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Keywords = Fourier neural operator

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18 pages, 2511 KB  
Article
Fourier Neural Operator for Turbine Wake Flow Prediction with Out-of-Distribution Generalization
by Shan Ai, Chao Hu and Yong Ma
Mathematics 2026, 14(8), 1275; https://doi.org/10.3390/math14081275 (registering DOI) - 11 Apr 2026
Abstract
Amid the global transition to carbon neutrality, tidal current energy has become a strategic sustainable energy resource due to its high predictability, power density, and environmental compatibility. Horizontal-axis turbines show great potential for marine energy harvesting, yet the large-scale commercialization of tidal turbines [...] Read more.
Amid the global transition to carbon neutrality, tidal current energy has become a strategic sustainable energy resource due to its high predictability, power density, and environmental compatibility. Horizontal-axis turbines show great potential for marine energy harvesting, yet the large-scale commercialization of tidal turbines is severely hindered by complex wake dynamics and the lack of reliable, efficient prediction tools for out-of-distribution (OOD) operating conditions. Traditional high-fidelity CFD methods are computationally prohibitive for engineering optimization, while conventional data-driven surrogate models suffer from poor extrapolation performance, extrapolation collapse near training parameter boundaries, and the absence of uncertainty quantification. To address these bottlenecks, this study focuses on the OOD extrapolation of wake flow prediction across tip speed ratio (TSR) distributions for a single horizontal-axis tidal turbine. A CFD-generated spatiotemporal benchmark dataset is constructed for comparative OOD evaluation across various TSR conditions with 9504 total samples. A novel physics-constrained Fourier neural operator framework named TSR-FNO is proposed to improve OOD generalization. The model integrates TSR–Lipschitz regularization to suppress extrapolation collapse and Monte Carlo Dropout to provide reliable uncertainty estimation. Extensive experiments demonstrate that the proposed method effectively reduces prediction error in unseen TSR regimes, mitigates performance degradation in far-field extrapolation, and produces well-calibrated uncertainty estimates consistent with actual prediction confidence. This work provides a data-driven surrogate modeling strategy for fast and reliable wake prediction on a common CFD-generated benchmark, supporting the efficient design, array layout optimization, and engineering deployment of tidal current energy systems. Full article
15 pages, 2437 KB  
Article
A Hybrid Self-ONN and Vision Mamba Architecture for Robust Radio Interference Recognition in GNSS Applications
by Nursultan Meirambekuly, Margulan Ibraimov, Bakyt Khaniyev, Beibit Karibayev, Alisher Skabylov, Nursultan Uzbekov, Sungat Koishybay, Timur Dautov, Ainur Khaniyeva and Bagdat Kozhakhmetova
Electronics 2026, 15(7), 1498; https://doi.org/10.3390/electronics15071498 - 3 Apr 2026
Viewed by 258
Abstract
Radio-frequency interference (RFI) poses a critical challenge for modern high-precision Global Navigation Satellite System (GNSS) applications, as both intentional and unintentional interference can significantly degrade positioning accuracy and reliability. With increasingly sophisticated interference sources, robust and computationally efficient automatic recognition methods are required [...] Read more.
Radio-frequency interference (RFI) poses a critical challenge for modern high-precision Global Navigation Satellite System (GNSS) applications, as both intentional and unintentional interference can significantly degrade positioning accuracy and reliability. With increasingly sophisticated interference sources, robust and computationally efficient automatic recognition methods are required for next-generation GNSS receivers. Although deep learning approaches show strong potential for interference detection, their high computational cost often limits deployment in resource-constrained navigation hardware. This paper proposes a hybrid deep learning architecture for radio interference recognition in high-precision GNSSs. The framework employs a dual-branch design integrating complementary signal representations. A Self-Organizing Operational Neural Network (Self-ONN) extracts nonlinear temporal features from raw one-dimensional signals, while a Vision Mamba state-space model processes two-dimensional time-frequency spectrograms obtained via Short-Time Fourier Transform (STFT). The fused features enable accurate classification of diverse interference types with high computational efficiency. Experiments on a synthetic dataset demonstrate that the proposed model achieves 99.83% accuracy and F1-score, outperforming ResNet18, VGG16, and Vision Transformer while reducing computational complexity by up to 42% and improving inference speed by up to 35%, supporting its applicability for intelligent interference monitoring in GNSS receivers. Full article
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27 pages, 2697 KB  
Article
Physics-Guided Heterogeneous Dual-Path Adaptive Weighting Network: An Adaptive Framework for Fault Diagnosis of Air Conditioning Systems
by Ziyu Zhao, Caixia Wang, Xiangyu Jiang, Yanjie Zhao and Yongxing Song
Processes 2026, 14(7), 1101; https://doi.org/10.3390/pr14071101 - 29 Mar 2026
Viewed by 260
Abstract
Aiming to address the complex coupling of transient impulses and steady-state components in vibration signals of scroll compressors in air conditioning systems, this study proposes a physically driven heterogeneous dual-path adaptive weighting network (PDW-Net). The approach constructs a physics-inspired weighting module based on [...] Read more.
