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Search Results (1,011)

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Keywords = graph convolutional neural network

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31 pages, 2256 KB  
Article
Trust Assessment of Distributed Power Grid Terminals via Dual-Domain Graph Neural Networks
by Cen Chen, Jinghong Lan, Yi Wang, Zhuo Lv, Junchen Li, Ying Zhang, Xinlei Ming and Yubo Song
Electronics 2026, 15(6), 1211; https://doi.org/10.3390/electronics15061211 - 13 Mar 2026
Viewed by 171
Abstract
As distributed terminals are increasingly integrated into modern power systems with high penetration of renewable energy and decentralized resources, access control mechanisms must support continuous and highly detailed trust assessment. Existing approaches based on machine learning primarily rely on network traffic features from [...] Read more.
As distributed terminals are increasingly integrated into modern power systems with high penetration of renewable energy and decentralized resources, access control mechanisms must support continuous and highly detailed trust assessment. Existing approaches based on machine learning primarily rely on network traffic features from a single source and analyze terminals in isolation, which limits their ability to capture complex device states and correlated attack behaviors. This paper presents a trust assessment framework for distributed power grid terminals that combines multidimensional behavioral modeling with dual domain graph neural networks. Behavioral features are collected from network traffic, runtime environment, and hardware or kernel events and are fused into compact representations through a variational autoencoder to mitigate redundancy and reduce computational overhead. Based on the fused features and observed communication relationships, two graphs are constructed in parallel: a feature domain graph reflecting behavioral similarity and a topological domain graph capturing communication structure between terminals. Graph convolution is performed in both domains to jointly model individual behavioral risk and correlation across terminals. A fusion mechanism based on attention is further introduced to adaptively integrate embeddings specific to each domain, together with a loss function that enforces both shared and complementary representations across domains. Experiments conducted on the CIC EV Charger Attack Dataset 2024 show that the proposed framework achieves a classification accuracy of 96.84%, while maintaining a recall rate above 95% for the low trust category. These results indicate that incorporating multidimensional behavior perception and dual domain relational modeling improves trust assessment performance for distributed power grid terminals under complex attack scenarios. Full article
(This article belongs to the Special Issue Advances in Data Security: Challenges, Technologies, and Applications)
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24 pages, 4228 KB  
Article
From Layout to Data: AI-Driven Route Matrix Generation for Logistics Optimization
by Ádám Francuz and Tamás Bányai
Mathematics 2026, 14(5), 910; https://doi.org/10.3390/math14050910 - 7 Mar 2026
Viewed by 254
Abstract
This study proposes an end-to-end mathematical framework to automatically transform warehouse layout images into optimization-ready route matrices. The objective is to convert visual spatial information into a discrete, graph-based representation suitable for combinatorial route optimization. The problem is formulated as a mapping from [...] Read more.
This study proposes an end-to-end mathematical framework to automatically transform warehouse layout images into optimization-ready route matrices. The objective is to convert visual spatial information into a discrete, graph-based representation suitable for combinatorial route optimization. The problem is formulated as a mapping from continuous image space to a structured grid representation, integrating image segmentation, graph construction, and Traveling Salesman Problem (TSP)-based routing. Synthetic warehouse layouts were generated to create labeled training data, and a U-Net convolutional neural network was trained to perform multi-class segmentation of warehouse elements. The predicted grid representation was then converted into a graph structure, where feasible cells define vertices and adjacency defines edges. Shortest path distances were computed using Breadth-First Search, and the resulting distance matrix was used to solve a TSP instance. The segmentation model achieved approximately 98% training accuracy and 95–97% validation accuracy. The generated route matrices enabled successful construction of feasible and optimal round-trip routes in all tested scenarios. The proposed framework demonstrates that warehouse layouts can be automatically transformed into discrete mathematical representations suitable for logistics optimization, reducing manual preprocessing and enabling scalable integration into digital logistics systems. Full article
(This article belongs to the Special Issue Soft Computing in Computational Intelligence and Machine Learning)
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34 pages, 4142 KB  
Article
Subject-Independent Multimodal Interaction Modeling for Joint Emotion and Immersion Estimation in Virtual Reality
by Haibing Wang and Mujiangshan Wang
Symmetry 2026, 18(3), 451; https://doi.org/10.3390/sym18030451 - 6 Mar 2026
Viewed by 157
Abstract
Virtual Reality (VR) has emerged as a powerful medium for immersive human–computer interaction, where users’ emotional and experiential states play a pivotal role in shaping engagement and perception. However, existing affective computing approaches often model emotion recognition and immersion estimation as independent problems, [...] Read more.
