- The paper shows that tuned Treeffuser, a tree-based conditional diffusion model, achieved the best average performance across nine Belgian offshore wind farms, with 8.0% normalized MAE and 5.6% CRPS.
- The paper finds that conformalized quantile regression nearly matched Treeffuser at substantially lower computational cost, while Gaussian NGBoost struggled with asymmetric power distributions near cut-in and rated wind speeds.
- The paper demonstrates that combining five numerical weather forecasts reduced average MAE by up to 23% versus the weakest individual provider, highlighting weather ensembles as a practical way to mitigate forecast and location errors.
Overview and motivation
This paper presents a comparative study of probabilistic day-ahead wind power forecasting methods, evaluated on all nine wind farms in the Belgian offshore zone (over 2 GW of installed capacity) using four years of hourly data (2021–2024). The authors combine gradient boosting trees with three state-of-the-art probabilistic prediction techniques—conformalized quantile regression (CQR), natural gradient boosting (NGBoost), and conditional diffusion models (Treeffuser)—and benchmark the resulting forecasts against two deterministic engineering baselines: a manufacturer power curve approach and a calibrated analytical wake model. A distinguishing feature of the work is its use of an ensemble of five day-ahead weather forecasts rather than a single numerical weather prediction (NWP), and its explicit comparison against engineering methods, which the authors note is often overlooked in machine learning studies.
The motivation rests on two well-documented error sources when using meteorological data for day-ahead forecasting. First, the weather forecast error itself; second, a location error arising from the spatial mismatch between NWP grid points (typically 7–12 km apart) and turbine positions (roughly 1 km spacing). NWPs also neglect wake effects, blockage, turbulence intensity, shear, and veer. Tree-based learners are chosen because of their strong record in wind power forecasting competitions and their superiority over deep learning on tabular data.
Methodology
All three probabilistic methods operate on features derived from five day-ahead weather forecast providers (DWD ICON-EU and ICON-D2, ECMWF HRES, Météo-France ARPEGE-EU, and Met Office Global Hi-Res), augmented with lagged variables and per-hour summary statistics, including circular statistics for wind direction. Only the grid point closest to the center of the Belgian offshore zone is used, though the authors acknowledge that multiple grid points could further improve accuracy.
Conformalized quantile regression applies quantile regression via XGBoost and then calibrates intervals on a hold-out set by expanding them symmetrically by the empirical quantile of nonconformity scores, yielding distribution-free marginal coverage guarantees. Quantile crossing is resolved by sorting predictions to enforce monotonicity.
Natural gradient boosting estimates the parameters (μ,σ) of a Gaussian conditional distribution by minimizing the logarithmic score through natural-gradient descent, implemented via the xgb-distribution package for computational efficiency.
Conditional diffusion models use Treeffuser, a score-based diffusion model whose reverse process is learned by LightGBM regressors conditioned on the input features. Probabilistic forecasts are obtained by drawing 50 samples and computing empirical quantiles.
The engineering baselines are the manufacturer power curve applied per turbine, and the self-similar Gaussian wake model of Niayifar and Porté-Agel within PyWake, with wake recovery parameters calibrated on SCADA data from the Belgian-Dutch cluster following prior work by the same group. The wake model incorporates intra-farm and inter-farm wakes, IEC freestream turbulence intensity, Crespo-Hernández wake-added turbulence, and linear superposition of velocity deficits. Because the engineering models ignore grid losses, their outputs are rescaled by the ratio of maximum observed power to rated power.
Data cleaning addresses curtailment explicitly: observations coinciding with activated downward balancing bids are removed using Elia data, while economic curtailments ordered by the Balance Responsible Party—undetectable in the available data—are filtered heuristically by removing training observations below the 5th percentile of 0.5 m/s ERA-5-based wind speed bins. The authors note this proxy filtering as a limitation of the dataset.
