ML in wind forecasting: Traditional and modern approaches

Over the past decades, wind forecasting has undergone substantial evolution, shifting from traditional statistical approaches towards advanced machine learning (ML) and deep learning (DL) methodologies. Traditionally, forecasting methods have primarily relied on statistical and persistence-based models, such as autoregressive integrated moving averages (ARIMA) and Kalman filtering, as well as regression-based approaches, which capture linear patterns but struggle with the complex nonlinear behavior of wind processes [2,3]. These limitations have been significantly addressed by introducing modern ML techniques, including support vector machines (SVM), random forests (RF), gradient boosting models such as XGBoost and LightGBM, and ensemble learning, which have demonstrated enhanced capability in capturing nonlinear relationships and improving predictive accuracy under various environmental conditions [4–6].

Furthermore, recent trends emphasize the adoption of deep learning architectures like Convolutional Neural Networks (CNN), Recurrent Neural Networks (RNN), and Long Short-Term Memory (LSTM) models, owing to their superior performance in modeling temporal dependencies and high-dimensional data interactions intrinsic to wind forecasting tasks [8,10,25]. Hybrid approaches combining multiple models (e.g., CNN-LSTM, WaveNet-LSTM, Transformer-based models, and stacked ensembles) have also been increasingly employed, capitalizing on the complementary strengths of different architectures to reduce forecast error and uncertainty further [3,9,11]. Although these modern ML approaches have significantly improved predictive capabilities, there is still considerable room for growth, especially by adding more predictive inputs and advanced feature engineering techniques to handle the inherent variability and complexity of wind energy generation [19,24].

Role of climate drivers

Large-scale climate drivers, particularly ocean–atmosphere teleconnection patterns such as ENSO, PDO, AMO, NAO, and SAM, play a crucial role in modulating regional and global weather systems, including wind patterns. Numerous studies across meteorology and environmental sciences have highlighted the predictive value of such indices in capturing seasonal and interannual variability in climate phenomena. For instance, ENSO has been shown to significantly impact surface wind speeds across North America, Asia, and Australia, with distinct El Niño and La Niña phases resulting in anomalies in wind energy potential [24,26]. Similarly, the Atlantic Multidecadal Oscillation (AMO) and Pacific Decadal Oscillation (PDO) have been linked to persistent wind anomalies, affecting both wind direction and intensity on decadal scales [16,27].

Despite their known meteorological impacts, the integration of such large-scale indices into wind energy forecasting models remains relatively limited. A few recent works have begun exploring their utility for improving seasonal and monthly wind predictions. For example, Leminski et al. [15] demonstrated that climate index-driven ANN ensembles could outperform conventional climate models for seasonal wind forecasting in Canada. At the same time, Couto et al. [16] showed that using lagged ENSO indicators significantly reduced forecast errors in Brazil’s wind speed models. These findings suggest that such indices encapsulate persistent climatic signals, often months in advance, that could enhance the lead time and accuracy of wind forecasts. However, most studies remain isolated in context and do not systematically integrate these indices alongside machine learning-based approaches, marking a clear opportunity for advancing the SOTA in wind forecasting [28,29].

Feature selection techniques

Feature selection is a crucial step in time-series forecasting, especially when working with high-dimensional datasets that incorporate lagged variables and external predictors. Among various feature selection strategies, Minimum Redundancy Maximum Relevance (MRMR) has emerged as an effective filter-based method that selects features with high relevance to the target variable while minimizing redundancy among chosen features. This dual objective enhances model performance by reducing noise, mitigating overfitting, and improving generalization, particularly in machine learning models that are sensitive to input dimensionality [11,14,18].

While MRMR has been widely used in domains such as biomedical signal analysis, hydrology, and load forecasting, its application in wind power prediction remains sparse. Recent studies exploring MRMR in energy contexts demonstrate substantial performance gains. For instance, Huo et al. [11] combined MRMR with a PSO-tuned LSTM for short-term wind power forecasting, achieving lower RMSE and faster convergence compared to standard LSTM models. Similarly, Yang and Zhang [14] employed MRMR, along with VMD and attention mechanisms, to enhance the robustness of wind prediction under fluctuating weather patterns. Other studies have adopted multi-objective or genetic algorithm-based feature selection frameworks (e.g., Alharthi et al., [9]; Lv et al., [19]), which share the same core principle of balancing relevance and redundancy. The underutilization of MRMR in wind forecasting, despite its theoretical suitability for multivariate, time-lagged input spaces, presents a clear opportunity to refine predictive modeling pipelines and unlock further accuracy gains.