Virtual Reality (VR) has emerged as a powerful medium for immersive human–computer interaction, where users’ emotional and experiential states play a pivotal role in shaping engagement and perception. However, existing affective computing approaches often model emotion recognition and immersion estimation as independent problems, overlooking their intrinsic coupling and the structured relationships underlying multimodal physiological signals. In this work, we propose a modality-aware multi-task learning framework that jointly models emotion recognition and immersion estimation from a graph-structured and symmetry-aware interaction perspective. Specifically, heterogeneous physiological and behavioral modalities—including eye-tracking, electrocardiogram (ECG), and galvanic skin response (GSR)—are treated as relational components with structurally symmetric encoding and fusion mechanisms, while their cross-modality dependencies are adaptively aggregated to preserve interaction symmetry at the representation level and introduce controlled asymmetry at the task-optimization level through weighted multi-task learning, without introducing explicit graph neural network architectures. To support reproducible evaluation, the VREED dataset is further extended with quantitative immersion annotations derived from presence-related self-reports via weighted aggregation and factor analysis. Extensive experiments demonstrate that the proposed framework consistently outperforms recurrent, convolutional, and Transformer-based baselines. Compared with the strongest Transformer baseline, the proposed framework yields consistent relative performance gains of approximately 3–7% for emotion recognition metrics and reduces immersion estimation errors by nearly 9%. Beyond empirical improvements, this study provides a structured interpretation of multimodal affective modeling that highlights symmetry, coupling, and controlled symmetry breaking in multi-task learning, offering a principled foundation for adaptive VR systems, emotion-driven personalization, and dynamic user experience optimization. Full article
(This article belongs to the Section Computer)
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25 pages, 2728 KB  
Article
GDNN: A Practical Hybrid Book Recommendation System for the Field of Ideological and Political Education
by Yanli Liang, Hui Liu and Songsong Liu
Electronics 2026, 15(5), 1086; https://doi.org/10.3390/electronics15051086 - 5 Mar 2026
Viewed by 187
Abstract
Ideological and political education (IPE) is a cornerstone of higher education in China. As IPE-related book collections expand rapidly, university libraries face a growing challenge of information overload, which hinders the accurate characterization of student reading preferences and the efficient matching of resources [...] Read more.
Ideological and political education (IPE) is a cornerstone of higher education in China. As IPE-related book collections expand rapidly, university libraries face a growing challenge of information overload, which hinders the accurate characterization of student reading preferences and the efficient matching of resources to demand. To address these issues, this study proposes GDNN, a practical hybrid recommendation system designed for both warm-start and cold-start scenarios. For warm-start users with historical borrowing records, we develop the PPSM-GCN framework. This framework enhances the classical graph convolutional collaborative filtering model LightGCN by integrating a novel potential positive sample mining (PPSM) strategy, which effectively mitigates data sparsity and improves the modeling of latent interests. For cold-start users without interaction history, we introduce an embedding and MLP architecture. This deep neural network learns implicit reader–book associations from reader attributes and book metadata, enabling personalized recommendations even in the absence of historical data. Experimental results demonstrate that PPSM-GCN and the embedding and MLP method achieve significant performance gains in their respective scenarios. This research provides both technical support and practical insights for the precise delivery of IPE resources and the overall enhancement of educational effectiveness in higher education. Full article
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18 pages, 2882 KB  
Article
Fault Detection and Identification of Wind Turbines via Causal Spatio-Temporal Features and Variable-Level Normalized Flow
by Xiheng Gao, Weimin Li and Hongxiu Zhu
Math. Comput. Appl. 2026, 31(2), 35; https://doi.org/10.3390/mca31020035 - 1 Mar 2026
Viewed by 179
Abstract
Anomaly identification and fault localization of wind turbines through Supervisory Control and Data Acquisition (SCADA) data is a popular topic today, but most studies overlook the complex time-space interdependence between wind turbine (WT) SCADA variables, which results in low detection accuracy for anomalies [...] Read more.
