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Keywords = FourierGNN

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25 pages, 15932 KB  
Article
Lightweight Graph Neural Network-Driven Acoustic Anomaly Detection Method for Gas Pipeline Leakage Levels in Underground Utility Tunnels
by Wei Sun, Yang Li, Jinghu Yang and Ye Cheng
Sensors 2026, 26(13), 4114; https://doi.org/10.3390/s26134114 - 29 Jun 2026
Viewed by 519
Abstract
Gas pipeline leakages in urban underground utility tunnels pose a severe threat to public safety. Leakages of varying aperture sizes trigger differentiated risks of diffusion and explosion; thus, achieving precise identification of leakage hole size has become a critical issue in safety management. [...] Read more.
Gas pipeline leakages in urban underground utility tunnels pose a severe threat to public safety. Leakages of varying aperture sizes trigger differentiated risks of diffusion and explosion; thus, achieving precise identification of leakage hole size has become a critical issue in safety management. To address the difficulty of traditional methods in effectively separating the acoustic features of different leakage levels within complex utility tunnel environments, this paper proposes a gas pipeline leakage risk level identification method based on a lightweight Spatial–Temporal Graph Neural Network (ST-GNN). First, relying on a real utility tunnel simulation platform, acoustic signals under different pressures and leakage hole size are collected, and time-frequency magnitude features are constructed through Short-Time Fourier Transform (STFT). Furthermore, each acoustic sample is independently converted into a graph with STFT time frames as nodes, where temporal neighborhood edges and K-nearest neighbor edges jointly encode local dynamics and non-local spectral similarities. This transforms unstructured acoustic signals into graph-structured data that embodies spatial–temporal coupling relationships. Building upon this, a lightweight Chebyshev graph convolutional network is designed to progressively extract discriminative features strongly correlated with leakage levels using multi-layer convolution. Experimental results on the actual utility tunnel simulation platform dataset demonstrate that the proposed method achieves excellent performance in a three-level leakage classification task. The t-SNE visualization reveals the effective separation of features, progressing from complete mixing in the input layer to distinct separation in the output layer. Through multiple training statistics and ablation experiments, the impact of dataset size and the number of network layers on the identification performance is analyzed, validating the robustness of the proposed model under limited samples and the effectiveness of its lightweight structure. This provides a feasible solution for the automated and refined identification of gas pipeline leakage levels in underground utility tunnels. Full article
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25 pages, 795 KB  
Article
From Prediction to Planning: A Spectral-Temporal GNN and Bi-Directional Decoding RL Framework
by Peiming Zhang, Jiangang Lu, Jiajia Fu, Xinyue Di, Kai Fang, Jie Tang and Cui Yang
Signals 2026, 7(3), 47; https://doi.org/10.3390/signals7030047 - 19 May 2026
Viewed by 525
Abstract
Accurately capturing spatiotemporal dependencies and enabling effective decision support are core challenges in Intelligent Transportation Systems (ITS). Existing research often treats traffic prediction and path planning as isolated tasks. Moreover, mainstream prediction models struggle with long-term periodic patterns, while Reinforcement Learning (RL)-based planning [...] Read more.