Aiming to address the complex coupling of transient impulses and steady-state components in vibration signals of scroll compressors in air conditioning systems, this study proposes a physically driven heterogeneous dual-path adaptive weighting network (PDW-Net). The approach constructs a physics-inspired weighting module based on kurtosis and energy criteria, enabling adaptive reconstruction of transient impulses and steady-state vibration components. Feature extraction and decision-level fusion are achieved through a heterogeneous dual-branch network comprising a Fast Fourier Transform (FFT)-based one-dimensional convolutional neural network (1D-CNN) and a Short-Time Fourier Transform (STFT)-based two-dimensional convolutional neural network (2D-CNN). In experimental validation covering four typical fault conditions—condenser failure, refrigerant deficiency, refrigerant overcharge, and main shaft wear—the PDW-Net achieved an average diagnostic accuracy of 97.87% (standard deviation: 2.60%), with 100% accuracy in identifying refrigerant deficiency and normal operating states, demonstrating significant superiority over existing mainstream methods. Ablation studies reveal that the adaptive weighting mechanism contributes most substantially to performance, as its removal results in a 34.24 percentage point drop in accuracy. Replacing the heterogeneous dual-branch structure with a homogeneous counterpart reduces accuracy by 16.18 percentage points, robustly validating the efficacy of the physics-guided and heterogeneous fusion design. Full article
(This article belongs to the Section Process Control and Monitoring)
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26 pages, 12104 KB  
Article
A Dataset Establishment Method for Wind Turbine Wake and a Data-Driven Model of Wake Prediction
by Qinghong Tang, Yuxin Wu, Changhua Li, Peiyao Duan, Jiahao Wu and Junfu Lyu
Energies 2026, 19(5), 1385; https://doi.org/10.3390/en19051385 - 9 Mar 2026
Viewed by 411
Abstract
A cross-construction method is proposed to establish a wind turbine wake dataset with significantly reduced computational fluid dynamics (CFD) costs. This method involves adjusting one operating parameter, such as the tip speed ratio (TSR), while maintaining the others at their optimal values. This [...] Read more.
A cross-construction method is proposed to establish a wind turbine wake dataset with significantly reduced computational fluid dynamics (CFD) costs. This method involves adjusting one operating parameter, such as the tip speed ratio (TSR), while maintaining the others at their optimal values. This procedure is repeated across another parameter (inflow velocity) to generate a sparse but informative dataset. CFD simulations were performed using large eddy simulation (LES) coupled with an actuator line model (ALM) to generate data. A pre-training and fine-tuning network based on error classification (PFNEC) was developed, achieving high prediction accuracy with coefficients of determination of 0.9750 and 0.9851 for two validation conditions. Two models based on a softmax function and a residual block were designed, and they achieved the best performance, with coefficients of determination of 0.9921 and 0.9891 under different conditions. The Fourier embedding was applied to enhance input features of neural networks. Four samples added to the original dataset improved the prediction accuracy for extreme operating conditions, from coefficient of determination values of 0.7143 and 0.7034 to 0.9939 and 0.9886 with Fourier embedding. This cross-construction method can significantly reduce the cost of dataset establishment. The models exhibited reliable generalization and prediction accuracy. Full article
(This article belongs to the Section A3: Wind, Wave and Tidal Energy)
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108 pages, 1969 KB  
Article
Ramanujan–Santos–Sales Hypermodular Operator Theorem and Spectral Kernels for Geometry-Adaptive Neural Operators in Anisotropic Besov Spaces
by Rômulo Damasclin Chaves dos Santos and Jorge Henrique de Oliveira Sales
Axioms 2026, 15(3), 192; https://doi.org/10.3390/axioms15030192 - 6 Mar 2026
Viewed by 332
Abstract
We present Hyperbolic Symmetric Hypermodular Neural Operators (ONHSH), a novel operator learning framework for solving partial differential equations (PDEs) in curved, anisotropic, and modularly structured domains. The architecture integrates three components: hyperbolic-symmetric activation kernels that adapt to non-Euclidean geometries, modular spectral smoothing informed [...] Read more.
