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Keywords = Kolmogorov-Arnold Network

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24 pages, 11916 KB  
Article
Symmetry-Aware Stock Prediction Based on Optimized Multi-Module Collaborative Features with LSTM-CBAM-Time2Vec-KAN
by Huiyong Wu and Xiufeng Hong
Symmetry 2026, 18(7), 1198; https://doi.org/10.3390/sym18071198 (registering DOI) - 16 Jul 2026
Abstract
This study proposes a hybrid deep learning model named LSTM-CBAM-Time2Vec-KAN based on symmetry awareness and optimized multi-module collaborative features, aiming to improve the accuracy and stability of stock price prediction. To address common shortcomings in traditional forecasting models such as insufficient feature extraction, [...] Read more.
This study proposes a hybrid deep learning model named LSTM-CBAM-Time2Vec-KAN based on symmetry awareness and optimized multi-module collaborative features, aiming to improve the accuracy and stability of stock price prediction. To address common shortcomings in traditional forecasting models such as insufficient feature extraction, difficulties in parameter optimization, and inadequate utilization of temporal characteristics, the research innovatively exploits the symmetry inherent in financial time series, particularly their temporal periodicity and cross-dimensional feature consistency, to construct an intelligent prediction framework that integrates multiple modules. First, wavelet transform is applied to perform multi-scale decomposition and signal reconstruction on the raw stock price sequence, effectively extracting high signal-to-noise ratio features. Second, the Northern Goshawk Optimization (NGO) algorithm is employed to jointly optimize key hyperparameters of the model, including the LSTM hidden layer dimension and CBAM compression ratio, thereby resolving the challenge of parameter coupling across modules. Third, the CBAM attention mechanism enhances the importance of temporal features extracted by LSTM through a dual mechanism of channel and spatial attention, enabling the model to focus on critical price movement points. Meanwhile, Time2Vec encoding transforms temporal information into embedding representations with periodic properties, effectively capturing cyclical patterns at daily, weekly, and monthly trading intervals. Finally, the Kolmogorov–Arnold network (KAN) fuses multimodal features and produces precise predictive outputs. Experimental results show that the proposed model significantly outperforms all baseline models in four evaluation metrics, namely mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE), and coefficient of determination (R2), which verifies its superior prediction accuracy and robustness. Furthermore, analyses of stock price forecasting under different time spans and simulated trading performance under various trading strategies further demonstrate that this study provides a feasible and effective technical solution for financial time-series forecasting, with important theoretical research value and practical application value. Full article
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40 pages, 14779 KB  
Article
Wildfire Susceptibility Mapping in China Combining Machine Learning, Deep Learning, and Transformer-Based Models
by Uroš Durlević, Velibor Ilić, Milan M. Radovanović, Ana Milanović Pešić, Marko D. Petrović, Milan Milenković, Jasmina M. Jovanović and Emin Atasoy
Earth 2026, 7(4), 119; https://doi.org/10.3390/earth7040119 - 13 Jul 2026
Viewed by 205
Abstract
Long-term wildfire susceptibility mapping represents a significant component of disaster prevention and the protection of human communities, public health, and local ecosystems. In this study, a wildfire inventory was developed through multi-sensor fusion of satellite data (MODIS and VIIRS), comprising 153,305 fire events [...] Read more.
