temperature and noise scheduling with feedback corrections and short pulse interventions, and revives long-inactive experts through bias updates. We also introduce a token-weighted Load Balancing Loss (LBL) that normalizes by routed tokens to suppress long-term imbalance, and we use the Huber loss to improve robustness to anomalies and noise. Under the domain adaptation setting, the proposed Building-MoE achieves state-of-the-art (SOTA) performance, attaining average CVRMSE 23.21%, NMAE 15.29%, and NMBE 2.95%, with the vast majority of scenarios satisfying the ASHRAE Guideline 14 hourly thresholds (CVRMSE ≤ 30%, |NMBE| ≤ 10%). Under the direct transfer setting, Building-MoE also achieves SOTA performance, with averages of CVRMSE 27.22%, NMAE 18.26%, and NMBE 3.80%, and most scenarios likewise satisfying the same thresholds, demonstrating stable cross-building generalization.