We present Hyperbolic Symmetric Hypermodular Neural Operators (ONHSH), a novel operator learning framework for solving partial differential equations (PDEs) in curved, anisotropic, and modularly structured domains. The architecture integrates three components: hyperbolic-symmetric activation kernels that adapt to non-Euclidean geometries, modular spectral smoothing informed by arithmetic regularity, and curvature-sensitive kernels based on anisotropic Besov theory. In its theoretical foundation, the Ramanujan–Santos–Sales Hypermodular Operator Theorem establishes minimax-optimal approximation rates and provides a spectral-topological interpretation through noncommutative Chern characters. These contributions unify harmonic analysis, approximation theory, and arithmetic topology into a single operator learning paradigm. In addition to theoretical advances, ONHSH achieves robust empirical results. Numerical experiments on thermal diffusion problems demonstrate superior accuracy and stability compared to Fourier Neural Operators and Geo-FNO. The method consistently resolves high-frequency modes, preserves geometric fidelity in curved domains, and maintains robust convergence in anisotropic regimes. Error decay rates closely match theoretical minimax predictions, while Voronovskaya-type expansions capture the tradeoffs between bias and spectral variance observed in practice. Notably, ONHSH kernels preserve Lorentz invariance, enabling accurate modeling of relativistic PDE dynamics. Overall, ONHSH combines rigorous theoretical guarantees with practical performance improvements, making it a versatile and geometry-adaptable framework for operator learning. By connecting harmonic analysis, spectral geometry, and machine learning, this work advances both the mathematical foundations and the empirical scope of PDE-based modeling in structured, curved, and arithmetically. Full article
(This article belongs to the Special Issue Fractional Differential Equation and Its Applications)
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18 pages, 1234 KB  
Article
STFF-CANet Diagnosis Model of Aero-Engine Surge Based on Spatio-Temporal Feature Fusion
by Chunyan Hu, Yafeng Shen, Qingwen Zeng, Gang Xu, Jiaxian Sun and Keqiang Miao
Aerospace 2026, 13(3), 212; https://doi.org/10.3390/aerospace13030212 - 27 Feb 2026
Viewed by 241
Abstract
Aero engine surge diagnosis is a key technology in engine health management, and its diagnostic accuracy is of great significance for ensuring operational safety. Traditional threshold-based diagnostic methods are significantly affected by working conditions, which makes it difficult to achieve full working condition [...] Read more.