Anomaly identification and fault localization of wind turbines through Supervisory Control and Data Acquisition (SCADA) data is a popular topic today, but most studies overlook the complex time-space interdependence between wind turbine (WT) SCADA variables, which results in low detection accuracy for anomalies in critical moving components of the wind turbine. To address this problem, this paper proposes a fault detection and identification method based on a dynamic graph model with a causal spatio-temporal attention mechanism and variable-level normalized flow. First, it introduces a spatio-temporal attention mechanism under causality to extract the spatio-temporal attention mechanism under causality to extract spatio-temporal features of the variables and uses a graph convolutional neural network to represent the extracted spatio-temporal features as a dynamic graph. Secondly, a dynamic normalization flow is suggested for calculating the logarithmic density estimation between variables. Finally, the anomaly scores are calculated through logarithmic density estimation. Based on these scores, anomalies are detected and localized. Experimental validation on real SCADA data from wind turbines demonstrates that the method can effectively identify abnormal operating states and provide early warnings, achieving higher accuracy and greater stability. Full article
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22 pages, 5113 KB  
Article
Identification of Truck Travel Endpoints and Traffic Demand Prediction Based on Trajectory Data
by Xiaoyun Cheng, Yichen Yao, Jian Zou, Tingjia Zhang and Jitong Shao
Sustainability 2026, 18(5), 2306; https://doi.org/10.3390/su18052306 - 27 Feb 2026
Viewed by 159
Abstract
The rapid expansion of the logistics industry has led to sustained growth in freight demand across regions. Analyzing the factors that influence truck travel demand and extracting loading/unloading locations from truck trajectory data can offer a theoretical foundation and policy support for freight [...] Read more.
The rapid expansion of the logistics industry has led to sustained growth in freight demand across regions. Analyzing the factors that influence truck travel demand and extracting loading/unloading locations from truck trajectory data can offer a theoretical foundation and policy support for freight logistics planning and management. Accordingly, this study is structured around two core tasks: identifying truck trip endpoints and forecasting truck travel demand, aiming to thoroughly examine urban freight travel patterns and their influencing factors. First, truck GPS data is integrated with a non-parametric Lorenz curve fitting method, road network data, and Areas of Interest (AOI) to precisely identify truck route endpoints. Subsequently, a Multi-Feature Dynamic GCN-LSTM model is constructed to predict truck travel demand by comprehensively considering multi-dimensional regional characteristics. Using Xi’an, China, as a case study, the results show that the proposed framework provides a more precise spatial distribution of truck trips and effectively forecasts truck travel demand in the city. This research has significant implications for enhancing urban freight efficiency, optimising the layout and facilities of urban transport networks, developing evidence-based transport policies, and promoting logistics development. Full article
(This article belongs to the Section Sustainable Transportation)
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23 pages, 1745 KB  
Article
Graph Attention Networks in Exchange Rate Forecasting
by Joanna Landmesser-Rusek and Arkadiusz Orłowski
Econometrics 2026, 14(1), 11; https://doi.org/10.3390/econometrics14010011 - 25 Feb 2026
Viewed by 395
Abstract
Exchange rate forecasting is an important issue in financial market analysis. Currency rates form a dynamic network of connections that can be efficiently modeled using graph neural networks (GNNs). The key mechanism of GNNs is the message passing between nodes, allowing for better [...] Read more.
