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As the demand for renewable energy is increasing, wind speed forecasting (WSF) becomes increasingly popular and essential for wind power generation. Several methods have been developed in the literature for WSF. However, WSF accuracy is challenging to obtain due to its non-stationary and non-linear character. To overcome this issue, this study suggests a novel integrated forecasting model for WSF. In the majority of cases, decomposition techniques are essential for removing noise and extracting patterns from non-stationary and non-linear wind speed time series. Among these decomposition techniques, the most widely used decomposition methods based on frequency domain theory are the Fourier decomposition method (FDM), the empirical wavelet transform (EWT), and the variational mode decomposition (VMD). However, FDM decomposition gives inconsistent results, EWT has mixed problems, and VMD is unsuitable for non-stationary time series. Thus, a novel combined model based on empirical Fourier decomposition (EFD) techniques, long short-term memory (LSTM) neural networks, and the Grey Wolf optimizer (GWO) is proposed in this paper. Initially, the wind speed time series is decomposed using EFD into a set of sub-series and a residual, which is a stationary sub-series that can be easily modelled by a recurrent neural network (RNN). Further, the matching LSTM is used to forecast each sub-series and residual, while the GWO optimizes the sub-series estimated output, resulting in improved prediction precision and stability. In order to assess the model performance, five wind speed datasets from various places in India are employed. The findings show that the proposed model is the top performing model among the other ten models; The average statistical score obtained from all datasets reduces 11.01% in the mean absolute error (MAE), 10.68% in the root mean square error (RMSE) and 10.73% in the mean absolute percentage error (MAPE). Further, regularity conditions for universal consistency of proposed model is also proved mathematically. • A novel hybrid EFD-LSTM-GWO architecture for wind speed forecasting. • Resolving the mixed-mode, inconsistent, and non-stationary challenges. • Analysing the proposed model's universal consistency. • Outperformance of the proposed algorithm over other existing models. [ABSTRACT FROM AUTHOR]

Early rainfall prediction is very important to ensure the economic balance of any agriculture-dominated country, such as India. Deep learning has recently received considerable attention for predicting rainfall using historical data. However, rainfall depends on multiple factors like ElNino, rising sea levels, warming of the Atlantic Ocean, etc. The changing climate has also significantly increased rainfall variability. The current deep-learning approaches are either based on a limited set of predictors or do not utilize the time-series properties for the recurrence of similar climate conditions every 12 months. Besides, they perform poorly in predicting accurate rainfall estimates for the diverse areas of India due to limited data availability across various regions. Therefore, this paper presents a groundbreaking solution to address the challenge of limited data by introducing RfGan (Rainfall GAN), a novel variant of generative adversarial networks. RfGan aims to fulfill the crucial need for abundant data to ensure the effectiveness of model training. Moreover, a novel rainfall prediction method, RfGanNet, has been introduced that leverages the strengths of the proposed RfGan for data augmentation, long-short-term memory, and convolutional neural networks for rainfall prediction. The performance of RfGanNet has been validated for India and its clustered regions in terms of nine parameters: precision, recall, specificity, Matthews correlation coefficient, accuracy, F1-score, mean absolute error, mean square error and computation time. The experimental results of RfGan are compared against original and synthetic datasets generated from state-of-the-art methods, namely tabular gan (TGAN), Wasserstein gan (WGAN), and conditional tabular gan (CTGAN). The experimental results indicate that the proposed RfNet model, when trained using RfGan-generated data, surpassed all the other considered methods by achieving 97.22 % accuracy. Moreover, RfNet has been compared with other related deep Learning approaches to validate its efficacy. Additionally, an ablation study investigating various LSTM–CNN combinations has been conducted. The findings of the study indicate that oceanic and climate-related predictors have a noteworthy influence on Indian rainfall. Moreover, the study highlights the suitability of combining Bidirectional LSTM, CNN, and multiple predictors for accurate rainfall prediction. • Novel variant of generative adversarial network- RfGan is proposed. • Different combinations of LSTM and CNN for rainfall prediction are tested. • Novel classifier — RfNet is tested on different augmented datasets. • K-means clustered regions of India have been identified. [ABSTRACT FROM AUTHOR]