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.
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