Quantum Neural Networks for Wind Energy Forecasting: A Comparative Study of Performance and Scalability with Classical Models

Technical Summary: Quantum Neural Networks for Wind Energy Forecasting

Problem Statement
Quantum Machine Learning (QML) holds theoretical promise for enhancing classical learning through principles like superposition and entanglement. However, skepticism persists regarding its practical utility, particularly within the constraints of Noisy Intermediate-Scale Quantum (NISQ) devices. A significant gap exists in the literature regarding systematic benchmarks of Quantum Neural Network (QNN) architectures for real-world regression tasks. Specifically, there is limited empirical evidence guiding the selection of optimal QNN configurations, their scalability with respect to dataset size, and their computational cost compared to classical models in energy forecasting. This study addresses these gaps by evaluating QNNs for wind power prediction, a critical task for grid integration and operational planning where data complexity often challenges classical scalability.

Methodology
The study utilizes a real-world temporal dataset comprising 4,464 measurements from a wind turbine, recorded at 10-minute intervals. The input features include wind speed, direction, atmospheric pressure, and temperature, with generated power output as the target variable. To analyze scalability, the authors created subsets of 1,000, 2,000, 3,000, and 4,000 samples, further divided into 80% training and 20% testing sets, normalized via min-max scaling.

The experimental design focuses on a Classical-Quantum (CQ) paradigm using Qiskit Machine Learning. The core methodology involves:

1. Data Encoding: The Z Feature Map was selected over the ZZ Feature Map based on prior performance, chosen for its ability to produce shallow circuits suitable for simulation and near-term hardware.
2. Ansatz Design: Six distinct QNN configurations were constructed by combining the Z Feature Map with six different entanglement strategies: Full, Linear, Circular, Shifted-Circular Alternating (SCA), Reverse Linear, and Pairwise.
3. Optimization: Models were trained using classical optimizers (ADAM and L-BFGS-B) to minimize prediction error.
4. Benchmarking: Performance was compared against three classical regression models: k-Nearest Neighbors (kNN), Decision Tree Regressor (DTR), and Linear Regression (LR).

Evaluation metrics included the coefficient of determination ($R^2$), Root Mean Square Error (RMSE), training stability (via loss variance and spike analysis), and simulation time complexity.

Key Contributions
The paper provides four primary contributions:

1. Systematic Benchmarking: A comprehensive evaluation of six QNN configurations on a real-world wind energy regression task, analyzing predictive performance and stability across varying dataset sizes.
2. Scalability Analysis: An investigation into how dataset size impacts both model accuracy and simulation runtime, identifying a specific "point of diminishing returns."
3. Complexity Characterization: Empirical evidence demonstrating that QNN training time scales linearly ($O(n)$) with dataset size, with the total quantum gate count identified as the primary driver of computational cost.
4. Stability Framework: A proposed stability analysis framework comparing QNN learning dynamics across different circuit configurations using standard deviation, maximum loss spikes, and final loss values.

Experimental Results

• Predictive Performance: QNN configurations achieved competitive or superior performance compared to classical baselines. The best-performing configuration, QNN-3 (using the Circular entanglement strategy), reached an $R^2$ score of 0.94 and an RMSE of 174.67 kW on the largest test set. This outperformed the best classical model (kNN), which achieved an $R^2$ of 0.94 and an RMSE of 182.99 kW, representing a 4.5% reduction in prediction error.
• Scalability Trends: Performance improvements were most significant when increasing dataset size from 800 to 1,600 samples. Beyond 1,600 samples, further increases in data did not yield consistent improvements in $R^2$ or RMSE; in some cases, performance slightly declined. This suggests an optimal data-to-model complexity ratio for the tested architectures.
• Stability: QNN-6 (Pairwise entanglement) demonstrated the highest stability across all metrics, while QNN-2 showed the highest variability. Larger datasets generally contributed to smoother convergence and reduced loss variance.
• Computational Efficiency: Training time scaled linearly with dataset size. Configurations with lower total gate counts (QNN-5 and QNN-6, with 34 gates) were the most time-efficient, whereas QNN-1 (40 gates) required the longest training times.
• Error Distribution: Quantum models generally exhibited more symmetric and concentrated error distributions than classical models. However, a notable limitation was observed: QNNs occasionally produced physically invalid negative power outputs, a behavior not seen in kNN or DTR.

Significance and Claims
The authors claim that this study provides a structured, empirical evaluation of QNNs for regression tasks, demonstrating their viability as a complementary alternative to classical machine learning, particularly in data-limited scenarios. The findings suggest that while QNNs can match or exceed classical performance, their scalability is constrained by an optimal data-to-complexity ratio and the computational cost of gate-heavy circuits.

The paper modestly concludes that QNNs are promising but not yet a wholesale replacement for classical methods. It highlights the necessity of future work to incorporate advanced classical baselines (e.g., XGBoost, LSTM), perform hyperparameter optimization, and develop methods to enforce physical constraints (such as non-negative power outputs) within the QNN modeling process. The study serves as a foundational benchmark for understanding the trade-offs between model complexity, dataset size, and computational cost in the current NISQ era.