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.

This study examines zero-shot cross-topology generalization for DC power flow under varying load and renewable generation. A leakage-safe primary protocol uses 3500 physically generated IEEE-30 scenarios for development and internal evaluation, and 1000 IEEE-57 scenarios for external evaluation and reserve. Each bus is represented by 16 operating and topological features. The proposed KENO-Krylov operator combines bounded neural initialization, positive local preconditioning, explicit Kirchhoff residuals, and a 20-step Krylov/CG-like recurrence with a hard slack-bus constraint, using 2523 trainable parameters. On the locked IEEE-30 test, it achieves R² = 0.999999 and angle MAE 0.00159°. On unseen IEEE-57, it retains R² = 0.9440 and angle MAE 0.783°, but the median relative KCL residual remains 0.1433. Supplementary paired experiments quantify three renewable-generation regimes, external component ablations, and larger and radial networks. At the highest prescribed renewable scale, mean generation covers 49.63% and 53.25% of demand on IEEE-30 and IEEE-57. On 500 new IEEE-118 scenarios, angle MAE increases to 7.719° and median KCL to 0.974; radial stress tests reveal further accuracy limitations. Learned corrections slightly improve angle MAE over PCG-20, whereas convergent numerical solvers are more accurate and reused Cholesky factorization is faster in the measured setting. Nominal 90% uncertainty calibration does not transfer externally. The evidence supports comparative point-prediction transfer within the stated synthetic DC experiments, not universal topology generalization, operational security, or validity for nonlinear AC systems.