Point forecast results
Treeffuser with hyperparameter tuning achieves the best MAE on every wind farm, averaging 8.0% of installed capacity versus 16.9% for the power curve and 11.9% for the calibrated wake model—a 53% improvement over the power curve and up to 33% over the wake model. The wake model itself improves MAE by roughly 30% over the power curve, underscoring the importance of wake modeling. Per-farm normalized MAE values are summarized below:
| Wind farm |
Power curve |
Wake model |
NGBoost |
CQR |
Treeffuser |
| Belwind |
15.6% |
10.5% |
7.5% |
7.2% |
7.0% |
| C-Power |
15.3% |
10.8% |
7.7% |
7.3% |
7.0% |
| Mermaid |
14.5% |
12.2% |
9.2% |
9.0% |
9.0% |
| Nobelwind |
17.6% |
12.2% |
8.4% |
8.3% |
8.1% |
| Norther |
14.3% |
10.9% |
8.5% |
8.2% |
7.9% |
| Northwester 2 |
20.7% |
15.2% |
9.3% |
8.9% |
8.9% |
| Northwind |
21.1% |
11.8% |
8.2% |
7.9% |
7.6% |
| Rentel |
16.8% |
11.8% |
8.8% |
8.7% |
8.5% |
| Seastar |
15.8% |
11.9% |
8.8% |
8.5% |
8.4% |
| Average |
16.9% |
11.9% |
8.5% |
8.2% |
8.0% |
The advantage over the wake model varies across farms, which the authors attribute to machine learning implicitly capturing factors beyond wakes—including residual active curtailment strategies—in addition to mitigating weather forecast error. This carries a practical implication: when the target quantity is potential rather than actual generation, analytical wake models offer an alternative to curtailment filtering because they treat the wind speed and direction forecast as exact inputs and remain unbiased under curtailment.
Probabilistic forecast results
On out-of-sample CRPS, tuned Treeffuser again ranks first on every farm (average 5.6%), followed by CQR (5.7%) and NGBoost (6.0%). Two findings stand out. First, contrary to the claims of the original Treeffuser paper that hyperparameter tuning is unnecessary, the untuned Treeffuser variant exhibits severe overfitting here—training CRPS of 1.8% against test CRPS of 6.0%—and ranks among the worst performers. Second, NGBoost's comparatively poor performance concentrates in operating regions 1 and 3 of the power curve (below cut-in and above rated wind speed), where the conditional power distribution is asymmetric. In region 1, NGBoost's normalized MAE of 1.7% is nearly triple that of Treeffuser (0.6%), and illustrative examples show NGBoost producing confidence intervals containing negative power. Since only the Gaussian variant was tested, this result reflects the parametric assumption rather than a fundamental deficiency of natural gradient boosting; the authors suggest mixtures of Gaussians or Beta distributions as extensions.
A notable trade-off concerns computation: Treeffuser requires substantially more training and inference time than CQR, which achieves near-identical performance at lower cost. CQR therefore emerges as a practical alternative where compute budgets matter.
Value of the weather ensemble
Training Treeffuser with different input configurations isolates the contribution of the ensemble. The ensemble of five forecasts reduces average MAE by up to 23% relative to the worst single provider (Météo-France), and approaches the MAE obtained when feeding ERA-5 reanalysis data—which largely eliminates weather forecast error by construction. This result supports the claim that multi-provider ensembles allow the learning model to absorb part of the day-ahead weather forecast error, an option unavailable to deterministic engineering pipelines that require a single wind speed and direction input.
Limitations and open questions
Several caveats bear directly on the reported results. The study uses a single NWP grid point; the authors themselves note that incorporating multiple grid points is a promising but untested extension. Curtailment filtering relies on a percentile-based proxy for economically motivated curtailments that cannot be identified from the available data, potentially biasing both ML and benchmark targets. The NGBoost conclusion is conditional on the Gaussian assumption and does not establish that parametric boosting is inferior in general. Region 4 (above cut-out) is excluded due to insufficient observations, so performance during storm and cut-out events—the conditions known to produce the largest day-ahead errors—is not assessed. Finally, the computational cost of conditional diffusion sampling (50 draws per forecast) is reported qualitatively but not systematically quantified, leaving open whether reduced sample counts or distillation could close the efficiency gap with CQR without sacrificing accuracy.
Conclusion
Using four years of data spanning the entire Belgian offshore fleet, this work demonstrates that tree-based machine learning paired with modern probabilistic prediction methods substantially outperforms both naive and wake-aware engineering baselines for day-ahead wind power forecasting, with the conditional diffusion model delivering the best point and probabilistic accuracy (average normalized MAE of 8.0%, CRPS of 5.6%). Conformalized quantile regression offers comparable quality at lower computational cost, while NGBoost's Gaussian assumption proves ill-suited near cut-in and rated speeds. Exploiting an ensemble of weather forecasts improves point accuracy by up to 23%, approaching the error floor imposed by the weather forecast itself. Analytical wake models retain value where interpretability matters or unbiased potential-generation estimates under curtailment are required.
