State Transport Routing for Short-horizon Adaptation in Multi-horizon Photovoltaic Forecasting

• Recent measurements reflect current operating conditions, but directly extrapolating short-term trends can cause substantial errors when those trends do not persist over longer horizons.The paper frames the challenge as incorporating recent operating information while preserving reliable longer-term predictions.Source: §1 · p. 2
• Rather than modifying forecasting architectures, the study adapts an already trained model’s output using recent power measurements for short-horizon predictions.The introduction situates this approach alongside models including N-HiTS, TimeMixer, PatchTST, iTransformer, DLinear, and TSMixer.Source: §1 · p. 2
• STR combines a frozen model forecast with trajectories based on the latest measured power and its recent trend, using horizon-conditioned routing and a residual correction for the first 120 min.Predictions beyond that interval remain identical to the original model’s outputs.Source: §1 · p. 2
• The evaluation asks whether explicit state routing beats residual correction, transfers across frozen neural models, and varies in effectiveness by horizon, architecture, and operating condition.Source: §1 · p. 2
• Across four public PV datasets, STR improves forecasting accuracy beyond a nominally parameter-matched residual adapter; its PVDAQ evaluation also reports no reliable improvement for LightGBM.The study applies STR to five neural forecasting models under a common PVDAQ protocol.Source: §1 · p. 3

2.1. Multi-horizon PV forecasting

• Rather than developing another forecasting architecture, STR adapts predictions after training, refining short-horizon forecasts while preserving longer-horizon outputs.Prior work reviewed includes Transformer-based and recurrent models, as well as hierarchical, multiscale, and exogenous-variable approaches.Source: §2.1 · p. 3

2.2. Forecast combination and short-range state information

• STR combines a frozen backbone’s output with two trajectories from recent measurements, adjusting their contributions by horizon and restricting the correction to the short term.The reviewed alternatives include persistence and trend extrapolation, whose assumptions may become less reliable as the horizon grows.Source: §2.2 · pp. 3–4

2.3. Output adaptation and positioning of STR

• Unlike stacking complete forecasts, STR retains a single frozen predictor and adds state trajectories; its residual-adapter control does not distinguish latest-level and trend assumptions.The comparison examines the contribution of explicit state trajectories under the same experimental protocol.Source: §2.3 · p. 4

3.1. Problem formulation and design objective

• The backbone maps available power history and prediction-time covariates to an H-step forecast, which STR adapts without changing the backbone parameters.Source: §3.1 · pp. 4–5

3.2. Candidate state transports

• STR forms three candidate paths: the backbone forecast, latest power held constant, and a recent-trend extrapolation.The slope path is a simple extrapolation, not a physical ramp model, and follows each dataset’s native sampling interval; routing uses a local-state descriptor and horizon embedding, with dataset-specific inputs.Source: §3.2 · p. 5

3.3. Horizon-conditioned routing and exact bypass

• A horizon-conditioned router weights the candidate trajectories and adds a residual correction for the first 120 minutes, then returns the backbone prediction unchanged.The cutoff corresponds to the forecast step at the dataset’s native sampling interval.Source: §3.3 · p. 6

3.4. Matched mechanistic control

• The matched control uses the same descriptor, hidden projection, nominal parameter count, optimization settings, and long-horizon bypass, but replaces state combination with an additive correction.Inactive routing logits mean nominal parameter matching does not establish identical effective capacity for every residual-adapter design.Source: §3.4 · p. 6

3.5. Backbones and optimization

• GEFCom uses a compact convolutional backbone, while Gatton, Solar-Energy, and PVDAQ use TimeMixer; adapters are trained for 24 epochs with AdamW.Three seeds are used; PVDAQ varies adapter training on a single pretrained backbone checkpoint, rather than backbone retraining.Source: §3.5 · pp. 7–8

3.6. Backbone interface and transfer protocol

• STR operates on forecast outputs without hidden representations, and each backbone receives a separately trained adapter with no router-weight sharing.This tests reuse of the design across models, not direct transfer of a trained adapter.Source: §3.6 · p. 8