Aero engine surge diagnosis is a key technology in engine health management, and its diagnostic accuracy is of great significance for ensuring operational safety. Traditional threshold-based diagnostic methods are significantly affected by working conditions, which makes it difficult to achieve full working condition coverage. Moreover, due to issues such as varying feature thresholds across conditions, weak signal characteristics, and low identifiability, the diagnostic accuracy remains limited. To address these challenges, this paper proposes an STFF-CANet (Spatio-Temporal Feature Fusion Cross-Attentional Network) diagnosis model of aero engine surge based on spatio-temporal feature fusion. The model first employs a Convolutional Neural Network (CNN) to extract spatial features from the frequency domain of dynamic signals via Fast Fourier Transform (FFT). Simultaneously, a Bidirectional Long Short-Term Memory (BiLSTM) network is used to capture temporal features from signals optimized by Variational Mode Decomposition (VMD). A cross-attention mechanism is further introduced to achieve deep fusion of spatiotemporal features, thereby enhancing the capability to identify weak fault characteristics. In addition, the sliding window slice method is used to expand the sample size for the small sample fault data of the engine surge of an aero engine. This ensures both informational continuity between slices and statistical stability of features, effectively mitigating the difficulty of diagnosing early and weak surge characteristics under small-sample conditions. Experimental results demonstrate that the model achieves an F1-score, Recall, Precision, and Accuracy of 97.96%, 97.52%, 98.43%, and 99.01%, respectively, in surge fault classification. These outcomes meet the practical requirements for aero engine surge diagnosis and provide an effective solution for early fault warning in complex industrial equipment. Full article
(This article belongs to the Section Aeronautics)
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24 pages, 17028 KB  
Article
Lithology Identification via MSC-Transformer Network with Time-Frequency Feature Fusion
by Shiyi Xu, Sheng Wang, Jun Bai, Kun Lai, Jie Zhang, Qingfeng Wang and Jie Zhang
Appl. Sci. 2026, 16(4), 1949; https://doi.org/10.3390/app16041949 - 15 Feb 2026
Viewed by 369
Abstract
Real-time lithology identification during drilling faces challenges such as indistinct boundaries and difficulties in feature extraction. To address these, this study proposes the MSC-Transformer, a novel model integrating time-frequency features with a deep neural network. A series of drilling experiments were conducted using [...] Read more.
Real-time lithology identification during drilling faces challenges such as indistinct boundaries and difficulties in feature extraction. To address these, this study proposes the MSC-Transformer, a novel model integrating time-frequency features with a deep neural network. A series of drilling experiments were conducted using an intelligent drilling platform, during which triaxial vibration signals were collected from five types of rock specimens: anthracite, granite, bituminous coal, sandstone, and shale. Short-time Fourier Transform (STFT) was applied to generate multi-channel power spectral density (PSD) maps, which were then fused into a three-channel tensor to preserve directional frequency information and used as inputs to the model. The proposed MSC-Transformer combines a multi-scale convolutional (MSC) module with a lightweight Transformer encoder to jointly capture local texture patterns and global dependency features, thereby enabling accurate classification of complex lithologies. Experimental results demonstrate that the model achieves an average accuracy of 98.21 ± 0.49% on the test set, outperforming convolutional neural networks (CNNs), visual geometry group (VGG), residual network (ResNet), and bidirectional long short-term memory (Bi-LSTM) by 5.93 ± 0.90%, 2.54 ± 1.11%, 6.38 ± 2.63%, and 10.56 ± 3.11%, respectively, with statistically significant improvements (p < 0.05). Ablation studies and visualization analyses further validate the effectiveness and interpretability of the model architecture. These findings indicate that lithology recognition based on time-frequency representations of vibration signals is both stable and generalizable, offering technical support for real-time intelligent lithology identification during drilling operations. Full article
(This article belongs to the Section Computing and Artificial Intelligence)
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20 pages, 5587 KB  
Article
Fourier Neural Operators for Fast Multi-Physics Sensor Response Prediction: Applications in Thermal, Acoustic, and Flow Measurement Systems
by Ali Sayghe, Mohammed Mousa, Salem Batiyah and Abdulrahman Husawi
Sensors 2026, 26(4), 1165; https://doi.org/10.3390/s26041165 - 11 Feb 2026
Viewed by 522
Abstract
Accurate and rapid prediction of sensor responses is critical for real-time measurement systems, digital twin implementations, and sensor design optimization. Traditional numerical methods such as Finite Element Method (FEM) and Computational Fluid Dynamics (CFD) provide high-fidelity solutions but suffer from prohibitive computational costs, [...] Read more.