Accurately capturing spatiotemporal dependencies and enabling effective decision support are core challenges in Intelligent Transportation Systems (ITS). Existing research often treats traffic prediction and path planning as isolated tasks. Moreover, mainstream prediction models struggle with long-term periodic patterns, while Reinforcement Learning (RL)-based planning often suffers from inefficient exploration in sparse topologies. To address these issues, this paper proposes a unified framework combining a spectral-temporal Graph Neural Network (GNN) and bi-directional decoding RL. Specifically, a time-frequency dual-stream adaptive learning module is introduced for prediction. Fast Fourier Transform (FFT) and Gated Recurrent Unit (GRU) are employed to capture global frequency periodicities and local temporal dynamics, respectively. Their adaptive fusion effectively mitigates the long-sequence information forgetting problem. For path planning, the task is formulated as sequence generation. A graph-aware attention encoder with adjacency masking is designed, and heuristic feature embeddings are incorporated to guide efficient exploration. Furthermore, a bi-directional autoregressive decoding strategy enhances robustness against topological bottlenecks. On PEMSD4 and PEMSD8, the proposed predictor achieves MAE/RMSE/MAPE values of 18.211/30.433/12.006 and 13.587/23.566/8.955, respectively. Path-planning simulations on the PEMSD4-derived sparse topology further demonstrate stable bi-directional RL optimization, faster convergence with heuristic guidance, and a sparsity-aware encoder that reduces redundant attention interactions in sparse road networks. These results validate the effectiveness of the proposed “predict-then-plan” paradigm. Full article
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32 pages, 21569 KB  
Article
Fractal Waves and Caustic Signatures in a Superdeterministic Framework: Benchmarking PINNs and PI-GNNs for the Fractional Klein–Gordon Equation
by Luis Rojas and José Garcia
Fractal Fract. 2026, 10(5), 287; https://doi.org/10.3390/fractalfract10050287 - 24 Apr 2026
Cited by 2 | Viewed by 615
Abstract
While superdeterministic and fractal spacetime models offer compelling alternative perspectives on quantum foundations, the simulation and validation of effective wave dynamics in such non-differentiable, deterministic settings remain computationally and theoretically challenging. To address this, a framework built around the Fractional Nonlinear Klein–Gordon Equation [...] Read more.
While superdeterministic and fractal spacetime models offer compelling alternative perspectives on quantum foundations, the simulation and validation of effective wave dynamics in such non-differentiable, deterministic settings remain computationally and theoretically challenging. To address this, a framework built around the Fractional Nonlinear Klein–Gordon Equation (FNKGE), defined through the spectral fractional Laplacian, was developed. This equation was solved and benchmarked through a comparative study between Physics-Informed Neural Networks (PINNs) with Fourier features and Physics-Informed Graph Neural Networks (PI-GNNs). Additionally, detection patterns were simulated via deterministic agents, and theoretical links between fractal geometry, computational irreducibility, and deviations from statistical independence were formalized. Regarding the computational evaluation, superior accuracy was achieved by the PI-GNNs, yielding a mean relative error of 0.5% (ϵ¯=0.005), alongside faster convergence and a more well-conditioned Hessian spectrum compared to PINNs. Crucially, a continuous power-law decay (S(ky)ky1.8) was revealed by the spectral analysis of the simulated detection patterns, confirming the emergence of classical optical caustics rather than discrete quantum-interference peaks. Furthermore, a modified dispersion relation that accurately predicts linear instability regimes was derived, and specific boundary artifacts in non-periodic domains were identified. Taken together, the FNKGE is validated by these results as a viable effective model for fractal wave phenomenology and as a robust benchmark for physics-informed learning architectures. Full article
(This article belongs to the Section Engineering)
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30 pages, 1142 KB  
Review
Beyond the Backbone: A Quantitative Review of Deep-Learning Architectures for Tropical Cyclone Track Forecasting
by He Huang, Difei Deng, Liang Hu, Yawen Chen and Nan Sun
Remote Sens. 2025, 17(15), 2675; https://doi.org/10.3390/rs17152675 - 2 Aug 2025
Cited by 2 | Viewed by 3995
Abstract
Accurate forecasting of tropical cyclone (TC) tracks is critical for disaster preparedness and risk mitigation. While traditional numerical weather prediction (NWP) systems have long served as the backbone of operational forecasting, they face limitations in computational cost and sensitivity to initial conditions. In [...] Read more.