4.1. Datasets and chronological partitions

• The four datasets retain native targets and normalizations, use chronological partitions, and follow dataset-specific preprocessing and evaluation conventions.Solar-Energy’s reported table counts are eligible forecast-origin windows, not raw time rows.Source: §4.1 · pp. 8–9, Table 1 · p. 9

4.2. Mechanism evaluation

• The mechanism evaluation compares STR with a residual adapter using the same frozen predictions, state descriptor, training procedure, long-horizon bypass, and nominal parameter count.The residual adapter replaces trajectory combination with an additive correction; the comparison isolates explicit state routing within the implemented architecture.Source: §4.2 · pp. 9–10

4.3. Backbone-transfer evaluation

• On PVDAQ, five neural backbones and LightGBM are evaluated with frozen backbone parameters and predictions under a shared protocol.Each backbone receives separately trained STR and nominally parameter-matched residual adapters; three seeds, 29,211 test origins, and no backbone-specific tuning are used. Reported backbone scores differ from the external benchmark because seed-aggregation procedures differ.Source: §4.3 · p. 10

4.4. External benchmark

• The external benchmark compares 13 learning-based methods on four public PV datasets using common chronological splits, forecast origins, history lengths, targets, and available inputs.Model selection uses selection sets, and newly trained methods are evaluated with three seeds; the GEFCom weather experiment and hardware-specific latency comparisons are reported separately.Source: §4.4 · pp. 10–11

4.5. Metrics and paired uncertainty

• Dataset-specific scaled MAE is averaged across horizons, while paired temporal resampling estimates uncertainty in method differences.PVDAQ external paired intervals use 5,000 circular seven-day block draws; pairing is by forecast origin and mask, not matched checkpoint seed, and the two difference estimands can have opposite signs.Source: §4.5 · pp. 11–12

4.6. Efficiency

• STR’s computational overhead is assessed through adapter parameters, training time, and inference latency, with latency measured against the backbone in the same session.Latency uses batch size one, 30 warm-up runs, and 200 timed repetitions; GPU neural and CPU tree-model timings are reported separately.Source: §4.6 · p. 13

5.1. Structured routing versus matched residual correction

• STR has lower dataset-specific scaled MAE than the nominally parameter-matched residual adapter on all four tasks, with paired 95% intervals excluding zero.Table 2 reports dataset-specific scaled MAE multiplied by 100; reductions and intervals use the same units.Source: §5.1 · p. 13, Table 2 · p. 13

5.2. Transfer across frozen neural backbones

• On PVDAQ, STR reduces all-horizon nMAE by 0.0201–0.2364 percentage points across five neural backbones, with paired 95% intervals excluding zero against both original backbones and matched residual adapters.LightGBM's interval crosses zero, so its experiment does not establish an improvement.Source: §5.2 · p. 14, Table 3 · p. 14, Figure 2 · p. 15

5.3. Horizon-resolved adaptation

• Horizon-specific gains vary: DLinear improves at all eight routed horizons, while some estimates for TimeMixer, TSMixer, and iTransformer are negative or include zero.Only the first eight of sixteen equally weighted PVDAQ horizons are adapted, so the all-horizon reduction is half the mean routed-horizon reduction, apart from rounding.Source: §5.3 · p. 15, Table 4 · p. 16

5.4. Exact long-horizon preservation

• Predictions from 135 to 240 min are identical to the frozen backbone outputs; this preserves their errors as well as their forecasts.The equality follows from the architecture and does not show that STR improves third- or fourth-hour accuracy.Source: §5.4 · pp. 15–16

5.5. External benchmark comparison

• Across GEFCom, Gatton, Solar-Energy, and PVDAQ, the original TimeMixer-based STR system ranks third, first, third, and fifth, respectively; tree ensembles lead PVDAQ.On PVDAQ, LightGBM, XGBoost, and CatBoost have all-horizon nMAE values of 4.5405%, 4.5753%, and 4.6068%.Source: §5.5 · p. 16
• External paired comparisons favor some methods but remain inconclusive for TSMixer, iTransformer, TimesNet, and TimeXer; no frozen paired interval was available for N-HiTS.For TSMixer and iTransformer, the difference changes sign depending on the seed-aggregation procedure.Source: §5.5 · p. 16