Long-term wildfire susceptibility mapping represents a significant component of disaster prevention and the protection of human communities, public health, and local ecosystems. In this study, a wildfire inventory was developed through multi-sensor fusion of satellite data (MODIS and VIIRS), comprising 153,305 fire events across China for the period 2001–2024. In addition to historical incidents, 14 predictive variables were processed, representing geomorphological, climatological, hydrological, vegetative, and anthropogenic conditions. This study evaluates long-term spatial wildfire susceptibility based on long-term mean environmental and climatic conditions. Methodologically, the research applies six models from machine learning (ML), deep learning (DL), and transformer-based approaches: Random Forest (RF), Extreme Gradient Boosting (XGBoost), Deep Neural Network (DNN), Fourier Multi-Layer Perceptron (F-MLP), Kolmogorov–Arnold Network (KAN), and Feature Tokenizer (FT) Transformer. The results were integrated into an ensemble susceptibility map with a spatial resolution of 500 m using Geographic Information Systems (GIS), indicating that 7.4% of China’s territory is classified as having a very high wildfire susceptibility. In addition to the national-scale assessment, a local differentiation was conducted across 34 province-level divisions, revealing that Fujian Province (86.8%) and the Guangxi Zhuang Autonomous Region (82.9%) had the largest shares of areas classified as high and very high wildfire susceptibility. Performance evaluation under spatial block-based validation demonstrated that the Random Forest model achieved the highest predictive power, with an area under the curve (AUC) of 87.8%, followed by XGBoost (87.3%) and Fourier MLP (86.6%). Based on the combined SHAP (Shapley additive explanations) analysis of all applied models, soil moisture, elevation, and terrain slope were identified as the most influential factors affecting wildfire occurrence in China. Overall, the findings contribute to more effective wildfire prevention and risk management strategies at both the local and national levels. Full article
(This article belongs to the Special Issue Special Issue Series: Young Investigators in Earth Science)
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31 pages, 15107 KB  
Article
Ultra-Short-Term Wind Power Forecasting Using a Two-Stage Signal Decomposition and iTransformer-LSTM-KAN Hybrid Framework
by Zilin He, Zhiqi Gao, Huan Feng, Jiahua Zhou, Shuran Liu and Yunfeng Gao
Mathematics 2026, 14(14), 2510; https://doi.org/10.3390/math14142510 - 12 Jul 2026
Viewed by 268
Abstract
Accurate ultra-short-term wind power forecasting is of great significance for grid integration scheduling and the secure operation of power systems. However, due to meteorological disturbances and turbine operating states, wind power series generally exhibit non-stationary, multi-scale fluctuations and strong nonlinearity. To improve forecasting [...] Read more.
Accurate ultra-short-term wind power forecasting is of great significance for grid integration scheduling and the secure operation of power systems. However, due to meteorological disturbances and turbine operating states, wind power series generally exhibit non-stationary, multi-scale fluctuations and strong nonlinearity. To improve forecasting accuracy, this paper proposes an ultra-short-term wind power forecasting model based on a two-stage signal decomposition and a hybrid architecture combining iTransformer, LSTM, and KAN. First, a cascaded decomposition module is constructed using the wavelet transform (WT) and ICEEMDAN to attenuate the non-stationarity of the original power series and to extract multi-scale features. An iTransformer branch is then employed to model global dependencies among multiple variables, while an LSTM branch captures temporal dynamics in the historical power series. Subsequently, a cross-attention mechanism is introduced to achieve cross-branch feature fusion, and a KAN output layer is adopted to enhance the model’s representation of the wind speed–power nonlinear mapping. A particle swarm optimization (PSO) algorithm, combined with a cosine annealing strategy, is used to optimize key hyperparameters and improve training stability. Experimental results using SCADA data from a 150 MW wind farm in southern Hunan Province show that the proposed model achieves an MAE of 9.8327 MW, an RMSE of 13.1872 MW, an SMAPE of 18.8474%, and an R2 of 0.7798. These values correspond to the fixed main comparison protocol used for baseline evaluation, while the ablation study reports multi-seed mean and standard deviation results to assess module-level robustness. Compared with LSTM and WT-ICEEMDAN-CNN-LSTM, the proposed model achieves clear improvements in forecasting accuracy and fitting capability. Additional cross-wind-farm validation on a second wind farm shows that WT-ICEEMDAN-iTransformer-LSTM-KAN-PSO (hereafter referred to as ILKP) maintains the best overall performance, achieving an MAE of 27.2193 MW, an RMSE of 36.1862 MW, an SMAPE of 27.8429%, and an R2 of 0.5189, demonstrating transferability and robustness under different operating conditions. Full article
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25 pages, 1714 KB  
Article
Learning Acoustic Biomarkers in Depression Speech Using a Fractional Kolmogorov–Arnold Network
by Junkang Yang, Yuchen Lu and Yuxuan Zhang
Fractal Fract. 2026, 10(7), 469; https://doi.org/10.3390/fractalfract10070469 - 11 Jul 2026
Viewed by 128
Abstract
Speech-based depression detection provides a non-invasive and low-cost approach for supporting mental health screening. However, existing deep models often learn acoustic representations through fixed nonlinear transformations, which limits their ability to characterise gradual, nonlocal, and depression-related time–frequency variations in speech. To address this [...] Read more.