Accurate forecasting of tropical cyclone (TC) tracks is critical for disaster preparedness and risk mitigation. While traditional numerical weather prediction (NWP) systems have long served as the backbone of operational forecasting, they face limitations in computational cost and sensitivity to initial conditions. In recent years, deep learning (DL) has emerged as a promising alternative, offering data-driven modeling capabilities for capturing nonlinear spatiotemporal patterns. This paper presents a comprehensive review of DL-based approaches for TC track forecasting. We categorize all DL-based TC tracking models according to the architecture, including recurrent neural networks (RNNs), convolutional neural networks (CNNs), Transformers, graph neural networks (GNNs), generative models, and Fourier-based operators. To enable rigorous performance comparison, we introduce a Unified Geodesic Distance Error (UGDE) metric that standardizes evaluation across diverse studies and lead times. Based on this metric, we conduct a critical comparison of state-of-the-art models and identify key insights into their relative strengths, limitations, and suitable application scenarios. Building on this framework, we conduct a critical cross-model analysis that reveals key trends, performance disparities, and architectural tradeoffs. Our analysis also highlights several persistent challenges, such as long-term forecast degradation, limited physical integration, and generalization to extreme events, pointing toward future directions for developing more robust and operationally viable DL models for TC track forecasting. To support reproducibility and facilitate standardized evaluation, we release an open-source UGDE conversion tool on GitHub. Full article
(This article belongs to the Section AI Remote Sensing)
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24 pages, 4618 KB  
Article
A Sensor Data Prediction and Early-Warning Method for Coal Mining Faces Based on the MTGNN-Bayesian-IF-DBSCAN Algorithm
by Mingyang Liu, Xiaodong Wang, Wei Qiao, Hongbo Shang, Zhenguo Yan and Zhixin Qin
Sensors 2025, 25(15), 4717; https://doi.org/10.3390/s25154717 - 31 Jul 2025
Cited by 6 | Viewed by 1544
Abstract
In the context of intelligent coal mine safety monitoring, an integrated prediction and early-warning method named MTGNN-Bayesian-IF-DBSCAN (Multi-Task Graph Neural Network–Bayesian Optimization–Isolation Forest–Density-Based Spatial Clustering of Applications with Noise) is proposed to address the challenges of gas concentration prediction and anomaly detection in [...] Read more.
In the context of intelligent coal mine safety monitoring, an integrated prediction and early-warning method named MTGNN-Bayesian-IF-DBSCAN (Multi-Task Graph Neural Network–Bayesian Optimization–Isolation Forest–Density-Based Spatial Clustering of Applications with Noise) is proposed to address the challenges of gas concentration prediction and anomaly detection in coal mining faces. The MTGNN (Multi-Task Graph Neural Network) is first employed to model the spatiotemporal coupling characteristics of gas concentration and wind speed data. By constructing a graph structure based on sensor spatial dependencies and utilizing temporal convolutional layers to capture long short-term time-series features, the high-precision dynamic prediction of gas concentrations is achieved via the MTGNN. Experimental results indicate that the MTGNN outperforms comparative algorithms, such as CrossGNN and FourierGNN, in prediction accuracy, with the mean absolute error (MAE) being as low as 0.00237 and the root mean square error (RMSE) maintained below 0.0203 across different sensor locations (T0, T1, T2). For anomaly detection, a Bayesian optimization framework is introduced to adaptively optimize the fusion weights of IF (Isolation Forest) and DBSCAN (Density-Based Spatial Clustering of Applications with Noise). Through defining the objective function as the F1 score and employing Gaussian process surrogate models, the optimal weight combination (w_if = 0.43, w_dbscan = 0.52) is determined, achieving an F1 score of 1.0. By integrating original concentration data and residual features, gas anomalies are effectively identified by the proposed method, with the detection rate reaching a range of 93–96% and the false alarm rate controlled below 5%. Multidimensional analysis diagrams (e.g., residual distribution, 45° diagonal error plot, and boxplots) further validate the model’s robustness in different spatial locations, particularly in capturing abrupt changes and low-concentration anomalies. This study provides a new technical pathway for intelligent gas warning in coal mines, integrating spatiotemporal modeling, multi-algorithm fusion, and statistical optimization. The proposed framework not only enhances the accuracy and reliability of gas prediction and anomaly detection but also demonstrates potential for generalization to other industrial sensor networks. Full article
(This article belongs to the Section Industrial Sensors)
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16 pages, 3968 KB  
Article
Winter Wheat Yield Prediction and Influencing Factors Analysis Based on FourierGNN–Random Forest Combined Modeling
by Jianqin Ma, Yijian Chen, Bifeng Cui, Yu Ding, Xiuping Hao, Yan Zhao, Junsheng Li and Xianrui Su
Agronomy 2025, 15(3), 641; https://doi.org/10.3390/agronomy15030641 - 3 Mar 2025
Cited by 3 | Viewed by 2647
Abstract
In order to investigate the changes in winter wheat yield and the factors influencing it, five meteorological factors—such as rainfall and soil moisture—collected from the experimental area between 2010 and 2022 were used as characteristic features. A combined model of GNN (Graph Neural [...] Read more.
