Reducing Multi-Horizon Photovoltaic Forecast Error through Tree-Anchored Expert Combination

Research question

• The study tests whether MAE-aligned combination reduces a strong direct tree’s residual error across 16 photovoltaic forecast horizons.LightGBM is the reference under the same information and target definitions.Source: §1 · pp. 2, 4

Motivation

• Power variability and recent-observation usefulness may change with lead, but the data do not establish cloud-motion causes or weather-specific expert roles.The study instead tests whether individually weaker forecasts contribute useful residual information when combined with the tree.Source: §1 · p. 2

Scope

• The study isolates static MAE-fitted weights rather than adding weather clustering or joint feature-search modules, and does not directly compare published error values.Its evaluation period had already been inspected in earlier research, so the study does not claim independent validation.Source: §1 · pp. 3–4

Approach

• The eight-model bank uses a constrained linear combiner fitted to absolute error, allowing weak candidates to receive zero weight.Equal averaging can increase MAE when members’ errors outweigh cancellation.Source: §1 · pp. 3–4

2.1. Eight Candidates for One Forecasting Task

• The task uses two co-located Nevada PVDAQ systems, 96 quarter-hour historical observations, and 16 direct forecasts from 15 to 240 minutes ahead.The tree uses a direct head for each horizon rather than recursively feeding its predictions back as observations.Source: §2.1 · pp. 4–5
• The bank pairs LightGBM with seven neural temporal representations; candidates are fixed-weight predictors, not weather-labelled specialists or input-dependent routers.Their architectural differences motivate testing combined value, not assigning experts to weather classes.Source: §2.1 · pp. 5–6
• Power is scaled by each system’s observed training maximum; retrospective ERA5 weather lacks operational issue times, so this is not an issue-time weather-forecast evaluation.The paper calls the resulting metrics sMAE and sRMSE, not capacity-normalized errors or accuracy percentages.Source: §2.1 · p. 6

2.2. Separation of Development Stages

• The frozen 16 × 8 prediction matrix precedes combiner fitting, and calendar-separated training and development stages precede the 2016 evaluation.The prepared data include 56,078 evaluation windows.Source: §2.2 · pp. 7–9
• Overlapping windows, repeated targets, co-location, and shared tree predictions prevent treating evaluation entries or random seeds as independent replications.Although evaluation labels do not change policy choices, the 2016 period had already been inspected; later baseline and optional-prefix controls are exploratory follow-ups.Source: §2.2 · p. 9

3.1. Shared Weights as the Main Design

• Shared weights use one vector across all 16 horizons, with seven free coefficients rather than 112 for horizon-specific weights.Both shared and horizon-specific parameterizations fit pooled absolute or squared error on Fusionfit.Source: §3.1 · p. 10
• Policy selection searches tree-prefix and mixing-strength candidates, while Confirmation accepts only a strictly improving policy or retains the tree.The historical optional-prefix control adds k = 0 candidates, testing the compulsory tree-prefix restriction.Source: §3.1 · pp. 11–12

3.2. Checking Why Combination Helps

• Error accounting decomposes realized policy loss relative to the tree into member-error and cancellation terms, but describes observed losses rather than causal effects.The diagnostic uses the actual policy weights, including any tree mixture; future-target cancellation is unknown at issue time.Source: §3.2 · p. 12

3.3. Baselines and Uncertainty

• The historical ensemble and smart-persistence proxy provide additional baselines, but neither comparison isolates the unregularized shared-MSE fitting effect.The historical ensemble uses a penalty toward uniform weights; the persistence proxy lacks panel geometry and cloud advection.Source: §3.3 · p. 14
• Block-bootstrap intervals are conditional on the fitted bank and decisions, and do not account for retraining variability, research-history selection, or independent-site generalization.Intervals are pointwise and unadjusted for the main tables and horizon curves; the analysis reports effect sizes without claiming confirmatory status.Source: §3.3 · pp. 14–15

4.1. Does Combination Beat the Strong Tree?

• 3.21% and 3.46%: shared-MAE and horizon-specific-MAE policies reduce sMAE relative to LightGBM, but the original ensemble has the lowest sRMSE.Equal weights perform worse, and both singleton selectors retain the tree at every horizon.Source: §4.1 · p. 15, Table 2 · p. 16

4.2. Does MAE Alignment Help the Accuracy Target?

• 0.000440 and 0.000762: MSE-to-MAE fitting reduces sMAE for shared and horizon-specific weights, respectively, under the common raw first-horizon tree constraint.The shared contrast's four-contrast Bonferroni sensitivity interval spans zero; the horizon-specific contrast remains positive, so the point estimates are not uniform evidence across uncertainty conventions.Source: §4.2 · pp. 16–17, Table 3 · p. 17