Identified gaps

While recent advancements in machine learning have significantly improved short-term wind power forecasting, most existing models are constrained by their reliance on purely local meteorological variables and a limited set of engineering features. A key gap in the literature is the near-total absence of large-scale oceanic climate indices, such as ENSO, PDO, AMO, and SAM, in short-term forecasting models, despite strong empirical evidence showing their influence on regional wind variability across multiple continents [7,16,26]. Existing studies that use these indices have primarily focused on seasonal forecasting or climate model interpretation rather than on direct integration with machine-learning-based predictive models for operational wind energy management [15,24,30]. Consequently, valuable predictive signals encoded in these climate oscillations remain underexploited in the data-driven forecasting community.

In parallel, another overlooked area is the integration of advanced feature selection methods, particularly MRMR, within the wind power modeling pipeline. Although studies in hydrology and load forecasting have demonstrated that MRMR can enhance model accuracy by reducing redundancy and optimizing feature sets [11,18,19], the wind forecasting literature has yet to systematically explore this potential. Most models either use manually selected inputs or apply simplistic, correlation-based filters, which risk overfitting or the inclusion of irrelevant features [9,14]. The joint absence of oceanic teleconnection indices and structured feature selection limits both the scope and the efficiency of current forecasting approaches. Addressing these gaps by incorporating climate drivers and robust selection mechanisms, such as MRMR, holds strong potential to elevate the accuracy, interpretability, and generalizability of wind energy prediction models.

Climate indices and problem formulation

This study’s primary focus is on analyzing the dynamics of wind power generation at the “Pawan Danavi” wind farm in Sri Lanka’s northwestern province. Recognized for its high wind density and feasibility for wind farm deployment, this region provides a unique context for our investigation. The dataset, graciously provided by the wind farm authorities at Lanka Transformers Private Limited, covers monthly average power generation from January 2015 to December 2019 [31].

We investigate the relationship between monthly wind power generation (WP), monthly mean wind speed (WS) and eleven large-scale climate modes: North Atlantic Oscillation (NAO), Arctic Oscillation (AO), Atlantic Meridional Mode (AMM), Atlantic Multidecadal Oscillation (AMO), Central Pacific (CP), Eastern Pacific (EP), El Niño–Southern Oscillation (ENSO), Multivariate ENSO Index (MEI), Oceanic Niño Index (ONI), Pacific Decadal Oscillation (PDO), and Southern Oscillation Index (SOI). Our assumed functional form is shown in Equation 1, which serves as the cornerstone for exploring how these modes of climate variability influence wind-power dynamics in our study region [32].

(1)

Forecast horizon clarification

In this study, our objective is contemporaneous () wind-power nowcasting, where monthly wind power for month t is estimated using predictors observed within the same month, including the current-month wind speed (), contemporaneous climate indices, and their lagged values. This formulation intentionally retains because the task corresponds to operational power-curve modeling rather than ahead-of-time forecasting. We do not perform h-step-ahead predictions (e.g., ) since such forecasting would require excluding and restricting the predictor set to information available only at . To ensure clarity, all results presented in this work should therefore be interpreted as nowcasting rather than multi-step forecasting.

Data preprocessing

In the first stage, all raw time-series, monthly wind power generation (WP), average wind speed, and the twelve climate indices, were subjected to systematic cleaning and imputation. Outliers in WP and WS were identified using the interquartile range (IQR) rule and replaced via linear interpolation to preserve temporal continuity. At the same time, missing values in the climate indices (typically fewer than 2% of all monthly records) were filled using a climatological mean for the corresponding calendar month [33]. Following imputation, each variable was detrended to remove any long-term drift and then normalized to a zero mean and unit variance (z-score), ensuring that differences in scale would not bias subsequent statistical analyses or machine learning algorithms [34].

Next, we applied an initial correlation filtering step to prune redundant predictors and mitigate multicollinearity. A Pearson correlation matrix was computed among WS, WP, and all indices; pairs of predictors with were flagged, and from each highly correlated pair, the variable with the weaker correlation to WP was dropped. To further guard against variance inflation, we calculated variance inflation factors (VIF) for the remaining set and retained only those indices with . This filtering yielded a parsimonious subset of climate modes that exhibit independent, statistically significant relationships with wind power generation, forming the basis for our modeling in Section 4.2.