In order to investigate the changes in winter wheat yield and the factors influencing it, five meteorological factors—such as rainfall and soil moisture—collected from the experimental area between 2010 and 2022 were used as characteristic features. A combined model of GNN (Graph Neural Network), based on the Fourier transform and the Random Forest algorithm was developed to predict winter wheat yield. Matrix multiplication in Fourier space was performed to predict yield, while the Random Forest algorithm was employed to quantify the contribution of various yield factors to winter wheat yield. The combined model effectively captured the dynamic dependencies between yield factors and time series, improving predictive accuracy by 5.00%, 10.00%, and 27.00%, and reducing the root mean square error by 26.26%, 29.31%, and 88.20%, respectively, compared to the StemGNN, Informer, and Random Forest models. The predicted outputs ranged from 520 to 720 g/m2, with an average error of 2.69% compared to the actual measure outputs. Under the insufficient real-time irrigation mode, winter wheat yield was highest at 90% irrigation upper limit and 70% irrigation lower limit, with a medium fertilization level (850 mg/kg). The yield showed an overall decreasing trend as both irrigation limits and fertilizer application decreased. Rainfall and soil moisture were the most significant factors influencing winter wheat yield, followed by air temperature and evapotranspiration. Solar radiation and sunshine duration had the least impact. The results of this study provide a valuable reference for accurately predicting winter wheat yield. Full article
(This article belongs to the Section Precision and Digital Agriculture)
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14 pages, 1644 KB  
Article
Spatio-Temporal Photovoltaic Power Prediction with Fourier Graph Neural Network
by Shi Jing, Xianpeng Xi, Dongdong Su, Zhiwei Han and Daxing Wang
Electronics 2024, 13(24), 4988; https://doi.org/10.3390/electronics13244988 - 18 Dec 2024
Cited by 17 | Viewed by 3530
Abstract
The strong development of distributed energy sources has become one of the most important measures for low-carbon development worldwide. With a significant quantity of photovoltaic (PV) power generation being integrated to the grid, accurate and efficient prediction of PV power generation is an [...] Read more.
The strong development of distributed energy sources has become one of the most important measures for low-carbon development worldwide. With a significant quantity of photovoltaic (PV) power generation being integrated to the grid, accurate and efficient prediction of PV power generation is an essential guarantee for the security and stability of the electricity grid. Due to the shortage of data from PV stations and the influence of weather, it is difficult to obtain satisfactory performance for accurate PV power prediction. In this regard, we present a PV power forecasting model based on a Fourier graph neural network (FourierGNN). Firstly, the hypervariable graph is constructed by considering the electricity and weather data of neighbouring PV plants as nodes, respectively. The hypervariance graph is then transformed in Fourier space to capture the spatio-temporal dependence among the nodes via the discrete Fourier transform. The multilayer Fourier graph operator (FGO) can be further exploited for spatio-temporal dependence information. Experiments carried out at six photovoltaic plants show that the presented approach enables the optimal performance to be obtained by adequately exploiting the spatio-temporal information. Full article
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