5.6. Efficiency and recorded training cost

• With TimeMixer already trained and frozen, fitting the STR adapter takes 25.8 s; across five neural backbones, added full-system median latency is 1.14–1.49 ms.Adapter fitting cost is not the training time of a complete forecasting system.Source: §5.6 · p. 17

5.7. Boundary and failure analysis

• STR's effect varies with recent-power volatility; group intervals were unavailable, and the test periods cannot establish stability across seasons.Solar-Energy's low-volatility group has a 0.000407 increase in train-standardized macro MAE. GEFCom includes one test month, and certified calendar dates are unavailable for Solar-Energy.Source: §5.7 · pp. 17–18

6.1. Mechanism and backbone transferability

• STR improves on the implemented residual control across four tasks, and five neural backbones gain in aggregate on PVDAQ with independently fitted STR weights.The matched-control result supports the tested design comparison, not every possible residual adapter; LightGBM’s paired interval crosses zero, so reliable improvement is not established for that ensemble.Source: §6.1 · p. 18

6.2. Horizon-dependent behavior

• Most routed-horizon gains occur early, but TSMixer and some other backbones regress at individual later steps within the routing window.The exact bypass leaves 135–240 min predictions unchanged, retaining their existing errors and not establishing 120 min as an optimal cutoff for every task.Source: §6.2 · p. 18

6.3. Computational considerations

• The PVDAQ adapter adds 1,204 trainable parameters and 0.906 ms (5.2%) additional TimeMixer median latency in the benchmark session.The adapter-only fit is 25.8 s; the separate transfer session measures 1.49 ms (8.5%) additional latency, with a larger added fraction for smaller backbones, and energy consumption was not measured.Source: §6.3 · p. 19

6.4. Weather conditioning

• Weather conditioning does not show a consistent gain: DLinear W1 gains under temporal pairing, but one of three seeds regresses, while TimeMixer shows no stable aggregate gain.The 56 origins with conflicting power and radiation trends are exploratory and cannot identify whether weather changed outcomes through the residual or routing logits.Source: §6.4 · p. 19

6.5. Limitations and future work

• Transfer was tested on five neural backbones and LightGBM at one PVDAQ site, and exposed public test periods mean the intervals do not substitute for independent evaluation.The discussion calls for prospective evaluation across multiple sites and seasons, with receipt records and direct energy measurements where efficiency is claimed.Source: §6.5 · p. 19

7. Conclusions

• STR combines the original forecast with trajectories based on the latest measured power and recent power trend, preserving all predictions beyond 120 min..Source: §7 · p. 19
• STR reduces error relative to the matched residual adapter on four public PV tasks and improves five neural backbones on PVDAQ with positive paired confidence intervals for aggregate results.The adapters were trained separately, so the result establishes reuse of the STR design across tested backbones, not transfer of trained router weights.Source: §7 · p. 20
• No reliable gain is observed for LightGBM, and some volatility groups and individual horizons show worse results; direct weather conditioning also provides no consistent improvement.The supported scope is a short-horizon adaptation option for the evaluated neural models, not a replacement forecasting architecture or a method shown to benefit all model families.Source: §7 · p. 20

Data availability

• PVDAQ measurements and historical GFS forecasts are identified as available through the Open Energy Data Initiative and NCAR Geoscience Data Exchange, respectively.The reproducibility package documents Gatton and Solar-Energy source manifests and preprocessing; derived code and prediction tables are planned after license and repository-metadata review.Source: Data availability · p. 20

Funding

• This research received no external funding..Source: Funding · p. 20

• ChatGPT assisted with language revision.Source: Declaration of generative AI and… · p. 20
• The authors reviewed the manuscript.Source: Declaration of generative AI and… · p. 20
• The authors remain responsible for the manuscript’s content.Source: Declaration of generative AI and… · p. 20