Feature engineering

To capture temporal dependencies and lagged impacts of both atmospheric and oceanic drivers on wind power, we constructed lagged features for WP, WS, and each climate index at lags of 1–12 months. Specifically, for each variable (where ), we generated new predictors for . Missing values introduced by lagging at the beginning of the series were handled by forward filling the first non-missing observation, ensuring complete feature matrices for all time steps from January 2016 onward. All lagged variables were then standardized (zero mean, unit variance) using the parameters estimated on the training set to maintain consistency across cross-validation folds [35].

Following feature construction, we applied the MRMR algorithm (Experiment D) to select a compact, informative subset of lagged predictors. MRMR ranks features by maximizing their mutual information with the target (WP) while minimizing pairwise redundancy among themselves. We implemented MRMR via the classic “max-dependency” criterion using a mutual information estimator, retaining the top k features that yielded the best performance on a held-out validation set. This step reduced the dimensionality from lagged predictors to a targeted subset (typically 2–20 features), improving model interpretability and mitigating overfitting in subsequent regression or machine-learning analyses.

Experimental setups

We designed four dataset configurations to isolate the effects of wind data, oceanic indices, lagged information, and feature selection on model performance:

Model training and evaluation

To prevent overfitting while respecting the temporal structure of the data, we adopted a two-stage evaluation protocol based on time-ordered splits. First, we partitioned the monthly series into an initial training/validation portion and a chronologically subsequent, fully independent test set, ensuring that the test months always occur after all training and validation months. Second, within the training portion, we implemented a blocked time-series cross-validation scheme: the data are kept in chronological order, and each fold uses an earlier contiguous block of months for training and a later, non-overlapping block for validation. No temporal shuffling is applied, so future observations are never used to predict the past. For each experimental setup (A–D) and candidate model, we report the mean and standard deviation of RMSE and across these time-ordered folds, together with the final performance on the independent test set. This protocol avoids temporal leakage and provides a more robust assessment of model generalization on autocorrelated, seasonally structured monthly wind-power data.

Model uncertainty and predictive intervals

To quantify robustness and mitigate the risk of overfitting associated with high-dimensional predictor spaces, we computed predictive uncertainty for all Gaussian Process Regression (GPR) models evaluated in Experiments A–D. For each time-ordered cross-validation fold, the GPR posterior variance provides a natural measure of predictive dispersion. We therefore report the mean predictive trajectory together with the associated predictive intervals, defined as

where and denote the posterior mean and standard deviation of the GPR model, respectively. These intervals quantify model confidence under temporally consistent training/validation splits and provide an interpretable measure of robustness against overfitting.

Machine learning paradigms

We selected 25 SOTA machine learning models characterized by relatively low algorithmic complexity, ensuring a balance between predictive performance and computational efficiency. Our chosen suite spans linear regressions, decision trees, support vector machines, Gaussian process regressions, ensemble methods, kernel-based learners, and feed-forward neural networks, each implemented in optimized libraries for scalable training and inference while reflecting best practices in modern ML research. Please see the Supplementary File 1 for a detailed introduction to each of these SOTA ML models with their hyperparameter values.

Cost functions for model groups

Linear and tree-based models.

Linear regression (Ordinary Least Squares):

Minimize the sum of squared residuals:

(2)

Decision trees (CART for Regression):

For node , let . The node cost is

(3)

and splits are chosen to minimize the weighted sum of child-node costs.

Bagged trees:

Each tree is fit by minimizing the same on a bootstrap sample; the ensemble prediction is the average over trees.

Boosted trees:

Initialize and add trees sequentially by

(4)

Support vector and kernel methods.

Support vector machines (Hinge Loss):

For labels , solve

(5)

Polynomial & Gaussian-Kernel SVMs:

Replace with a kernel (e.g., or ) in the same hinge-loss objective.

Least-squares kernel regression:

Minimize

(6)

where is the RKHS norm induced by K.

Gaussian process and neural network models.

Gaussian Process Regression (GPR):

Let be the covariance matrix with entries . The log-marginal likelihood is

(7)

Feed-forward neural networks:

With parameters θ, minimize the mean squared error:

(8)

where is the network output; for classification, replace MSE with cross-entropy.

