Organizations: School of Computer Science and Technology, Huaibei Normal University, China · Chair of Robotics, Artificial Intelligence and Real-time Systems, Technical University of Munich, Germany
A strong direct tree model may remain the best standalone photovoltaic forecaster, yet a weighted combination can reduce its residual errors. We examine whether complementary temporal predictors can lower the tree's mean absolute error (MAE) over 15--240 minutes without weaker ensemble members degrading performance. The candidate bank contains LightGBM and seven neural implementations with different temporal representations. A combiner fitted to MAE has nonnegative weights that sum to one. Unhelpful candidates can receive zero weight, while the tree anchors the combination and provides a development-stage fallback. The main design shares weights across horizons; horizon-specific weights and alternative losses test whether further complexity is needed. On 56,078 windows from two co-located public PVDAQ systems, the historical shared-MAE policy reduces scaled MAE by 3.21% relative to the tree. The latest bounded neural correction does not reduce MAE further than this static combination. The results support selective combination of complementary predictions in this bank rather than equal averaging or indiscriminate addition of modules. Both analyses reuse a previously inspected evaluation period. They do not establish independent replication, weather-specific causation or universal gains from eight experts.
Figures & tables
Figure 1: Candidate representations for the same power-forecasting task. Model-specific input preparation feeds seven neural implementations and one direct tree predictor. The tree is the baseline and combination anchor; the remaining forecasts are retained only through their fitted weights. Each produces 16 direct forecasts, giving a 16×8 prediction matrix at each origin. The matrix cells show dimensions rather than measured values. Future weather comes from retrospective ERA5. All expert predictions are frozen before fitting the combiner.
Weights
Fit loss
Vectors
Free coeff.
Solver
Shared
MSE
1
7
SLSQP
Shared
MAE
1
7
Linear program
Leadwise
MSE
16
112
SLSQP
Leadwise
MAE
16
112
Linear program
Table 1: Matched coefficient-fitting design. Every condition uses the same eight-expert predictions and Fusionfit windows. These degrees of freedom count only simplex coefficients before boundary solutions. Policy selection is a separate step.
Figure 2: Fusion and policy selection. (a) The factorial design crosses fitting loss with shared or horizon-specific simplex weights. (b) A policy uses the tree through horizon k and blends it with the fitted combination afterwards; k=0 removes the compulsory tree prefix. (c) Distinct development stages fit the experts and weights, select (k,α) , and confirm the selected policy or return to the tree. Confirmation does not search for a replacement candidate. Counts are windows, not independent observations. Evaluation labels have no role in these decisions, although the evaluation period was inspected in earlier research.
Method
sMAE
sRMSE
Gain (%)
Equal eight-member weights
0.028874
0.066017
-9.94
Tree / accepted singletons
0.026262
0.066494
+0.00
Original eight-member ensemble
0.026095
0.064109
+0.64
Shared MSE, accepted
0.025945
0.065726
+1.21
Shared MAE, accepted
0.025420
0.064348
+3.21
Leadwise MSE, accepted
0.026262
0.066494
+0.00
Table 2: Matched eight-member comparison. Entries average three seed-specific losses, not predictions. Positive gain denotes lower sMAE than the tree. Persistence controls are reported in the supplement.
Contrast
Reduction
95% interval
MAE gain, shared
0.000440
[0.000062, 0.000752]
MAE gain, leadwise
0.000762
[0.000459, 0.001030]
Leadwise gain, MSE
-0.000242
[-0.000316, -0.000182]
Leadwise gain, MAE
0.000080
[-0.000012, 0.000182]
Leadwise gain, MAE (accepted)
0.000066
[0.000010, 0.000124]
Table 3: Paired sMAE reductions. Circular UTC-day block resampling uses 14-day blocks and 10,000 draws. Intervals are conditional, exploratory and unadjusted for multiple comparisons or research selection.
Figure 3: Paired sMAE reductions at all 16 horizons. Positive values favor MAE fitting in (a) and horizon-specific MAE weights in (b). Raw policies share the first-horizon tree constraint, so the first zero is imposed, not estimated. Points average seed-specific losses. Bars are conditional pointwise 95% intervals from 14-day UTC blocks and are not adjusted for screening horizons. The curves are exploratory and do not define a switching threshold.
Family
A
C
A−C
Shared MSE
0.002023
0.002422
-0.000399
Shared MAE
0.000823
0.001661
-0.000839
Leadwise MSE
0.002256
0.002413
-0.000157
Leadwise MAE
0.000903
0.001822
-0.000919
Table 4: Descriptive A/C accounting relative to the tree for the raw factorial policies. A negative difference A minus C denotes improvement. More cancellation alone is not the objective.