Exchange rate forecasting is an important issue in financial market analysis. Currency rates form a dynamic network of connections that can be efficiently modeled using graph neural networks (GNNs). The key mechanism of GNNs is the message passing between nodes, allowing for better modeling of currency interactions. Each node updates its representation by aggregating features from its neighbors and combining them with its own. In convolutional graph neural networks (GCNs), all neighboring nodes are treated equally, but in reality, some may have a greater influence than others. To account for this changing importance of neighbors, graph attention networks (GAT) have been introduced. The aim of the study was to evaluate the effectiveness of GAT in forecasting exchange rates. The analysis covered time series of major world currencies from 2020 to 2024. The forecasting results obtained using GAT were compared with those obtained from benchmark models such as ARIMA, GARCH, MLP, GCN, and LSTM-GCN. The study showed that GAT networks outperform numerous methods. The results may have practical applications, supporting investors and analysts in decision-making. Full article
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22 pages, 814 KB  
Article
Graph Convolution Neural Network and Deep Q-Network Optimization-Based Intrusion Detection with Explainability Analysis
by Kelvin Mwiga, Mussa Dida, Leandros Maglaras, Ahmad Mohsin, Helge Janicke and Iqbal H. Sarker
Sensors 2026, 26(5), 1421; https://doi.org/10.3390/s26051421 - 24 Feb 2026
Viewed by 397
Abstract
As networks expand in size and complexity, coupled with an exponential increase in intrusions on network and IoT systems, this leads to traditional models failing to capture increasingly intricate correlations among network components accurately. Graph Convolution Networks (GCNs) have recently acquired prominence for [...] Read more.
As networks expand in size and complexity, coupled with an exponential increase in intrusions on network and IoT systems, this leads to traditional models failing to capture increasingly intricate correlations among network components accurately. Graph Convolution Networks (GCNs) have recently acquired prominence for their capacity to represent nodes, edges, or entire graphs by aggregating information from adjacent nodes. However, the correlations between nodes and their neighbours, as well as related edges, differ. Assigning higher weights to nodes and edges with high similarity improves model accuracy and expressiveness. In this paper, we propose the GCN-DQN model, which integrates GCN with a multi-head attention mechanism and DQN (Deep Q Network) to adaptively adjust attention weights optimizing its performance in intrusion detection tasks. After extensive experiments using the UNSW NB15 and CIC-IDS2017 dataset, the proposed GCN-DQN outperformed the baseline model in classification accuracy. We also applied LIME and SHAP techniques to provide explainability to our proposed intrusion detection model. Full article
(This article belongs to the Special Issue Advanced Applications of WSNs and the IoT—2nd Edition)
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81 pages, 3981 KB  
Review
Graph Learning in Bioinformatics: A Survey of Graph Neural Network Architectures, Biological Graph Construction and Bioinformatics Applications
by Lijia Deng, Ziyang Dong, Zhengling Yang, Bo Gong and Le Zhang
Biomolecules 2026, 16(2), 333; https://doi.org/10.3390/biom16020333 - 23 Feb 2026
Viewed by 521
Abstract
Graph Neural Networks (GNNs) have become a central methodology for modelling biological systems where entities and their interactions form inherently non-Euclidean structures. From protein interaction networks and gene regulatory circuits to molecular graphs and multi-omics integration, the relational nature of biological data makes [...] Read more.
