A machine-learning model that uses local patterns among renewable-energy sensors usually produced the lowest forecast errors in tests across three real-world datasets, according to the study. It was not a clean sweep: on the wind-power-plant dataset, STAEformer had lower mean absolute error (MAE) and root mean squared error (RMSE), while SPALT and HSTGNN recorded the best relative squared error (RSE), which compares performance with a location-specific training-set average.
The method, called SPALT, is a linear model tree: a branching model whose leaves use linear models to make predictions. It groups similarly trending series locally, selectively injects spatial features and uses Reduced Error Pruning while retaining spatio-temporal locality as the tree is simplified. The study asks whether those local relationships can improve energy-production forecasting from geo-referenced time series.
Three datasets, several model families
The experiment covered 332 photovoltaic plants, 134 wind turbines and 60 wind power plants. The three datasets used five-, 10- and 15-minute resolutions, respectively, and were split into temporal training, validation and test partitions. The reported training and testing instance counts were 382,464 and 95,616; 540,288 and 135,072; and 691,200 and 172,800, respectively.
Researchers compared SPALT with tree-based methods, including regression trees, random forests and XGBoost, and with several neural forecasting architectures. They scored the models by MAE, RMSE and RSE, and also recorded tree-node counts, average RMSE rank and running time.
A broad lead with one clear exception
On UKPV, SPALT was ahead of a regression tree at both reported horizons. At six forecast steps, SPALT's MAE was 8.29 ± 4.3, compared with 11.36 ± 5.6 for the tree. At 18 steps, SPALT recorded 11.67 ± 5.4, versus 16.00 ± 7.0 for RT. The figures are reported as means with standard deviations.
When methods were ranked by average RMSE, SPALT came first. Its lead was close to three rank positions at six steps and close to two at 12 and 18 steps. After a false-discovery-rate correction, Wilcoxon signed-rank tests comparing SPALT with XGB and XGB+PCNM returned p < 0.001 at each of those horizons.
Forecasting became harder as the horizon lengthened: average performance worsened and standard deviations grew across the tested results. Even at the 18-step horizon, however, SPALT's RSE remained below 1.0.
Locality mattered more clearly than pruning for accuracy
In an internal comparison, SPALT had better reported results than SPALT-NP-NS, the version without spatio-temporal locality, across all datasets and horizons. The difference was significant at α=0.001 after the study's multiple-comparison correction. Locality features were introduced in roughly 64% to 77% of leaf nodes, the terminal branches of the model tree.
Pruning showed a narrower effect. In the pruning-alone comparison, it was associated with a roughly 23% to 35% reduction in node count, a difference reported as significant at α=0.001. The same comparison found no significant change in MAE, RMSE or RSE. In these tests, the result was a more compact tree without a consistent change in predictive error.
Speed and replication still matter
SPALT was not the fastest method. Its running time was slower than RT and XGB but faster than RF and all tested neural architectures, and the reported time increased almost linearly with the number of instances. The authors' asymptotic analysis assigns SPALT the same learning-time complexity as a linear model tree without locality features or pruning. That theoretical statement concerns how computing work grows; it does not mean the measured runtimes were identical.
The evidence has a narrow base. The evaluation covered three renewable-energy datasets: photovoltaic plants, wind turbines and wind power plants. UKPV and SDWPF were publicly available, WPP was unavailable for commercial reasons, and preprocessing plus train/validation/test partition code was reported as available at the cited GitHub repository.
Paper data and sources
Original title: Modeling spatio-temporal locality in multi-step forecasting of geo-referenced time series
Authors: Annunziata D'Aversa, Gianvito Pio, Michelangelo Ceci
Journal/Repository: Machine Learning, Volume 114, article number 231 (2025)
Status: Peer-reviewed
First online: 2026-08-26
DOI: 10.1007/s10994-025-06875-1
Original paper · Full text