Performance evaluation metrics

This section examines key performance metrics for evaluating the accuracy, reliability, and efficiency of the developed wind power prediction models. In addition to Root Mean Squared Error (RMSE) and Coefficient of Determination (), training time, prediction speed, and model size are also considered to provide a more comprehensive evaluation. These metrics collectively enhance our understanding of the models’ strengths, limitations, and computational efficiency.

Root Mean Squared Error (RMSE).

The RMSE is a widely used metric to measure the average magnitude of the errors between the predicted values and the observed values. It comprehensively assesses the model’s accuracy, with lower values indicating better performance.

(9)

Where: N is the total number of observations.

Coefficient of determination ().

The Coefficient of Determination, often denoted as , assesses the proportion of the variance in the dependent variable (wind power generation) that is predictable from the independent variables (features). It ranges between 0 and 1, where higher values indicate better explanatory power.

(10)

Where: is the observed value, is the predicted value, and is the mean of the observed values.

Mean Squared Error (MSE).

The MSE measures the average of the squared differences between predicted and observed values, providing a direct assessment of variance in the errors.

(11)

Mean Absolute Error (MAE).

The MAE quantifies the average magnitude of errors in the same units as the target variable, treating all deviations equally.

(12)

Mean Absolute Percentage Error (MAPE).

The MAPE expresses forecast errors as a percentage of actual values, facilitating comparison across different scales.

(13)

Baseline skill metrics

To contextualize the performance of the machine-learning models, we implemented two simple reference baselines commonly used in wind-energy forecasting:

• Climatology baseline: , representing the long-term monthly mean of the training period.
• Persistence baseline: , corresponding to a simple one-month persistence model.

These baselines provide lower-bound skill references that allow direct comparison of the raw improvements obtained by incorporating climate indices, lagged features, and MRMR selection. We report RMSE and for both baselines alongside the ML results.

Feature analysis and selection

The heatmap visualized in Fig 2 represents the correlation matrix of the wind power generation dataset. Each square in the grid represents the correlation between two variables, providing a comprehensive overview of the relationships in the dataset. Warmer colors indicate stronger positive correlations, while cooler colors represent negative correlations. This visualization facilitates the identification of significant associations between variables, informing subsequent stages of data preprocessing and model development.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 2. Correlation heatmap illustrating the relationships between wind power generation and various climate indices.

The color gradient represents correlation values, with red indicating strong positive correlations and blue indicating strong negative correlations. The WIND and POWER variables exhibit a strong positive correlation (0.95), while other indices, such as AMO, ENSO, and MEI, show varying degrees of influence on wind power. This analysis helps identify key climate factors that affect wind power variability.

https://doi.org/10.1371/journal.pone.0344167.g002

To delve deeper into the temporal dynamics, a lag correlation analysis was employed to assess the influence of past data on wind power generation. The outcomes are depicted in Fig 3.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 3. Lagged correlation analysis between wind power generation and various climate indices.

Each subplot shows the correlation coefficients for different lag periods (in months), with the highest correlation highlighted in red. The best lag for each climate index is indicated, demonstrating the temporal influence of climate variability on wind power. Notably, WIND vs. POWER exhibits the strongest correlation (0.88) at a 12-month lag, while other indices such as AMM, AMO, NAO, and PDO show moderate correlations at varying lag periods. This analysis helps identify the optimal time delay for incorporating climate indices into wind power forecasting models.

https://doi.org/10.1371/journal.pone.0344167.g003

Each input was scrutinized for correlation with the output in this phase, accounting for time lag. The optimal lag time was determined based on a threshold of a correlation value exceeding ±0.40. Subsequently, the original dataset was restructured to include only inputs and time lags that met this criterion, streamlining it for more focused and effective model training.

Comparative analysis of experiments A–D

Fig 4 presents a side-by-side comparison of the predictive accuracy (measured by RMSE) for 25 candidate models under four distinct feature-engineering schemes: (a) wind data only (Experiment A), (b) wind plus raw oceanic indices (Experiment B), (c) wind, indices, and their 1–12 month lags (Experiment C), and (d) the same lagged features after MRMR-based selection down to three predictors (Experiment D). In each panel, model identifiers are listed on the vertical axis in ascending order of RMSE, while the horizontal axis shows the RMSE magnitude. Bars are color-coded from dark purple (lowest RMSE, best accuracy) to yellow (highest RMSE, poorest accuracy), and a shared color bar alongside each panel reinforces this visual ranking.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 4. Comparison of predictive performance for 25 candidate models across four test conditions.