Graph Neural Networks (GNNs) have become a central methodology for modelling biological systems where entities and their interactions form inherently non-Euclidean structures. From protein interaction networks and gene regulatory circuits to molecular graphs and multi-omics integration, the relational nature of biological data makes GNNs particularly well-suited for capturing complex dependencies that traditional deep learning methods fail to represent. Despite their rapid adoption, the effectiveness of GNNs in bioinformatics depends not only on model design but also on how biological graphs are constructed, parameterised and trained. In this review, we provide a structured framework for understanding and applying GNNs in bioinformatics, organised around three key dimensions: (1) graph construction and representation, including strategies for deriving biological networks from heterogeneous sources and selecting biologically meaningful node and edge features; (2) GNN architectures, covering spectral and spatial formulations, representative models such as Graph Convolutional Networks (GCNs), Graph Attention Networks (GATs), Graph Sample and AggregatE (GraphSAGE) and Graph Isomorphism Network (GIN), and recent advances including transformer-based and self-supervised paradigms; and (3) applications in biomedical domains, spanning disease–gene association prediction, drug discovery, protein structure and function analysis, multi-omics integration and biomedical knowledge graphs. We further examine training considerations, including optimisation techniques, regularisation strategies and challenges posed by data sparsity and noise in biological settings. By synthesising methodological foundations with domain-specific applications, this review clarifies how graph quality, architectural choice and training dynamics jointly influence model performance. We also highlight emerging challenges such as modelling temporal biological processes, improving interpretability, and enabling robust multimodal fusion that will shape the next generation of GNNs in computational biology. Full article
(This article belongs to the Special Issue Application of Bioinformatics in Medicine)
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22 pages, 2918 KB  
Article
MV-RiskNet: Multi-View Attention-Based Deep Learning Model for Regional Epidemic Risk Prediction and Mapping
by Beyzanur Okudan and Abdullah Ammar Karcioglu
Appl. Sci. 2026, 16(4), 2135; https://doi.org/10.3390/app16042135 - 22 Feb 2026
Viewed by 311
Abstract
Regional epidemic risk prediction requires holistic modeling of heterogeneous data sources such as demographic structure, health capacity, geographical features and human mobility. In this study, a unique and multi-modal epidemiological data set integrating demographic, health, geographic and mobility indicators of Türkiye and its [...] Read more.
Regional epidemic risk prediction requires holistic modeling of heterogeneous data sources such as demographic structure, health capacity, geographical features and human mobility. In this study, a unique and multi-modal epidemiological data set integrating demographic, health, geographic and mobility indicators of Türkiye and its neighboring countries was collected. Türkiye’s neighboring countries are Greece, Bulgaria, Georgia, Armenia, Iran, and Iraq. This dataset, created by combining raw data from these neighboring countries, provides a comprehensive regional representation that allows for both quantitative classification and spatial mapping of epidemiological risk. To address the class imbalance problem, Conditional GAN (CGAN), a class-conditional synthetic example generation approach that enhances high-risk category representation was used. In this study, we proposed a multi-view deep learning model named MV-RiskNet, which effectively models the multi-dimensional data structure by processing each view into independent subnetworks and integrating the representations with an attention-based fusion mechanism for regional epidemic risk prediction. Experimental studies were compared using Multi-Layer Perceptron (MLP), Convolutional Neural Network (CNN), Long Short-Term Memory (LSTM), Autoencoder classifier, and Graph Convolutional Network (GCN) models. The proposed MV-RiskNet with CGAN model achieved better results compared to other models, with 97.22% accuracy and 97.40% F1-score. The generated risk maps reveal regional clustering patterns in a spatially consistent manner, while attention analyses show that demographic and geographic features are the dominant determinants, while mobility plays a complementary role, especially in high-risk regions. Full article
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17 pages, 2108 KB  
Article
Graph Neural Networks for City-Scale Electric Vehicle Charging Demand and Road-Network Flow Forecasting: Empirical Ablations on Graph Structure and Exogenous Features
by Ruei-Jan Hung
Electronics 2026, 15(4), 859; https://doi.org/10.3390/electronics15040859 - 18 Feb 2026
Viewed by 206
Abstract
City-scale forecasting is essential for both electric-vehicle (EV) charging operations (e.g., peak management and resource allocation) and urban mobility management (e.g., road-network flow monitoring and incident response). Spatio-temporal graph neural networks (STGNNs) are a natural candidate for these problems, yet their performance often [...] Read more.
