Physical-prior-regularized decoupled exogenous-aware network for trustworthy multi-energy load forecasting in commercial park-level integrated energy systems

Accurate day-ahead multi-energy load forecasting (MELF) is essential for the coordinated operation of commercial park-level integrated energy systems (CPIESs). However, cooling, heating, and electricity loads in CPIESs often exhibit strong seasonal variation, day-type dependence, cross-load coupling, and frequent near-zero intervals, making it difficult to ensure both forecasting accuracy and trajectory plausibility. To address these challenges, this study proposes a lightweight physical-prior-regularized decoupled exogenous-aware network (PDENet) for trustworthy day-ahead MELF. PDENet organizes historical loads, exogenous context, target-day forecasts, and physically motivated soft priors according to the practical information flow of day-ahead operation. Specifically, it decouples intra-load temporal evolution from inter-load interaction, augments load representations with historical exogenous context, and uses target-day exogenous forecasts to retrieve historically relevant daily patterns. During training, soft priors related to non-negativity, temporal smoothness, weather-consistent thermal response, and reduced simultaneous cooling/heating demand under mild-weather conditions are introduced to improve the plausibility of predicted load trajectories. Experiments on a real-world CPIES dataset from Hebei, China, show that PDENet achieves RMSE values of 256.22, 109.93, and 145.21 kW and R 2 values of 0.973, 0.975, and 0.984 for cooling, heating, and electricity loads, respectively. Compared with MSE-only training, regularization-aligned diagnostics show that the full loss reduces negative-violation, trajectory-curvature, and thermal-inconsistency magnitudes by 80.24%, 63.87%, and 86.39%, respectively. External validation on the Kitakyushu campus dataset further supports the cross-system robustness of PDENet. These results indicate that PDENet improves forecasting accuracy and trajectory plausibility, offering a practical data-driven route toward trustworthy day-ahead MELF in CPIESs.