4.3. Are More Weight Parameters Needed?

• With MAE fitting, horizon-specific weights improve raw sMAE by only 0.000080 over shared weights, and the 14-day interval spans zero.The evidence for 105 additional coefficients is sensitive to temporal resampling; the accepted horizon-specific score is 0.000066 lower, but that comparison includes policy decisions and does not isolate coefficient dimensionality.Source: §4.3 · pp. 17–18, Figure 3 · p. 18

4.4. Member Error and Realized Cancellation

• 0.001200 lower weighted member error minus 0.000761 less cancellation yields a net shared-weight sMAE reduction of 0.000440 when fitting MAE rather than MSE.The corresponding horizon-specific reductions are 0.001354 in member error and 0.000591 in cancellation, yielding a 0.000762 sMAE reduction; these are realized-loss quantities, not causal evidence.Source: §4.4 · p. 19, Table 4 · p. 19

4.5. Robustness and Sensitivity

• The shared-weight MSE-to-MAE gain reverses in summer, while horizon-specific MAE gains over shared MAE in system 34 but slightly worsens it in system 35 and in winter.The optional-prefix control weakens a universal tree-first rule, but does not identify when a recursively applied tree would fail; subgroup summaries are not independent replications.Source: §4.5 · pp. 19–21, Figure 4 · p. 20

4.6. Matched Public Retraining without Future Weather

• Only PatchTST, N-HiTS-PV, and TimeXer-PV receive positive neural weights in the matched retraining fits; four candidates receive zero static weight.The authors caution that this does not show the inactive architectures are generally ineffective, only that this dataset and fitting recipe do not justify equal weighting or eight active branches.Source: §4.6 · pp. 22–23, Table 5 · p. 23
• The latest bounded neural correction yields slightly higher aggregate MAE than the static combination, although its RMSE-derived score improves slightly.It is a negative incremental result, not the source of the paper's MAE gain.Source: §4.6 · pp. 21, 23

5.1. What the Accuracy Result Supports

• Shared weights recover most of the historical accepted gain without the 105 extra free coefficients required by horizon-specific fitting.Matched-label retraining gives the same qualitative result without future weather.Source: §5.1 · p. 24
• The tree anchor, MAE objective, and simplex weights that permit zeros address the accuracy problem by targeting reported error while limiting dilution by weak candidates.The optional-prefix results do not support a universal tree-only rule for a fixed initial duration; the latest joint correction fails to improve MAE in the retraining check.Source: §5.1 · p. 24

5.2. What Remains Unresolved

• The data do not establish that cloud fluctuations, ramp events, or a meteorological variable cause the remaining errors.Historical data use retrospective ERA5, while retraining removes weather inputs; weather-specific robustness would require issue-time weather, prespecified regimes, and within-regime error comparisons.Source: §5.2 · pp. 24–25
• Co-located systems and a previously inspected evaluation period do not provide independent site replications.Overlapping targets and seeds are not independent; subgroup reversals and adjustment sensitivity limit stable-improvement claims, and differing protocols preclude interpreting the analyses as numerical replication.Source: §5.2 · p. 25
• Confirmation should freeze the static tree-anchored MAE combination and matched-label tree comparator before testing a new site or time period.The proposed check should use a prespecified practical threshold; member-removal tests and published-time weather evidence are needed for claims of indispensable experts or weather-driven improvement.Source: §5.2 · p. 25

• The study targets reducing residual MAE from a strong direct tree over 15–240-minute photovoltaic power forecasts.Source: §6 · p. 25
• 3.21% lower historical scaled MAE came from the anchored, shared-MAE combination; a separate retraining check without future weather lowered daylight, equal-system MAE by 1.78% against a tree with the same training-label access.Both analyses reuse an exposed period and use different protocols.Source: §6 · p. 26
• Within this bank, the results support selective combination over indiscriminate averaging, but not a need for eight active experts, horizon-specific weights, or the latest joint correction.Independent confirmation is needed before claiming transferable accuracy gains or operational weather-forecasting benefit.Source: §6 · p. 26

• PVDAQ is publicly available.Source: Data and Code Availability · p. 26
• The matched retraining records include a frozen feature/split protocol, code and data hashes, three seed predictions, an independent metric audit, and hashes for 126 remote model/configuration artifacts.Frozen predictions, configuration records, and non-fitting audit scripts are retained locally.Source: Data and Code Availability · p. 26
• Public archival release and redistribution checks remain pending; no public reproducibility deposit is claimed.Source: Data and Code Availability · p. 26