Accurate and rapid prediction of sensor responses is critical for real-time measurement systems, digital twin implementations, and sensor design optimization. Traditional numerical methods such as Finite Element Method (FEM) and Computational Fluid Dynamics (CFD) provide high-fidelity solutions but suffer from prohibitive computational costs, limiting their applicability in time-sensitive applications. This paper presents a novel framework utilizing Fourier Neural Operators (FNO) as surrogate models for fast multi-physics sensor response prediction across thermal, acoustic, and flow measurement domains. Unlike conventional neural networks that learn finite-dimensional mappings, FNO learns operators between infinite-dimensional function spaces by parameterizing the integral kernel in Fourier space, enabling resolution-invariant predictions with remarkable computational efficiency. We demonstrate the framework’s efficacy through three comprehensive case studies: (1) thermal sensor response prediction achieving R2>0.98 with 8300× speedup over FEM, (2) acoustic sensor array modeling with mean absolute error below 0.5 dB and 4000× speedup over BEM, and (3) flow sensor characterization with velocity field prediction accuracy exceeding 97% and 31,000× speedup over CFD. The proposed FNO-based surrogate models are trained on simulation datasets generated from high-fidelity numerical solvers and validated against simulation holdout data for all three case studies, with additional experimental validation conducted for the thermal sensor case. Results indicate that FNO architectures effectively capture the underlying physics governing sensor behavior while reducing inference time from minutes to milliseconds. The framework enables real-time sensor calibration, uncertainty quantification, and design optimization, opening new possibilities for intelligent measurement systems and Industry 4.0 applications. We also investigate the spectral characteristics of FNO predictions, addressing the inherent low-frequency bias through a hybrid architecture combining FNO with local convolutional layers. The primary contributions of this work include: (1) the first systematic application of FNO-based surrogate modeling specifically tailored for sensor response prediction across multiple physics domains, (2) a novel H-FNO architecture that combines spectral operators with local convolutions to mitigate spectral bias in sensor applications, and (3) comprehensive validation including both simulation and experimental data for practical deployment. This work establishes FNO as a powerful tool for accelerating sensor simulation and advancing the field of AI-enhanced instrumentation and measurement. Full article
(This article belongs to the Section Physical Sensors)
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6 pages, 194 KB  
Proceeding Paper
Audio-Based Drone Detection System Using FFT and Machine Learning Models
by Leonardo Vicente Jimenez, Gabriel Sánchez Pérez, José Portillo-Portillo, Linda Karina Toscano Medina, Aldo Hernández Suárez, Jesús Olivares Mercado and Héctor Manuel Pérez Meana
Eng. Proc. 2026, 123(1), 30; https://doi.org/10.3390/engproc2026123030 - 10 Feb 2026
Viewed by 605
Abstract
In recent years, the use of drones, also known as unmanned aerial vehicles (UAVs), has experienced a rapid increase due to their wide availability, compact size, low cost, and ease of operation. These devices have found applications in various areas, facilitating human work [...] Read more.
In recent years, the use of drones, also known as unmanned aerial vehicles (UAVs), has experienced a rapid increase due to their wide availability, compact size, low cost, and ease of operation. These devices have found applications in various areas, facilitating human work by covering large distances and operating in inaccessible or dangerous zones. However, their use has also been associated with malicious activities, such as property damage or threats to public security, which highlights the need to develop efficient and precise UAV detection systems. Although approaches based on neural networks have been proposed, they require large amounts of data for training and more computational resources for operation, which limits their applicability. In this study, we propose an alternative approach based on an analysis of audio features obtained through the fast Fourier transform (FFT) algorithm and classification using machine learning (ML) models. Our approach aims to detect the presence of drones using a minimal number of samples, meeting the requirements of efficiency, accuracy, robustness, low cost, and scalability necessary for a functional detection system. Full article
(This article belongs to the Proceedings of First Summer School on Artificial Intelligence in Cybersecurity)
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19 pages, 3671 KB  
Article
Detecting Rail Surface Contaminants Using a Combined Short-Time Fourier Transform and Convolutional Neural Network Approach
by Gerardo Hurtado-Hurtado, Tania Elizabeth Sandoval-Valencia, Luis Morales-Velázquez and Juan Carlos Jáuregui-Correa
Modelling 2026, 7(1), 35; https://doi.org/10.3390/modelling7010035 - 9 Feb 2026
Viewed by 586
Abstract
Condition monitoring of railway track surfaces is crucial for ensuring the safety, operational efficiency, and effective maintenance of railway systems. This work presents a data-driven modelling and an experimental methodology for identifying and classifying contaminants on railway tracks using vibration analysis and artificial [...] Read more.
