Research Questions and Hypotheses

The four specific research questions are investigated with the help of a few testable hypotheses. We look at a mixed method, hypothetico-deductive or exploratory based research design in terms of a theory and data driven optimal solution generation.

An overview of the research objectives and approach, expected outcomes, and the statistical tests that were performed.

: Feature Completeness Matrix {#tbl:feature-completeness-matrix}

Research Question 1: Forecasting Model Performance

RQ1: How do hybrid neural-physical forecasting models (HNSM, ENSM) compare with traditional statistical methods and state-of-the-art deep learning architectures with regards to long-term (26-year) renewable energy capacity (in Turkey) forecasts in terms of multiple performance dimensions (accuracy, physical plausibility, uncertainty calibration)?

Forecasting is the basis of energy transition planning. It is important to establish whether any hybrid physics-informed model really does improve upon existing approaches and, if so, by how much, to justify such methodological newness. In this way, knowing the mechanisms behind the performance differences informs future modelling efforts (S-curve dynamics vs attention vs constraints).

Hypothesis H1.1 (Accuracy Superiority):

The ENSM model performance (forecasts accuracy measured by R², MAE, RMSE on the 2022-2024 holdout test set for aggregate renewable capacity) is not statistically different from the best-performing benchmark model of the 17 comparators ($H_0$).

Alternative hypothesis ($H_1$) is the ENSM model has superior forecast accuracy. There is a p-value < 0.01 in the Diebold-Mariano test. The effect size Cohen's d > 0.8 is large. It outperformed all 17 benchmark models with performance targets: R² ≥ 0.95, MAE ≤ 2.0 GW, RMSE ≤ 3.5 GW.

Prior research indicates physics-informed neural networks outperform pure data-driven models in domains with known physics laws [raissi2019physics]; [2021]; [Karniadakis]; [et]; [al.]. Energy capacity forecasting follows basic rules (energy equations, stopping to be negative, limits on capacity factor) that should create the same benefits. It is assumed that the ENSM model produces less extreme outliers in comparisons with those benchmarks that rely upon exclusive concentration either on growth or dynamics or on volatility or fluctuations.

Hypothesis H1.2 (Physical Plausibility):

According to the null hypothesis ($H_0$), the proportion of physically implausible forecasts, such as negative capacity, CF > 1.0 and energy balance exceeding 1%, produced by ENSM is no greater than deep learning benchmarks.

The alternative hypothesis ($H_1$) states that ENSM does not produce physically implausible forecasts over the period 2024–2050 in 100 Monte Carlo simulations while more than 50% of deep learning benchmarks produce more than 5% physically implausible forecasts. These benchmarks include LSTM, GRU, BiLSTM, Transformer, CNN, CNN-LSTM and Attention.

It is learned implicitly from data as standard deep learning architectures do not have mechanisms for physical constraints. Nevertheless, training data may not include the boundary regions where constraints are violated, resulting in extrapolation errors. ENSM applying (hard) a mathematical guarantee to enforce physical plausibility using output transformation layers and penalty terms provides a clear advantage for policy-type applications in which an implausible projection loses stakeholder credibility.

Hypothesis H1.3 (Uncertainty Calibration):

Null hypothesis ($H_0$): The calibration of ENSM's 95% prediction intervals (as assessed by Prediction Interval Coverage Probability, PICP) on the holdout test set does not significantly differ from 95% (null distribution: binomial with p=0.95, n=3 years).

The ENSM method generates well calibrated predictive intervals since the predictive intervals coverage probabilities (PICP) of 93% ≤ PICP ≤ 97% are not significantly different to 95% (α=0.05). While at least half of the comparators show significant miscalibration (PICP < 90% or PICP > 100%, where the latter means overly-conservative).

Monte Carlo dropout is important because it quantifies uncertainty in a theoretically founded way. The tuning of hyperparameters and architectural choices decides calibration. Hypothesis H1.3 evaluates whether ENSM provides uncertainty estimates that are practically useful, which has a lot of importance.

Research Question 2: Reinforcement Learning Algorithm Comparison

RQ2: What algorithms (among 13 candidates across policy gradient, evolutionary, fuzzy, multi-agent, and meta-learning categories) achieve superior performance for multi-objective, high-dimensional, long-horizon optimization of energy transition and what characteristics (sample- and convergence-stability, computational cost, solution diversity) distinguish the top performers from inferior alternatives?

The selection algorithm in a RL influences the quality of solution. However, there are no systematic comparisons performed in energy systems literature. A single algorithm is used in most of the studies without justification for choice or benchmarking options. To fill this gap we develop and test empirical guidance for future applications, while testing theoretical hypotheses about which algorithms are suitable for long-horizon problems.

Hypothesis H2.1 (Target Achievement):

*Null hypothesis ($H_0$):* None of the 13 RL algorithms is capable to achieve a simultaneous satisfaction of all 4 targets (capacity ≥218 GW, renewable share ≥90%, CO₂ reduction ≥87%, cost ∈ [$200B,$450B], USD 2023) with >80% success rate in 100 independent training runs.

*Alternative hypothesis ($H_1$):* At least one algorithm from the policy gradient category (MAPPO, SAC, or TD3) achieves target satisfaction in at least 95% of runs and there is a significant difference (p < 0.01 in proportion test) between policy gradient and evolutionary, fuzzy, multi-agent, and meta-learning category results.