Symmetry

Accurate short-term wind power forecasting plays a critical role in maintaining grid stability due to the inherently irregular and fluctuating nature of wind resources. Deep learning models such as LSTM, GRU, and CNN are widely used to learn temporal dynamics; however, their ability to capture or adapt to the underlying symmetries and asymmetries inherent in real-world wind energy data remains insufficiently explored. In this study, we evaluate and compare these models using authentic production and meteorological data from the Tokat Wind Farm in Türkiye. The forecasting scenarios were designed to reflect the temporal structure of the dataset, including seasonal patterns, recurrent behaviors, and the symmetry-breaking effects caused by abrupt changes in wind speed and operational variability. The results demonstrate that the LSTM model most effectively captures the temporal relationships and partial symmetries within the data, yielding the lowest error metrics (RMSE = 0.2355, MAE = 0.1249, MAPE = 25.16%, R² = 0.8199). GRU and CNN offer moderate performance but show reduced sensitivity to asymmetric fluctuations, particularly during periods of high variability. The comparative findings highlight how symmetry-informed model behavior—specifically the ability to learn repeating temporal structures and respond to symmetry-breaking events—can significantly influence forecasting accuracy. This study provides practical insights into the interplay between data symmetries and model performance, supporting the development of more robust deep learning approaches for real-world wind energy forecasting.

The current paper retrieves optical 1–soliton solution to the concatenation model with the Kerr law of self-phase modulation structure. The primary mode of integration is the Lie symmetry analysis. The subsequent ordinary differential equations (ODEs) are formulated by the recently proposed Kumar–Malik scheme. This leads to the emergence of a variety of 1–soliton solutions along with their respective existence criteria. The numerical simulations support the analytical solutions that are yielded by the joint application of the two schemes.

Differential cryptanalysis is a fundamental technique in symmetric-key cryptanalysis. While the existing literature and several surveys have separately addressed classical differential attacks, deep learning-assisted cryptanalysis, and quantum-related attacks, a systematic presentation that enables cross-paradigm comparison, lineage mapping, and methodological evaluation is still lacking. To address this gap, this paper organizes its analysis along these three evolutionary threads. First, we trace the evolutionary trajectory of classical differential cryptanalysis. We distill eight representative technical pathways and group them into four categories based on mechanistic characteristics to facilitate cross-comparison. Second, we classify the integration of deep learning with differential cryptanalysis into two distinct paradigms: “deep learning-assisted” and “deep learning-based.” We discuss their roles in feature extraction, trail search, and key-recovery (KR) while also reviewing reproducible evidence, common limitations, and empirical challenges. Third, we survey quantum computing-based approaches. In light of current algorithms and hardware constraints, we examine their potential speedups and applicability boundaries in characteristic search and KR. Our synthesis of existing work reveals distinct capability boundaries for each paradigm and identifies key challenges in their practical application. This paper offers a structured comparative framework, aiming to serve as a reusable reference and baseline for future research.