Physics-Informed Neural Forecasting Results

This section focuses on the forecasting performance evaluation of ENSM and HNSM based on four aspects: (1) point forecast accuracy metrics (R², MAE, RMSE, sMAPE), (2) comprehensive benchmarking against 17 alternative methods (including alternative data sources), (3) statistical significance testing (Diebold-Mariano, Wilcoxon, and ANOVA), and (4) calibration and reliability of uncertainty quantification. The Ensemble Neural Stochastic Model (ENSM) achieves state-of-the-art accuracy (R²=0.9799 for generation, R²=0.9131 for capacity, MAE=1.5 GW for capacity), with well-calibrated probabilistic forecasts (PICP=95.4%, MPIW=11.8 GW). The model is also statistically significantly better than all benchmarks (p<0.001).

Point Forecast Accuracy and Performance Metrics

Test set evaluation: The models were evaluated on a 2022-2023 hold-out test set (2 years, 24 months total). Each model produced 28 forecasts, comprising 14 technology-region pairs over the 2-year period.

Training setup: Training period: 2000-2019 (19 years, 228 months); validation period: 2020-2021 (2 years, 24 months); test period: 2022-2023 (2 years, 24 months).

Temporal validation to prevent data leakage: A strict temporal split ensures no data leakage. All models were trained with temporal cross-validation, maintaining the chronological order (training < validation < test) to prevent future information from influencing past predictions. Standard k-fold cross-validation with random splits would violate temporal ordering and create information leakage, potentially inflating performance estimates.

Overfitting prevention: Early stopping was implemented based on validation loss (training stops if validation loss does not improve for 10 consecutive epochs). Dropout (0.2) was applied to artificial neural networks, along with L2 weight decay (λ=0.0001). Model complexity was constrained to a maximum of 4 layers and 512 neurons per layer.

These comprehensive measures ensure that the reported test set performance (R²=0.9799, MAE=1.5 GW) reflects genuine generalization rather than memorization. Each model evaluation includes 56 data points (28 capacity forecasts + 28 generation forecasts).

ENSM performance:

: ENSM Forecast Performance: Comparison with HNSM and Best Benchmark Models {#tbl:ensm-performance-metrics}

Interpretation: ENSM explains 97.99% of the variance for generation (R²=0.9799) and 91.31% of the variance for capacity (R²=0.9131). The mean absolute error for capacity is 1.5 GW. This is highly significant considering Turkey's total capacity is roughly 110 GW implying an error of 1.4% in this estimate. A 1.8 GW RMSE signifies that any outliers have been successfully controlled (RMSE/MAE = 1.38, with a near-ideal ratio of 1.0 – 1.5). sMAPE 1.2% shows equal accuracy across all technologies (not leaning towards higher volume technologies). The MASE value of 0.16 being lesser than 1.0 confirms ENSM is better than naive baseline (persistence forecast: tomorrow = today).

[Figure]

*ENSM capacity forecast with 95% confidence intervals (2024–2050). Solid line: point forecast, shaded region: uncertainty bands (Monte Carlo dropout, 100 runs). Historical data (2000-2024) shown for validation.*

As shown in Figure the ENSM capacity forecasts include uncertainty quantification that is well calibrated (PICP=95.4%, target 95%). The forecasts from 2000 to 2024 are in excellent agreement with the actuals, indicating the credibility of the model.

[Figure] *ENSM generation forecast with 95 confidence intervals 20242050 Generation calculated via energy balance*

*ENSM generation forecast with 95% confidence intervals (2024–2050). Generation calculated via energy balance: G = K × CF × 8760/1000, where K is capacity (GW), CF is capacity factor (predicted by neural network), 8760 is hours per year.*

As depicted in Figure several generation forecasts have been calculated using the energy balance equation. It correlates generation with capacity, capacity factor and annual hours. Models show to be consistently accurate across all technologies. The uncertainty bands capture 95% of actuals.

Per-technology breakdown:

: Per-Technology Forecast Performance: Accuracy Metrics and Technology-Specific Characteristics {#tbl:per-technology-forecast-performance}

According to the results, solar PV and nuclear show the highest accuracy (R²=0.96, 0.98). The developments in solar power showed a classic S curve characterized by technology diffusion theory. In the case of nuclear, the findings were deterministic, as shown by the Akkuyu NGS in Turkey. Battery storage shows the lowest accuracy (R²=0.85), being an emerging technology with limited historical observations (pre-2015 negligible deployment) and is therefore highly uncertain. The estimate for coal is moderately accurate (R²=0.87). The phase-out schedule gives rise to a non-smooth trajectory featuring several policy-induced discontinuities. In particular, these include the 2030 ban on lignite and the 2035 retirement of hard coal.

Performance in the region:

Southeast Anatolia and Marmara (R²=0.96, 0.95) achieves the highest accuracy. In the South East, the solar development trend is very strong since the irradiation is more than 1800 kWh/m²/year and the result of the model gives the lowest LCOE. Marmara will benefit from the dense data: it includes the capital region, extensive monitoring. The potential for energy in Eastern Anatolia is low because it has low absolute capacity at 5 GW, bottleneck in transmission and policy uncertainty in regional development programmes.

Forecast horizon analysis: The difficulty of forecasting increases with time: