Provenance:Dataset:Turkey-Energy-v2024Model:ENSM-v4.0 / HNSM-v4.0Run:18 Oct 2025forecast_ensm_v40_202510…Deterministic

Chapter 3ENSM R²=0.979917 BenchmarksQ1 Journal Standard

Forecast Results — ENSM & HNSM

Two complementary models were developed for long-horizon Turkey renewable capacity forecasting (2024–2050): the HNSM (Hybrid Neural S-curve Model) combining physical S-curve constraints with a learnable correction term, and the ENSM (Enhanced Neural S-curve Model) that integrates a GRU encoder with the S-curve prior. The ENSM achieves R²=0.9799 — significantly outperforming all 16 benchmark models.

Interpretation Guardrail

Forecasts are generated on historical Turkey energy data (2000–2024). Long-horizon projections carry increasing uncertainty. Prediction intervals (PICP=94.2%) account for stochastic model uncertainty. Physical constraints prevent thermodynamically infeasible trajectories.

Model Parameters

HNSM — Hybrid Neural S-curve Model

Carrying capacity K_max239.41 GW

Growth rate α0.0972 yr⁻¹

Inflection year t₀2024.39

R² (capacity)0.9131

R² (generation)0.7446

Capacity 2024119.03 GW

Capacity 2050218.93 GW

Generation 2024345.6 TWh

Generation 2050723.7 TWh

PICP (95% CI)94.2%

MPIW11.8 GW

ENSM — Enhanced Neural S-curve Model ✓ Primary

R² (capacity)0.9799

ArchitectureGRU(128→64→32→16) + S-curve physical constraints

Training period2000–2024

Forecast horizon2024–2050

OptimizerAdam

Learning rate0.001

Batch size16

Epochs500

Dropout0.3

L2 regularisation0.001

MC dropout samples100

ENSM — Capacity & Generation Projections (2024–2050)

S-curve trajectory bounded by K_max=239.41 GW. Physical constraint prevents exceeding carrying capacity. Uncertainty bands: PICP=94.2%, MPIW=11.8 GW.

Year	Capacity (GW)	S-curve % of K_max	Generation (TWh)	Notes
2024	119.00	49.7%	345.6	Training data endpoint
2030	151.56	63.3%	454.0	Near-term forecast
2035	176.48	73.7%	542.4	Mid-term projection
2040	196.35	82.0%	618.6	Approaching inflection plateau
2045	210.95	88.1%	680.9	Saturation approach
2050	221.10	92.4%	619.7	Final forecast — 91.5% of K_max

ENSM Capacity Forecast — 95% Confidence Interval

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17-Model Benchmark Comparison

ENSM is compared against 16 state-of-the-art models on the same Turkey energy dataset (2000–2024, 80/20 train-test split, 5-fold time-series cross-validation). Statistical significance confirmed by 78 Diebold-Mariano tests (all p<0.001). Paired t-test: t=9.21, Cohen's d=1.19 (large effect size).

Rank	Model	R²	MAE (GW)	RMSE (GW)	MAPE (%)
1	🏆ENSM (Ours)	0.9799	1.24	1.81	1.12%	↑ Best — this work
2	LSTM	0.8932	3.47	4.92	3.21%	+9.7% worse R²
3	Transformer	0.8821	3.78	5.24	3.54%
4	GRU	0.8614	4.12	5.67	3.89%
5	BiLSTM	0.8502	4.38	6.01	4.12%
6	CNN-LSTM	0.8391	4.61	6.34	4.35%
7	Attention LSTM	0.8279	4.83	6.67	4.58%
8	HNSM (S-curve only)	0.8134	5.12	7.05	4.87%
9	ARIMA	0.7841	5.84	7.94	5.61%
10	Random Forest	0.7523	6.41	8.63	6.18%
11	Gradient Boosting	0.7312	6.78	9.12	6.54%
12	SVR	0.7011	7.24	9.71	6.98%
13	XGBoost	0.6823	7.61	10.24	7.34%
14	MLP	0.6512	8.14	10.87	7.89%
15	Linear Regression	0.5934	9.23	12.34	8.91%
16	Exponential Smoothing	0.5121	10.84	14.21	10.43%
17	Naive (Baseline)	0.3421	15.67	19.84	15.12%

Lower is better for MAE/RMSE/MAPE. Higher is better for R². ENSM R²=0.9799 represents a 10% improvement over second-best (LSTM R²=0.8932).

Figures

17-Model Performance Ranking (R² Score) — **Fig. 3.4** — Ranking of all 17 forecasting models by R² score on Turkey capacity data 2000–2024. ENSM R²=0.9799 outperforms all benchmarks. Source: Forecast/outputs/01_Figures/11_Model_Selection/

Multi-Criteria Model Comparison — **Fig. 3.5** — Comparison of forecasting models across R², MAE, RMSE, MAPE metrics. ENSM achieves best performance across all four criteria.

Neural Network Activation Functions — **Fig. 2.8** — Comparison of activation functions used in the GRU architecture: ReLU, Leaky ReLU, ELU, Sigmoid, Tanh. Impact on training convergence and gradient flow.

S-curve Parameter Visualization — **Fig. 2.6** — Physical S-curve capacity trajectory with K_max=239.41 GW, α=0.0972 yr⁻¹, inflection t₀=2024.39. Shows physical constraint bounding the neural network predictions.

5-Fold Time-Series Cross-Validation Results — **Fig. 3.2** — Cross-validation performance across 5 temporal folds (2000–2019 training, 2020–2024 test). ENSM maintains R²>0.97 across all folds confirming temporal stability.

Statistical Validation Summary

Diebold-Mariano

DM statistic

8.43

78 pairwise tests, p<0.001

Wilcoxon Signed-Rank

Z statistic

7.92

p<0.001

Paired t-test

t statistic

9.21

Cohen's d=1.19 (large effect)

5-fold TS Cross-Validation

R² stability

>0.97

Across all temporal folds

Physical Consistency

Energy balance error

<0.1%

All 26 forecast years

Prediction Interval

PICP

94.2%

MPIW = 11.8 GW

📎 Cite this — Forecast Results

Önderol, S. (2025). Long-term renewable energy forecasting and multi-agent reinforcement learning optimization for Turkey's energy transition to 2050 (Doctoral dissertation). Erciyes University.

URL: https://renewabletransition.org/transition/results/forecast

Data: Turkey_Energy_Technology_Metrics (25 records, 106 columns, 2000–2024) · Model outputs: Forecast/outputs/comprehensive_results_20251017_231638.json · ← Back to Results · RL Comparison →