City-scale forecasting is essential for both electric-vehicle (EV) charging operations (e.g., peak management and resource allocation) and urban mobility management (e.g., road-network flow monitoring and incident response). Spatio-temporal graph neural networks (STGNNs) are a natural candidate for these problems, yet their performance often critically depends on the choice of a predefined graph prior and the availability/quality of exogenous signals. Importantly, we do not intentionally construct a poor graph; rather, we treat any predefined adjacency as a testable hypothesis and verify its alignment with the forecasting target via no-graph ablations and lightweight diagnostics (Δcorr, ED). In this work, we present a unified experimental pipeline based on a spatio-temporal graph convolutional network (STGCN) backbone and conduct systematic ablations on (i) whether and how a predefined static graph is used and (ii) how feature sets influence multi-step forecasting accuracy. We evaluate on two city-scale hourly datasets with heterogeneous node counts (UrbanEV: 275 nodes; CHARGED-AMS_remove_zero: 1388 nodes) and a 24 h input/6 h output setting. Across datasets, we find that a static graph can be beneficial only when it matches the true dependency structure; otherwise, it may degrade accuracy substantially. On UrbanEV, removing the graph component improves overall MAE from 116.21 ± 5.43 to 66.53 ± 1.71 (S = 5 seeds, 0–4), outperforming a persistence baseline (MAE 94.16). Feature ablations further analyze how occupancy and price signals affect UrbanEV accuracy (e.g., MAE 87.32 with all features under the evaluated feature setting). On CHARGED, the volume-only setting performs best among tested feature combinations (MAE 0.127), closely tracking a persistence baseline (MAE 0.139), while additional covariates may introduce noise under static modeling. We provide detailed multi-horizon results and discuss practical implications for when graph priors help or hurt in real deployments. Full article
(This article belongs to the Special Issue Intelligent Transportation Systems and Sustainable Smart Cities)
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27 pages, 17688 KB  
Article
Causal-Enhanced Spatio-Temporal Markov Graph Convolutional Network for Traffic Flow Prediction
by Jing Hu and Shuhua Mao
Symmetry 2026, 18(2), 366; https://doi.org/10.3390/sym18020366 - 15 Feb 2026
Viewed by 322
Abstract
Traffic flow prediction is a pivotal task in intelligent transportation systems. The primary challenge lies in accurately modeling the dynamically evolving and directional spatio-temporal dependencies inherent in road networks. Existing graph neural network-based methods suffer from three main limitations: (1) symmetric adjacency matrices [...] Read more.
