A Physics-Informed Bayesian Framework for Calibrated, Multi-Horizon Forecasting of Solar, Wind, and Hybrid Renewable Generation

Abstract

Renewable-generation forecasting is a probabilistic time-series problem in which point accuracy alone is insufficient for operational decision-making. This study proposes a physics-informed Bayesian framework for multi-horizon forecasting of solar, wind, and total renewable generation. The task is formulated as a 15-dimensional target–horizon problem covering three generation families and five forecast horizons: H1, H3, H6, H12, and H24. A leakage-safe data construction protocol generates causal predictors from meteorological observations, generation history, calendar cycles, lagged and rolling statistics, ramp descriptors, and physics-informed transformations. PI-BHTF partitions the 422-dimensional predictor space into solar, wind, temporal-calendar, and cross-context components, encodes them through parallel nonlinear branches, and combines the representations using cross-energy gated fusion. Its neural core uses a heteroscedastic predictive head and Monte Carlo dropout to distinguish input-dependent aleatoric uncertainty from epistemic variability, whereas the final hybrid forecasts are calibrated using residual quantiles computed from a chronologically held-out validation segment. Across three prespecified random seeds, the full PI-BHTF achieved a mean MAE of 0.0797 ± 0.0007 on the internal chronological test and 0.0686 ± 0.0006 on locked external SCADA validation. Performance and calibration varied substantially across target–horizon tasks, including marked short-horizon external undercoverage for wind generation. Component-wise ablation supported semantic feature partitioning and the heteroscedastic head, whereas the physics-informed features, cross-energy gate, and physics-consistency loss did not independently reduce aggregate MAE. PI-BHTF should therefore be interpreted as a reproducibly competitive framework that balances multi-horizon accuracy, structured representation, uncertainty estimation, and external transferability rather than as a universally dominant model.