Each pane displays models sorted by increasing RMSE (x-axis) with the model number on the y-axis, and bars are colored by RMSE magnitude (colorbar). Panels are arranged as (a) Experiment A, (b) Experiment B, (c) Experiment C, and (d) Experiment D. Lower RMSE (dark purple) indicates better accuracy, while higher RMSE (yellow) highlights poorer performance.

https://doi.org/10.1371/journal.pone.0344167.g004

Experiment A (wind only) yields RMSE values roughly in the range , with Models 18 and 10 achieving the best performance (dark purple) and Model 23 the worst (bright yellow). When raw oceanic indices are added in Experiment B, the entire RMSE distribution shifts upward (), indicating that the unfiltered indices introduce noise that many algorithms cannot effectively exploit. Experiment C’s inclusion of lagged features broadens the feature set but also injects temporal structure, compressing the RMSE spread to approximately (Please refer to Fig 5). Finally, Experiment D applies MRMR feature selection to extract only the top three predictors, namely (SHAP = 538.13), (SHAP = 70.95), and (SHAP = 37.29), and achieves the lowest observed minimum RMSE () while still exhibiting a few high-error outliers (Please refer to Fig 6).

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 5. Coefficient of determination (R²) for the top-performing models on the validation (blue circles) and test (orange squares) sets across four experiments (A–D).

Overlaid red and green rings indicate the model IDs selected for each validation and test point, respectively. Higher R² values denote stronger predictive accuracy.

https://doi.org/10.1371/journal.pone.0344167.g005

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 6. SHAP summary dot-plot for the three top MRMR-selected predictors (WIND, AMM_9, WIND_6).

Each point represents one forecast instance, plotted by its Shapley value (x–axis) to show the feature’s impact on the model’s output, and colored by the corresponding predictor value (blue = low, yellow = high). The current wind speed (WIND) dominates model behavior; higher WIND values consistently push predictions upward, while the nine-month Atlantic Meridional Mode index (AMM_9) and the six-month lagged wind (WIND_6) exert more moderate positive and negative influences, respectively.

https://doi.org/10.1371/journal.pone.0344167.g006

The degradation from Experiment A to B can be attributed to the relatively weak direct correlation between raw oceanic indices and the target variable. Although these indices contain climatological signals, their instantaneous values often reflect large-scale processes with longer time scales than the forecasting horizon; thus, when appended without temporal alignment or selection, they act as high-dimensional noise. Models that rely on distance- or variance-driven splits (e.g., tree-based methods) are particularly prone to overfitting to spurious fluctuations in these raw indices, thereby increasing RMSE.

Introducing 1–12 month lags in Experiment C enables models to capture autocorrelated patterns and delayed ocean–atmosphere coupling, which several algorithms leverage to improve forecasts (e.g., Model 3 achieves the lowest RMSE in that panel). Nevertheless, the enlarged feature space (156 raw + lags) increases the risk of multicollinearity and overparameterization. MRMR-based selection in Experiment D mitigates these issues by ranking features according to maximum relevance (high mutual information with the target) and minimum redundancy (low mutual information amongst themselves), thereby distilling the predictor set to the three most informative variables. This parsimonious representation sharply enhances the model’s focus on the dominant drivers, such as wind speed, and its temporally relevant echoes, yielding the overall lowest RMSEs across the candidate suite (Please refer to Tables 1 and 2).

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 1. Best-performing models on the validation set.

https://doi.org/10.1371/journal.pone.0344167.t001

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 2. Best-performing models on the test set.

https://doi.org/10.1371/journal.pone.0344167.t002

The stepwise enhancement of predictive performance from Experiments A through D underscores the complementary roles of oceanic teleconnection indices, temporal depth, and principled feature selection. In Experiment B, the inclusion of contemporaneous indices (ENSO, PDO, AMO, AMM, etc.) modestly enriched the feature space but introduced significant noise, as many indices exhibit weak instantaneous correlation with monthly wind power; this aligns with prior findings that raw climate modes can degrade short-term forecasts unless their temporal structure is exploited [15,16]. Experiment C’s full suite of 1–12-month lags harnesses the delayed coupling between ocean–atmosphere dynamics and regional wind patterns, compressing the RMSE spread by allowing models to learn autocorrelated signals, consistent with studies showing multi-month ENSO lags improve wind-speed forecasts [47]. Finally, Experiment D applies MRMR to distill 156 lagged predictors into the three most informative variables (, , ), eliminating redundant or spurious inputs; the resulting RMSE minima (  MWh) and far exceed benchmarks in the literature and mirror the success of MRMR–PSO–LSTM in other energy-forecasting domains [11,24].

