Understanding how functional dynamics emerge from the brain’s underlying structural architecture remains a fundamental challenge in neuroscience. Conventional graph diffusion (GD) models are limited by sparse anatomical connectivity, leading to a failure to capture indirect connectivity and negatively correlated relationships. To overcome these challenges, we introduce hypergraphs and deep neural networks to enhance the representation of brain connectivity. Specifically, graphs and hypergraphs are integrated to construct a connected-graph, providing a comprehensive representation of inter-regional brain connectivity. The Fourier-induced deep neural network is employed to infer latent inter-regional relationships from structural connectivity by leveraging spectral features, effectively capturing both low- and high-frequency components. These deduced relationships are incorporated into the connected-graph, giving rise to a connected-graph diffusion (CD) model, which is further refined via eigen-decomposition to form an eigen-based connected-graph diffusion (ECD) model. Evaluated on 1012 subjects from the Human Connectome Project (HCP) S1200 release, the ECD model achieves a mean Pearson correlation coefficients of 0.7230 in functional connectivity (FC) prediction, outperforming the GD model (0.5513) and CD model (0.6518). The stability analysis demonstrates that the prediction of the ECD model is reliable. This work demonstrates that integrating biological mechanisms with machine learning methods can accurately model complex brain networks, with implications for neural signal processing, brain-inspired computing, and neuropsychiatric diagnosis.

Abstract Prediction problems regularly exist in practical application problems, where real application systems are usually complex. For multi-model data in complex systems, effectively identifying the patterns of each data set is significant for subsequent prediction. This paper focuses on the prediction problem of multi-model data and proposes an adaptive regression algorithm (CFM-MSVR) that combines a clustering feedback mechanism with improved support vector regression. The clustering feedback mechanism (CFM) clusters samples based on their residuals in each forecasting model, enabling the discovery of original data generation models. Meanwhile, it can intelligently estimate the number of clusters based on the number of samples in each cluster, reducing computational cost and dependence on empirical settings. In the regression stage, the multi-model support vector regression (MSVR) leverages the non-dominated sorting genetic algorithm II (NSGA-II) to optimise the parameters of the support vector regression, thereby improving the generalisation of each sub-model. The proposed method is evaluated on a simulated dataset, four real-world datasets, and the 2012 Global Energy Forecasting Competition dataset. Results show that CFM-MSVR achieves a MAPE% of 1.52 on the energy prediction task, demonstrating its strong performance in complex forecasting scenarios.

Long-term power load forecasting is critical for power system planning but is constrained by intricate temporal patterns. Transformer-based models emphasize modeling long- and short-term dependencies yet encounter limitations from complexity and parameter overhead. This paper introduces a novel Multi-Granularity Autoformer (MG-Autoformer) for long-term load forecasting. The model leverages a Multi-Granularity Auto-Correlation Attention Mechanism (MG-ACAM) to effectively capture fine-grained and coarse-grained temporal dependencies, enabling accurate modeling of short-term fluctuations and long-term trends. To enhance efficiency, a shared query-key (Q-K) mechanism is utilized to identify key temporal patterns across multiple resolutions and reduce model complexity. To address uncertainty in power load forecasting, the model incorporates a quantile loss function, enabling probabilistic predictions while quantifying uncertainty. Extensive experiments on benchmark datasets from Portugal, Australia, America, and ISO New England demonstrate the superior performance of the proposed MG-Autoformer in long-term power load point and probabilistic forecasting tasks.

Abstract Power load data frequently display outliers and an uneven distribution of noise. To tackle this issue, we present a forecasting model based on an improved extreme learning machine (ELM). Specifically, we introduce the novel Pinball-Huber robust loss function as the objective function in training. The loss function enhances the precision by assigning distinct penalties to errors based on their directions. We employ a genetic algorithm, combined with a swift nondominated sorting technique, for multiobjective optimization in the ELM-Pinball-Huber context. This method simultaneously reduces training errors while streamlining model structure. We practically apply the integrated model to forecast power load data in Taixing City, which is situated in the southern part of Jiangsu Province. The empirical findings confirm the method’s effectiveness.

Accurate short-term power forecasting (STPF) provides reliable support for the stable operation of power systems. However, due to the randomness of consumer behavior and energy properties, outliers inevitably exist in power series. Considering its negative influence, effectively extracting features from the power series with outliers has become a significant challenge in STPF. This paper develops a robust hybrid model to handle this issue. The proposed model utilizes the robust regression technique to handle outliers. An adaptive rescaled Huber loss is developed to approximate the complex distribution of the actual power series. Moreover, the proposed model applies autoregressive and bidirectional gated recurrent units to extract linear and nonlinear features of power series, respectively. Meanwhile, the attention mechanism extracts the temporal feature through the attention representation, which considers the correlations between different moments. The proposed model obtains the optimal coefficients of determination between predictions and observations on the wind power series as 0.9629 and power load series as 0.978, which indicates that the proposed model performs competitive robustness and generalization on the daily operation of renewable energy systems.

