An improved Adam optimization algorithm combining adaptive coefficients and composite gradients based on randomized block coordinate descent is proposed to address issues of the Adam algorithm such as slow convergence, the tendency to miss the global optimal solution, and the ineffectiveness of processing high‐dimensional vectors. The adaptive coefficient is used to adjust the gradient deviation value and correct the search direction firstly. Then, the predicted gradient is introduced, and the current gradient and the first‐order momentum are combined to form a composite gradient to improve the global optimization ability. Finally, the random block coordinate method is used to determine the gradient update mode, which reduces the computational overhead. Simulation experiments on two standard datasets for classification show that the convergence speed and accuracy of the proposed algorithm are higher than those of the six gradient descent methods, and the CPU and memory utilization are significantly reduced. In addition, based on logging data, the BP neural networks optimized by six algorithms, respectively, are used to predict reservoir porosity. Results show that the proposed method has lower system overhead, higher accuracy, and stronger stability, and the absolute error of more than 86% data is within 0.1%, which further verifies its effectiveness.

With the advent of big data and the information age, the data magnitude of various complex networks is growing rapidly. Many real-life situations cannot be portrayed by ordinary networks, while hypergraphs have the ability to describe and characterize higher order relationships, which have attracted extensive attention from academia and industry in recent years. Firstly, this paper described the development process, the application areas, and the existing review research of hypergraphs; secondly, introduced the theory of hypergraphs briefly; then, compared the learning methods of ordinary graphs and hypergraphs from three aspects: matrix decomposition, random walk, and deep learning; next, introduced the structural optimization of hypergraphs from three perspectives: dynamic hypergraphs, hyperedge weight optimization, and multimodal hypergraph generation; after that, the applicability of three uncertain hypergraph models were analyzed based on three uncertainty theories: probability theory, fuzzy set, and rough set; finally, the future research directions of hypergraphs and uncertain hypergraphs were prospected.

With the rapid development of cyber-physical systems (CPS), constructing information systems with high-quality services has become an urgent requirement in both academia and industry. Hypergraphs are widely used in graph data analysis tasks due to their wide node-aware range and reasonable interpretability. This article proposes a model known as the relation-aggregated hypergraph neural network, which aims to better describe and apply complex structures and relationships in the physical world, thereby improving the management efficiency and service quality of service recommendation in CPS. First, explicit and implicit hyperedges are constructed based on the explicit and implicit relationships between nodes, respectively. Second, a global attention mechanism is adopted to calculate the importance between neighbor nodes that share implicit hyperedges with the current node, generating a relation-aggregated hypergraph. Finally, by weighting the generated hypergraph association matrix and passing the aggregated features through the hypergraph neural network, we obtain the embedding representation of nodes. Node classification experiments were conducted on three public network datasets, and the accuracy rates were 83.7%, 88.8%, and 84.9%, respectively, which were higher than those of the baseline model.

The rise of graph neural networks has greatly contributed to the development of recommendation systems, and self-supervised learning has emerged as one of the most important approaches to address sparse interaction data. However, existing methods mostly focus on the recommendation’s accuracy while neglecting the role of recommended item diversity in enhancing user interest and merchant benefits. The reason for this phenomenon is mainly due to the bias of popular items, which makes the long-tail items (account for a large proportion) be neglected. How to mitigate the bias caused by item popularity has become one of the hot topics in current research. To address the above problems, we propose a Popularity-Debiased Graph Self-Supervised for Recommendation (PDGS). Specifically, we apply a penalty constraint on item popularity during the data enhancement process on the user–item interaction graph to eliminate the inherent popularity bias. We generate item similarity graphs with the popularity bias removed to construct a self-supervised learning task under multiple views, and we design model optimization strategies from the perspectives of popular items and long-tail items to generate recommendation lists. We conduct a large number of comparison experiments, as well as ablation experiments, on three public datasets to verify the effectiveness and the superiority of the model in balancing recommendation accuracy and diversity.