Condition monitoring of railway track surfaces is crucial for ensuring the safety, operational efficiency, and effective maintenance of railway systems. This work presents a data-driven modelling and an experimental methodology for identifying and classifying contaminants on railway tracks using vibration analysis and artificial intelligence techniques. In this study, the railway dynamics were physically simulated using a 1:20 scaled test rig, where the rails were treated with various contaminants (oil, water, and sand), and the resulting vehicle vibrations were recorded by on-board accelerometers and gyroscopes. To construct the predictive model, a hybrid architecture was designed integrating Short-Time Fourier Transform (STFT) for time-frequency feature extraction and a multi-channel Convolutional Neural Network (CNN) for pattern recognition. Initial results indicate that accelerometer data, particularly from longitudinal and lateral vibrations, are more effective than gyroscope data for classifying certain contaminants. To enhance classification robustness, this work introduces a multi-channel CNN that simultaneously processes the most informative signals, leading to a significant improvement in detection accuracy across all tested contaminants. This study validates the effectiveness of the proposed methodology as a robust and reliable solution for contaminant detection, while also confirming the utility of the scaled testbed as a valuable platform for future research in railway dynamics. Full article
(This article belongs to the Section Modelling in Artificial Intelligence)
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44 pages, 1721 KB  
Systematic Review
Vibration-Based Predictive Maintenance for Wind Turbines: A PRISMA-Guided Systematic Review on Methods, Applications, and Remaining Useful Life Prediction
by Carlos D. Constantino-Robles, Francisco Alberto Castillo Leonardo, Jessica Hernández Galván, Yoisdel Castillo Alvarez, Luis Angel Iturralde Carrera and Juvenal Rodríguez-Reséndiz
Appl. Mech. 2026, 7(1), 11; https://doi.org/10.3390/applmech7010011 - 26 Jan 2026
Cited by 1 | Viewed by 1550
Abstract
This paper presents a systematic review conducted under the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) framework, analyzing 286 scientific articles focused on vibration-based predictive maintenance strategies for wind turbines within the context of advanced Prognostics and Health Management (PHM). The [...] Read more.
This paper presents a systematic review conducted under the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) framework, analyzing 286 scientific articles focused on vibration-based predictive maintenance strategies for wind turbines within the context of advanced Prognostics and Health Management (PHM). The review combines international standards (ISO 10816, ISO 13373, and IEC 61400) with recent developments in sensing technologies, including piezoelectric accelerometers, microelectromechanical systems (MEMS), and fiber Bragg grating (FBG) sensors. Classical signal processing techniques, such as the Fast Fourier Transform (FFT) and wavelet-based methods, are identified as key preprocessing tools for feature extraction prior to the application of machine-learning-based diagnostic algorithms. Special emphasis is placed on machine learning and deep learning techniques, including Support Vector Machines (SVM), Random Forest (RF), Convolutional Neural Networks (CNN), Long Short-Term Memory networks (LSTM), and autoencoders, as well as on hybrid digital twin architectures that enable accurate Remaining Useful Life (RUL) estimation and support autonomous decision-making processes. The bibliometric and case study analysis covering the period 2020–2025 reveals a strong shift toward multisource data fusion—integrating vibration, acoustic, temperature, and Supervisory Control and Data Acquisition (SCADA) data—and the adoption of cloud-based platforms for real-time monitoring, particularly in offshore wind farms where physical accessibility is constrained. The results indicate that vibration-based predictive maintenance strategies can reduce operation and maintenance costs by more than 20%, extend component service life by up to threefold, and achieve turbine availability levels between 95% and 98%. These outcomes confirm that vibration-driven PHM frameworks represent a fundamental pillar for the development of smart, sustainable, and resilient next-generation wind energy systems. Full article
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22 pages, 4947 KB  
Article
CV-EEGNet: A Compact Complex-Valued Convolutional Network for End-to-End EEG-Based Emotion Recognition
by Wenhao Wang, Dongxia Yang, Yong Yang, Yuanlun Xie, Xiu Liu, Yue Yu and Kaibo Shi
Sensors 2026, 26(3), 807; https://doi.org/10.3390/s26030807 - 26 Jan 2026
Cited by 1 | Viewed by 510
Abstract
In electroencephalogram (EEG)-based emotion recognition tasks, existing end-to-end approaches predominantly rely on real-valued neural networks, which mainly operate in the time–amplitude domain. However, EEG signals are a type of wave, intrinsically including frequency, phase, and amplitude characteristics. Real-valued architectures may struggle to capture [...] Read more.