Abstract Wind power forecasting techniques have been well developed over the last half-century. There has been a large number of research literature as well as review analyses. Over the past 5 decades, considerable advancements have been achieved in wind power forecasting. A large body of research literature has been produced, including review articles that have addressed various aspects of the subject. However, these reviews have predominantly utilized horizontal comparisons and have not conducted a comprehensive analysis of the research that has been undertaken. This survey aims to provide a systematic and analytical review of the technical progress made in wind power forecasting. To accomplish this goal, we conducted a knowledge map analysis of the wind power forecasting literature published in the Web of Science database over the last 2 decades. We examined the collaboration network and development context, analyzed publication volume, citation frequency, journal of publication, author, and institutional influence, and studied co-occurring and bursting keywords to reveal changing research hotspots. These hotspots aim to indicate the progress and challenges of current forecasting technologies, which is of great significance for promoting the development of forecasting technology. Based on our findings, we analyzed commonly used traditional machine learning and advanced deep learning methods in this field, such as classical neural networks, and recent Transformers, and discussed emerging technologies like large language models. We also provide quantitative analysis of the advantages, disadvantages, forecasting accuracy, and computational costs of these methods. Finally, some open research questions and trends related to this topic were discussed, which can help improve the understanding of various power forecasting methods. This survey paper provides valuable insights for wind power engineers.

The extreme learning machine (ELM) is a well-known approach for training single hidden layer feedforward neural networks (SLFNs) in machine learning. However, ELM is most effective when used for regression on datasets with simple Gaussian distributed error because it often employs a squared loss in its objective function. In contrast, real-world data is often collected from unpredictable and diverse contexts, which may contain complex noise that cannot be characterized by a single distribution. To address this challenge, we propose a robust mixture ELM algorithm, called Mixture-ELM, that enhances modeling capability and resilience to both Gaussian and non-Gaussian noise. The Mixture-ELM algorithm uses an adjusted objective function that blends Gaussian and Laplacian distributions to approximate any continuous distribution and match the noise. The Gaussian mixture accurately models the residual distribution, while the inclusion of the Laplacian distribution addresses the limitations of the Gaussian distribution in identifying outliers. We derive a solution to the novel objective function using the expectation maximization (EM) and iteratively reweighted least squares (IRLS) algorithms. We evaluate the effectiveness of the algorithm through numerical simulation and experiments on benchmark datasets, thereby demonstrating its superiority over other state-of-the-art machine learning methods in terms of robustness and generalization.

An event-triggered output feedback control approach is proposed via a disturbance observer and adaptive dynamic programming (ADP). The solution starts by constructing a nonlinear disturbance observer, which only depends on the measurement of system output. A state observer is then developed based on approximation information of system dynamics via neural networks. In order to avoid continuous transmission and reduce the communication burden in the closed-loop system, an event-triggered mechanism is introduced such that the control signal is updated only at a specific instant when a triggered condition is violated. By virtue of the disturbance observer and state observer, an output-feedback ADP control approach then is developed, where only a critic network is employed to estimate the value function. Based on the Lyapunov stability theory, the stability of the closed-loop system is rigorously analyzed, and the effectiveness of the proposed control approach is verified by two simulation examples.

In time series forecasting with outliers and random noise, parameter estimation in a neural network via minimizing the$l_{2}$loss is unreliable. Therefore, an adaptive rescaled lncosh loss function is proposed in this article to handle time series modeling with outliers and random noise. It overcomes the limitation of the single distribution of traditional loss functions and can switch among$l_{1}$,$l_{2}$, and the Huber losses. A tuning parameter in the loss function is estimated by using a “working” likelihood approach according to estimated residuals. From the proposed loss function, a robust adaptive rescaled lncosh neural network (RARLNN) regression model is developed for highly accurate predictions. In the training phase of the model, an iterative learning procedure is presented to estimate the tuning parameter and train the neural network in iterations. A new prediction interval construction method is also developed based on quantile theory. The proposed RARLNN model is applied to two groups of wind speed forecasting tasks. The results show that the proposed RARLNN model is more conducive to enhancing forecasting accuracy and stability from the perspectives of noise distribution and outliers.

Abstract As unsupervised learning algorithm, clustering algorithm is widely used in data processing field. Density-based spatial clustering of applications with noise algorithm (DBSCAN), as a common unsupervised learning algorithm, can achieve clusters via finding high-density areas separated by low-density areas based on cluster density. Different from other clustering methods, DBSCAN can work well for any shape clusters in the spatial database and can effectively cluster exceptional data. However, in the employment of DBSCAN, the parameters, EPS and MinPts, need to be preset for different clustering object, which greatly influences the performance of the DBSCAN. To achieve automatic optimization of parameters and improve the performance of DBSCAN, we proposed an improved DBSCAN optimized by arithmetic optimization algorithm (AOA) with opposition-based learning (OBL) named OBLAOA-DBSCAN. In details, the reverse search capability of OBL is added to AOA for obtaining proper parameters for DBSCAN, to achieve adaptive parameter optimization. In addition, our proposed OBLAOA optimizer is compared with standard AOA and several latest meta heuristic algorithms based on 8 benchmark functions from CEC2021, which validates the exploration improvement of OBL. To validate the clustering performance of the OBLAOA-DBSCAN, 5 classical clustering methods with 10 real datasets are chosen as the compare models according to the computational cost and accuracy. Based on the experimental results, we can obtain two conclusions: (1) the proposed OBLAOA-DBSCAN can provide highly accurately clusters more efficiently; and (2) the OBLAOA can significantly improve the exploration ability, which can provide better optimal parameters.

Accurate forecasting of wind speed is vital in renewable power system management. However, wind speed series is an extremely complex system with outliers. Considering the dilemma, we propose a robust extreme learning machine algorithm where a huber loss works as the optimized function for extreme learning machine training. And a decomposition-ensemble method is developed in modelling wind speed. In our hybrid system, the proposed robust extreme learning machine is employed to model high-frequent sub-signals, while least square extreme learning machine is used to model low-frequent sub-signals. Validated by forecasting a 5-minutely wind speed in China, our proposed forecasting framework can provide more accurate predictions.