Traffic flow prediction is a pivotal task in intelligent transportation systems. The primary challenge lies in accurately modeling the dynamically evolving and directional spatio-temporal dependencies inherent in road networks. Existing graph neural network-based methods suffer from three main limitations: (1) symmetric adjacency matrices fail to capture the causal propagation of traffic flow from upstream to downstream; (2) the serial combination of graph and temporal convolutions lacks an explicit modeling of joint spatio-temporal state transition probabilities; (3) the inherent low-pass filtering property of temporal convolutional networks tends to smooth high-frequency abrupt signals, thereby weakening responsiveness to sudden events. To address these issues, this paper proposes a causal-enhanced spatio-temporal Markov graph convolutional network (CSHGCN). At the spatial modeling level, we construct an asymmetric causal adjacency matrix by decoupling source and target node embeddings to learn directional traffic flow influences. At the spatio-temporal joint modeling level, we design a spatio-temporal Markov transition module (STMTM) based on spatio-temporal Markov chain theory, which explicitly learns conditional transition patterns through temporal dependency encoders, spatial dependency encoders, and a joint transition network. At the temporal modeling level, we introduce differential feature enhancement and high-frequency residual compensation mechanisms to preserve key abrupt change information through frequency-domain complementarity. Experiments on four datasets—PEMS03, PEMS04, PEMS07, and PEMS08—demonstrate that CSHGCN outperforms existing baselines in terms of MAE, RMSE, and MAPE, with ablation studies validating the effectiveness of each module. Full article
(This article belongs to the Section Computer)
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21 pages, 1511 KB  
Article
SKNet-GAT: A Novel Multi-Source Data Fusion Approach for Distribution Network State Estimation
by Huijia Liu, Chengkai Yin and Sheng Ye
Energies 2026, 19(4), 1012; https://doi.org/10.3390/en19041012 - 14 Feb 2026
Viewed by 214
Abstract
This paper tackles the growing uncertainty in distribution networks caused by distributed generation, load fluctuations, and frequent topological changes. It proposes a multi-source data fusion framework using enhanced selective convolution (SKNet) and graph attention networks (GAT). First, heterogeneous measurement data, including Phasor Measurement [...] Read more.
This paper tackles the growing uncertainty in distribution networks caused by distributed generation, load fluctuations, and frequent topological changes. It proposes a multi-source data fusion framework using enhanced selective convolution (SKNet) and graph attention networks (GAT). First, heterogeneous measurement data, including Phasor Measurement Unit (PMU) and Supervisory Control and Data Acquisition (SCADA) data, are processed through a unified normalization and outlier elimination technique to ensure data quality. Second, SKNet is utilized to extract spatiotemporal multi-scale features, improving the detection of both rapid disturbances and long-term trends. Third, the extracted features are fed into GAT to model node electrical couplings, while power flow residual constraints are embedded in the loss function to enforce the physical validity of the estimated states. This physics-informed design overcomes a key limitation of pure data-driven models and enables an end-to-end framework that integrates data-driven learning with physical mechanism constraints. Finally, comprehensive validation is performed on the improved IEEE 33-node and IEEE 123-node test systems. The test scenarios include Gaussian measurement noise, data outliers, missing measurements, and topological changes. The results show that the proposed method outperforms baseline models such as Multi-Scale Graph Attention Network (MS-GAT), Bidirectional Long Short-Term Memory (BiLSTM), and traditional weighted least squares (WLS). It achieves Root Mean Square Error (RMSE) reductions of up to 18% and Mean Absolute Error (MAE) reductions of up to 15%. The average inference latency is only 10–18 ms. Even under unknown topological changes, the estimation error increases by only 15–25%. These results demonstrate the superior accuracy, robustness, and real-time performance of the proposed method for intelligent distribution network state estimation. Full article
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32 pages, 6235 KB  
Article
Beyond Attention: Hierarchical Mamba Models for Scalable Spatiotemporal Traffic Forecasting
by Zineddine Bettouche, Khalid Ali, Andreas Fischer and Andreas Kassler
Network 2026, 6(1), 11; https://doi.org/10.3390/network6010011 - 13 Feb 2026
Viewed by 374
Abstract
Traffic forecasting in cellular networks is a challenging spatiotemporal prediction problem due to strong temporal dependencies, spatial heterogeneity across cells, and the need for scalability to large network deployments. Traditional cell-specific models incur prohibitive training and maintenance costs, while global models often fail [...] Read more.