In electroencephalogram (EEG)-based emotion recognition tasks, existing end-to-end approaches predominantly rely on real-valued neural networks, which mainly operate in the time–amplitude domain. However, EEG signals are a type of wave, intrinsically including frequency, phase, and amplitude characteristics. Real-valued architectures may struggle to capture amplitude–phase coupling and spectral structures that are crucial for emotion decoding. To the best of our knowledge, this work is the first to introduce complex-valued neural networks for EEG-based emotion recognition, upon which we design a new end-to-end architecture named Complex-valued EEGNet (CV-EEGNet). Beginning with raw EEG signals, CV-EEGNet transforms them into complex-valued spectra via the Fast Fourier Transform, then sequentially applies complex-valued spectral, spatial, and depthwise-separable convolution modules to extract frequency structures, spatial topologies, and high-level semantic representations while preserving amplitude–phase relationships. Finally, a complex-valued, fully connected classifier generates complex logits, and the final emotion predictions are derived from their magnitudes. Experiments on the SEED (three-class) and SEED-IV (four-class) datasets validate the effectiveness of the proposed method, with t-SNE visualizations further confirming the discriminability of the learned representations. These results show the potential of complex-valued neural networks for raw-signal EEG emotion recognition. Full article
(This article belongs to the Section Biomedical Sensors)
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33 pages, 18247 KB  
Article
Learning Debris Flow Dynamics with a Deep Learning Fourier Neural Operator: Application to the Rendinara–Morino Area
by Mauricio Secchi, Antonio Pasculli, Massimo Mangifesta and Nicola Sciarra
Geosciences 2026, 16(2), 55; https://doi.org/10.3390/geosciences16020055 - 24 Jan 2026
Viewed by 728
Abstract
Accurate numerical simulation of debris flows is essential for hazard assessment and early-warning design, yet high-fidelity solvers remain computationally expensive, especially when large ensembles must be explored under epistemic uncertainty in rheology, initial conditions, and topography. At the same time, field observations are [...] Read more.
Accurate numerical simulation of debris flows is essential for hazard assessment and early-warning design, yet high-fidelity solvers remain computationally expensive, especially when large ensembles must be explored under epistemic uncertainty in rheology, initial conditions, and topography. At the same time, field observations are typically sparse and heterogeneous, limiting purely data-driven approaches. In this work, we develop a deep-learning Fourier Neural Operator (FNO) as a fast, physics-consistent surrogate for one-dimensional shallow-water debris-flow simulations and demonstrate its application to the Rendinara–Morino system in central Italy. A validated finite-volume solver, equipped with HLLC and Rusanov fluxes, hydrostatic reconstruction, Voellmy-type basal friction, and robust wet–dry treatment, is used to generate a large ensemble of synthetic simulations over longitudinal profiles representative of the study area. The parameter space of bulk density, initial flow thickness, and Voellmy friction coefficients is systematically sampled, and the resulting space–time fields of flow depth and velocity form the training dataset. A two-dimensional FNO in the (x,t) domain is trained to learn the full solution operator, mapping topography, rheological parameters, and initial conditions directly to h(x,t) and u(x,t), thereby acting as a site-specific digital twin of the numerical solver. On a held-out validation set, the surrogate achieves mean relative L2 errors of about 6–7% for flow depth and 10–15% for velocity, and it generalizes to an unseen longitudinal profile with comparable accuracy. We further show that targeted reweighting of the training objective significantly improves the prediction of the velocity field without degrading depth accuracy, reducing the velocity error on the unseen profile by more than a factor of two. Finally, the FNO provides speed-ups of approximately 36× with respect to the reference solver at inference time. These results demonstrate that combining physics-based synthetic data with operator-learning architectures enables the construction of accurate, computationally efficient, and site-adapted surrogates for debris-flow hazard analysis in data-scarce environments. Full article
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22 pages, 2756 KB  
Article
DACL-Net: A Dual-Branch Attention-Based CNN-LSTM Network for DOA Estimation
by Wenjie Xu and Shichao Yi
Sensors 2026, 26(2), 743; https://doi.org/10.3390/s26020743 - 22 Jan 2026
Viewed by 309
Abstract
While deep learning methods are increasingly applied in the field of DOA estimation, existing approaches generally feed the real and imaginary parts of the covariance matrix directly into neural networks without optimizing the input features, which prevents classical attention mechanisms from improving accuracy. [...] Read more.