Figure 4: Factorial evidence and error accounting for raw policies. (a) Overall paired effects using 14-day blocks. Dark intervals are pointwise 95% intervals; pale intervals show Bonferroni sensitivity for four contrasts. This retrospective adjustment does not account for earlier research decisions. (b) The MSE-to-MAE gain equals (AMSE−AMAE)+(CMAE−CMSE) . Cancellation contributes negatively under both parameterizations. Bar heights are descriptive point estimates with no uncertainty bars.
Method
Lday
Daylight MAE (kW) ∗
Reduction (%)
Matched-label standalone tree
0.05086079
6.478810
0.00
Static tree-anchored combination
0.04995439
6.372286
1.78
Combination + bounded joint correction
0.04995897
6.372638
1.77
Table 5: Matched public retraining check for the exposed 2016 period. Daylight MAE is computed with equal-system weighting after averaging predictions. The independent tree receives all training labels available to the full pipeline. Percent reductions refer only to this table’s primary metric.
Solar power forecasting predicts photovoltaic generation and irradiance from weather, imagery, plant data, and recent output to support reliable grid and energy decisions.
Short-term photovoltaic power forecasting requires models to represent regular solar cycles and weather-driven fluctuations whose importance changes with the forecast horizon. This study develops a hierarchical ensemble that combines temporal neural models, historical analogs, state climatology, and gradient-boosted trees. Solar geometry and numerical weather forecasts describe the expected generation conditions, while horizon-specific convex weights combine complementary predictions. A separate calibration step uses available historical forecast errors to account for recent bias. The framework is evaluated on public PVDAQ data at 15--240-minute horizons and on three GEFCom2014 solar zones at hourly horizons up to four hours. On PVDAQ, the ensemble achieves a daylight capacity-normalized mean absolute error of 4.315%, reducing error by 4.11% relative to full-feature LightGBM and by 6.03% relative to fine-tuned Chronos-2 under identical calibration. Expert-removal experiments identify redundancy within the ensemble. Across three training seeds on GEFCom2014, learned fusion improves upon equal weighting but performs comparably to LightGBM. The results support horizon-specific combination as a useful forecasting strategy while showing that its advantage over strong individual models depends on the dataset and evaluation period.
Xu Yuqing, Zhou Liguo, Sun Ze +2
School of Computer Science and Technology, Huaibei Normal University, China
An ensemble can improve photovoltaic forecasts while adding components that contribute little or increase computation. We assess these effects through matched comparisons and ablations of a fixed heterogeneous predictor bank. Hourly experiments use GEFCom2014 and three additional public datasets, with chronological partitions and three seeds. Under retrospective ERA5 assistance, static fusion reduces scaled mean absolute error against matched boosting by 1.11%, 4.41%, and 1.63% on PVDAQ, OPSD, and Ausgrid; only OPSD remains supported after multiple-comparison correction. Weather gating offers no consistent incremental benefit. Exploratory member removals show group-level dependence alongside individual redundancy. A separate, previously inspected fifteen-minute case replaces one neural member with a tree predictor: normalized error falls by 1.72%, but measured inference is slower. These findings support component-wise evaluation with explicit limits on weather availability and test-set reuse.
Sun Ze, Zhou Liguo, Xu Yuqing +2
aSchool of Computer Science and Technology, Huaibei Normal University, China
Several energy management applications rely on accurate photovoltaic generation forecasts. Common metrics like mean absolute error or root-mean-square error, omit error-distribution details needed for stochastic optimization. In addition, several approaches use weather forecasts as inputs without analyzing the source of the prediction error. To overcome this gap, we decompose forecasting into a weather forecast model for environmental parameters such as solar irradiance and temperature and a plant characteristic model that captures site-specific parameters like panel orientation, temperature influence, or regular shading. Satellite-based weather observation serves as an intermediate layer. We analyze the error distribution of the high-resolution rapid-refresh numerical weather prediction model that covers the United States as a black-box model for weather forecasting and train an ensemble of neural networks on historical power output data for the plant characteristic model. Results show mean absolute error increases by 11% and 68% for two selected photovoltaic systems when using weather forecasts instead of satellite-based ground-truth weather observations as a perfect forecast. The generalized hyperbolic and Student's t distributions adequately fit the forecast errors across lead times.
Philipp Danner, Hermann de Meer
University of Passau, Innstraße 41, Passau, Germany