Traffic forecasting in cellular networks is a challenging spatiotemporal prediction problem due to strong temporal dependencies, spatial heterogeneity across cells, and the need for scalability to large network deployments. Traditional cell-specific models incur prohibitive training and maintenance costs, while global models often fail to capture heterogeneous spatial dynamics. Recent spatiotemporal architectures based on attention or graph neural networks improve accuracy but introduce high computational overhead, limiting their applicability in large-scale or real-time settings. We propose HiSTM (Hierarchical SpatioTemporal Mamba), a spatiotemporal forecasting architecture built on state-space modeling. HiSTM combines spatial convolutional encoding for local neighborhood interactions with Mamba-based temporal modeling to capture long-range dependencies, followed by attention-based temporal aggregation for prediction. The hierarchical design enables representation learning with linear computational complexity in sequence length and supports both grid-based and correlation-defined spatial structures. Cluster-aware extensions incorporate spatial regime information to handle heterogeneous traffic patterns. Experimental evaluation on large-scale real-world cellular datasets demonstrates that HiSTM achieves better accuracy, outperforming strong baselines. On the Milan dataset, HiSTM reduces MAE by 29.4% compared to STN, while achieving the lowest RMSE and highest R2 score among all evaluated models. In multi-step autoregressive forecasting, HiSTM maintains 36.8% lower MAE than STN and 11.3% lower than STTRE at the 6-step horizon, with a 58% slower error accumulation rate compared to STN. On the unseen Trentino dataset, HiSTM achieves 47.3% MAE reduction over STN and demonstrates better cross-dataset generalization. A single HiSTM model outperforms 10,000 independently trained cell-specific LSTMs, demonstrating the advantage of joint spatiotemporal learning. HiSTM maintains best-in-class performance with up to 30% missing data, outperforming all baselines under various missing data scenarios. The model achieves these results while being 45× smaller than PredRNNpp, 18× smaller than xLSTM, and maintaining competitive inference latency of 1.19 ms, showcasing its effectiveness for scalable 5/6G traffic prediction in resource-constrained environments. Full article
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18 pages, 8819 KB  
Article
Comparation of Graph Neural Networks and Traditional Machine Learning for Property Prediction in All-Inorganic Perovskite Materials
by Jingyu Liu, Xueqiong Su, Lishan Yang, Jiansen Ding, Jin Wang, Xing Ling, Yong Pan, Zhijun Wang, Wei Zhao and Yang Bu
Inorganics 2026, 14(2), 58; https://doi.org/10.3390/inorganics14020058 - 13 Feb 2026
Viewed by 344
Abstract
Machine learning (ML) methods have been widely explored for predicting material properties. However, due to the rapid development of ML techniques and the diversity of available models, performance comparisons between traditional and graph-based machine learning models remain limited. Therefore, we evaluate 11 conventional [...] Read more.
Machine learning (ML) methods have been widely explored for predicting material properties. However, due to the rapid development of ML techniques and the diversity of available models, performance comparisons between traditional and graph-based machine learning models remain limited. Therefore, we evaluate 11 conventional ML models alongside the graph neural network-based Crystal Graph Convolutional Neural Network (CGCNN) for predicting three key properties—formation energy (Ef), band gap (Eg), and energy above hull (Eh)—across a dataset comprising single perovskites, double perovskites, and their combined structures. The results demonstrate that for single perovskites, CGCNN exhibits gains of over 20% in the root mean square error (RMSE) relative to the second-best model (Gradient Boosting Regression), achieving values of 0.205 eV/atom (Ef), 0.718 eV (Eg), and 0.167 eV/atom (Eh). Prediction accuracy for double perovskites is significantly enhanced by training CGCNN on a combined dataset, particularly for Eh, where the coefficient of determination (R2) improves approximately 68.1-fold compared to models trained exclusively on double-perovskite data. Feature importance analysis via one-shot, permutation-based, and recursive feature elimination (RFE) methods reveals that optimal model performance requires retention of at least the top 20 critical features. Furthermore, feature utilization patterns of CGCNN across different prediction tasks are visualized. This work provides actionable guidelines for model selection and feature engineering in perovskite property prediction, establishing a benchmark for future ML-driven materials discovery. Full article
(This article belongs to the Special Issue Recent Progress in Perovskites)
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