While deep learning methods are increasingly applied in the field of DOA estimation, existing approaches generally feed the real and imaginary parts of the covariance matrix directly into neural networks without optimizing the input features, which prevents classical attention mechanisms from improving accuracy. This paper proposes a spatio-temporal fusion model named DACL-Net for DOA estimation. The spatial branch applies a two-dimensional Fourier transform (2D-FT) to the covariance matrix, causing angles to appear as peaks in the magnitude spectrum. This operation transforms the original covariance matrix into a dark image with bright spots, enabling the convolutional neural network (CNN) to focus on the bright-spot components via an attention module. Additionally, a spectrum attention mechanism (SAM) is introduced to enhance the extraction of temporal features in the time branch. The model learns simultaneously from two data branches and finally outputs DOA results through a linear layer. Simulation results demonstrate that DACL-Net outperforms existing algorithms in terms of accuracy, achieving an RMSE of 0.04° at an SNR of 0 dB. Full article
(This article belongs to the Section Communications)
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16 pages, 1206 KB  
Article
HASwinNet: A Swin Transformer-Based Denoising Framework with Hybrid Attention for mmWave MIMO Systems
by Xi Han, Houya Tu, Jiaxi Ying, Junqiao Chen and Zhiqiang Xing
Entropy 2026, 28(1), 124; https://doi.org/10.3390/e28010124 - 20 Jan 2026
Viewed by 419
Abstract
Millimeter-wave (mmWave) massive multiple-input, multiple-output (MIMO) systems are a cornerstone technology for integrated sensing and communication (ISAC) in sixth-generation (6G) mobile networks. These systems provide high-capacity backhaul while simultaneously enabling high-resolution environmental sensing. However, accurate channel estimation remains highly challenging due to intrinsic [...] Read more.
Millimeter-wave (mmWave) massive multiple-input, multiple-output (MIMO) systems are a cornerstone technology for integrated sensing and communication (ISAC) in sixth-generation (6G) mobile networks. These systems provide high-capacity backhaul while simultaneously enabling high-resolution environmental sensing. However, accurate channel estimation remains highly challenging due to intrinsic noise sensitivity and clustered sparse multipath structures. These challenges are particularly severe under limited pilot resources and low signal-to-noise ratio (SNR) conditions. To address these difficulties, this paper proposes HASwinNet, a deep learning (DL) framework designed for mmWave channel denoising. The framework integrates a hierarchical Swin Transformer encoder for structured representation learning. It further incorporates two complementary branches. The first branch performs sparse token extraction guided by angular-domain significance. The second branch focuses on angular-domain refinement by applying discrete Fourier transform (DFT), squeeze-and-excitation (SE), and inverse DFT (IDFT) operations. This generates a mask that highlights angularly coherent features. A decoder combines the outputs of both branches with a residual projection from the input to yield refined channel estimates. Additionally, we introduce an angular-domain perceptual loss during training. This enforces spectral consistency and preserves clustered multipath structures. Simulation results based on the Saleh–Valenzuela (S–V) channel model demonstrate that HASwinNet achieves significant improvements in normalized mean squared error (NMSE) and bit error rate (BER). It consistently outperforms convolutional neural network (CNN), long short-term memory (LSTM), and U-Net baselines. Furthermore, experiments with reduced pilot symbols confirm that HASwinNet effectively exploits angular sparsity. The model retains a consistent advantage over baselines even under pilot-limited conditions. These findings validate the scalability of HASwinNet for practical 6G mmWave backhaul applications. They also highlight its potential in ISAC scenarios where accurate channel recovery supports both communication and sensing. Full article
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