The demonstrable gains from integrating climate indices, lags, and MRMR selection yield immediate benefits for grid operators by reducing forecast uncertainty. More accurate monthly wind-power projections enable optimized dispatch scheduling, reduced reliance on expensive spinning reserves, and enhanced stability of mixed-renewable energy portfolios. However, our study is constrained by its single-site, monthly-resolution dataset (2015–2019, Pawan Danavi farm), which limits direct transferability to regions with different climate regimes or shorter-term operational horizons. Future work should extend this framework to multi-site, higher-frequency (daily or hourly) data, incorporate additional teleconnection patterns (e.g., the North Atlantic Oscillation and the Southern Annular Mode), and explore adaptive MRMR thresholds to maintain performance under non-stationary climate variability. Such advances will further solidify the bridge between large-scale climate science and operational wind energy forecasting.

Table 3 highlights the computational characteristics of the selected models under each experimental scenario. In Case A (wind data only), the Medium Tree model achieves the highest prediction throughput (9,182 obs/sec) and a small footprint (2,589 bytes), at the cost of moderate training time (3.76 s). Adding raw oceanic indices in Case B increases feature dimensionality, which inflates both the compact model size (to 9,095 bytes) and the code representation (to 5,587 bytes) while reducing prediction speed to 7,830 obs/sec; interestingly, training time halves to 1.79 s, likely due to simpler tree-structure adjustments on the enriched input. Case C’s Boosted Trees, operating on 156 lagged predictors, suffers the steepest drop in prediction speed (933 obs/sec) and balloons to a 762 KB model, reflecting the complexity of sequential ensemble fitting.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 3. Model specifications across the four experimental cases.

https://doi.org/10.1371/journal.pone.0344167.t003

Experiment D’s MRMR-pruned Boosted Trees (three predictors) recovers much of the lost efficiency: prediction speed rebounds to 5,499 obs/sec and model size contracts to 2,869 bytes (code size 692 bytes), with a modest increase in training time (3.90 s) compared to Case B. This balanced profile underscores the practical advantage of feature selection: by distilling inputs to the most informative variables (WIND, AMM_9, WIND_6), the model maintains high accuracy (see RMSE results) while minimizing computational and storage costs—key considerations for real-time forecasting systems and edge deployments.

In addition to MRMR-based dimensionality reduction, we evaluated model robustness using predictive intervals and fold-to-fold variability under time-blocked cross-validation. The narrow predictive intervals of the top-performing GPR models, together with low dispersion in RMSE across folds, indicate stable generalization despite the initially large predictor space. Comparisons with climatology and persistence baselines further demonstrate meaningful improvements in raw skill, confirming that the observed gains are not artifacts of overfitting but arise from informative lag and teleconnection signals.

The comprehensive evaluation of predictive performance and computational characteristics across all four experimental configurations (A–D) is further supported by detailed metric breakdowns and model parameters provided in the supplementary material. Specifically, the validation and test performance metrics, along with detailed model specifications and hyperparameter settings for each setup, are documented in S1-S16 Tables. These tables provide the foundational data for the comparative analysis of accuracy improvements and operational efficiency observed as the framework transitions from simple wind-only baselines to the MRMR-optimized feature sets.

Physical interpretation of the AMM teleconnection

The MRMR–SHAP analysis identifies three dominant predictors in the final feature set: the contemporaneous wind speed (WIND), a six-month lag of wind speed (WIND 6), and a nine-month lag of the Atlantic Meridional Mode index (AMM 9). While the importance of WIND and WIND 6 follows directly from local persistence and power-curve relationships, the role of AMM 9 warrants additional physical interpretation.

To examine whether AMM 9 represents a robust physical teleconnection rather than a spurious statistical artefact, we computed autocorrelation functions (ACF) for wind power and local wind speed, and cross-correlation functions (CCF) between wind power and AMM at lags from 0 to 12 months. The CCF shows a distinct peak at approximately 9 months, consistent with the feature ranking obtained by MRMR. We further evaluated partial correlations between wind power and AMM at each lag while controlling for major Indo–Pacific climate modes (e.g., ENSO, IOD, MJO). The partial-correlation analysis shows that the AMM signal at a nine-month lag remains statistically significant even after conditioning on these Indo–Pacific indices, suggesting that AMM captures additional, non-redundant information about the large-scale background state.

From a dynamical perspective, positive AMM phases are associated with anomalous warming in the tropical North Atlantic, which can modulate the strength and position of the Hadley and Walker circulations. These large-scale circulation anomalies can, in turn, influence the South Asian monsoon system and the low-level westerlies that govern near-surface wind fields over the study region on seasonal-to-annual time scales. The observed nine-month lag between AMM and local wind power is therefore consistent with a delayed adjustment of the coupled ocean–atmosphere system rather than an instantaneous teleconnection. Taken together, the CCF/ACF patterns, partial correlations, and physical-routes arguments support the interpretation of AMM 9 as a physically plausible teleconnection driver that complements Indo–Pacific modes in the final predictive model.

Limitations and future works

The primary objective of this study was to evaluate the predictive feasibility of bio-inspired optimization for congestion modelling rather than to benchmark computational efficiency [48–50]. All optimization algorithms were intentionally run with identical parameter settings to ensure fairness rather than peak performance. As a result, runtime profiling was not included, mainly because the dataset is relatively small and all algorithms completed within practical timeframes on standard computing hardware. Although this indicates that the proposed framework is computationally feasible for small- to medium-scale applications, a systematic runtime and scalability evaluation—particularly for real-time or statewide deployment—remains an important direction for future work.

While this study focuses primarily on evaluating the predictive performance of the proposed models, the relative influence of the four input variables can be inferred from the correlation analysis and the structure of the optimized model parameters. Because the dataset is compact and the feature set intentionally limited (AADT, crash rate, link length, precipitation), these variables already represent the dominant exposure, safety, and environmental factors relevant to congestion. A full post-hoc feature-importance analysis (e.g., SHAP, permutation importance, or sensitivity indices) was not included, as such methods typically require repeated perturbations or resampling, which can be unstable or uninformative in small datasets. Nevertheless, the observed correlations and the resulting model behavior consistently indicate that AADT and crash rate provide the strongest predictive signal, followed by link length and precipitation.

Although the proposed models achieve good performance, several limitations of the dataset must be acknowledged. First, the analysis is based on 472 records drawn from selected interstate highway segments in Virginia. This relatively small sample size, together with the focus on a single state and facility type, constrains the diversity of traffic, geometric, and environmental conditions represented in the data. As a result, the current findings should be interpreted as a proof-of-concept for Virginia’s interstate corridors rather than as directly generalizable to all roadway types, jurisdictions, or long-term temporal trends.

Second, the set of predictors is intentionally parsimonious and limited to variables consistently available across many state-level planning databases: AADT, crash rate, link length, and precipitation. While these variables capture key exposure, safety, and macro-level geometric effects, we did not have access to more operational features such as detailed traffic control device inventories, incident duration, lane-closure information, real-time speed and occupancy, or queue spillback characteristics. These additional factors are likely to further enrich the predictive signal for congestion and incident-related performance, but they are not systematically archived across all study links and were therefore beyond the scope of this work.

Third, performance differences between the training and testing phases—most notably in the MFO, optimized configuration, indicate a degree of overfitting that is expected in small structured datasets. Although the model was trained on a strictly separate training set, the limited sample size naturally limits the complexity it can reliably capture. Future work should evaluate the framework using resampling-based techniques such as k-fold cross-validation or bootstrapping on larger regional datasets, and consider incorporating regularization or early-stopping mechanisms to further strengthen robustness.

Additionally, the study did not incorporate an explicit feature-importance or sensitivity analysis beyond correlation-based exploration, primarily due to the limited dataset size, which can lead to unstable or non-generalizable importance rankings. Future work could integrate SHAP, permutation importance, or global sensitivity measures into analyses of larger multi-state datasets to provide a more robust interpretability assessment.

Future research should extend the present framework by (i) assembling larger multi-state datasets covering a wider range of facility types and temporal conditions, and (ii) incorporating richer operational covariates such as control strategies, incident timelines, and queue dynamics wherever such data are available. These extensions would enable a more thorough assessment of model transferability and support the development of guidelines for applying the proposed methods across different regions and network contexts.