Speech-based depression detection provides a non-invasive and low-cost approach for supporting mental health screening. However, existing deep models often learn acoustic representations through fixed nonlinear transformations, which limits their ability to characterise gradual, nonlocal, and depression-related time–frequency variations in speech. To address this issue, this paper proposes a Fractional Kolmogorov–Arnold Network (FKAN) for learning acoustic biomarkers from mel-spectrograms. The proposed FKAN introduces fractional coordinate encoding to describe non-integer-order temporal–frequency responses, fractional-gated RBF-KAN blocks to learn adaptive edge-wise functional mappings, and a prototype-based classifier to construct a depression-related acoustic state space. In this way, the model not only improves classification performance but also provides functional and geometric evidence for interpreting acoustic biomarkers. Experiments on two public depression speech datasets demonstrate the effectiveness of the proposed method. The FKAN achieves an accuracy of 0.95 and an average F1-score of 0.94 on DAIC-WOZ, and an accuracy of 0.94 and an average F1-score of 0.94 on MODMA. Ablation studies, parameter sensitivity analysis, cross-dataset evaluation, and visualisation results further confirm that the fractional components and prototype-based state representation contribute to both robust depression detection and interpretable acoustic pattern analysis. Full article
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22 pages, 3549 KB  
Article
EvoGame-CAKNet: Integrating Evolutionary Game Theory and Multi-Head Contextual Attention Augmented Kolmogorov Arnold Networks for Accurate Carbon Price Forecasting
by Yufei Xi, Jiangzhang Zhu, Peng Wang and Mingfang He
Mathematics 2026, 14(14), 2487; https://doi.org/10.3390/math14142487 - 10 Jul 2026
Viewed by 109
Abstract
Accurate carbon price for ecasting is crucial for the management of emission trading schemes and the formulation of low-carbon policies. However, existing models face three intertwined challenges: the interdependent multi-agent strategies among market participants, the long-term time dependence of high-dimensional environmental and economic [...] Read more.
Accurate carbon price for ecasting is crucial for the management of emission trading schemes and the formulation of low-carbon policies. However, existing models face three intertwined challenges: the interdependent multi-agent strategies among market participants, the long-term time dependence of high-dimensional environmental and economic covariates, and the severe nonlinearity under the constraint of small samples. This paper proposes the novel hybrid framework EvoGame-CAKNet. Firstly, an evolutionary game theory (EGT) is proposed to simulate the evolution of dynamic strategies of different market participants (enterprises, regulatory agencies, financial institutions), and policy effect signals are embedded as structured prior information. Secondly, a knowledge network (CAKNet) combining multi-head context attention is designed for adaptive long-distance feature aggregation across climate, macroeconomy, and policy dimensions. Finally, a Kolmogorov–Arnold network (KAN) is proposed to replace the traditional multi-layer perceptron decoder, using learnable unary activation functions to achieve better nonlinear fitting under data scarcity conditions. Experiments on four major carbon markets in Beijing, Shanghai, Hubei, and Guangdong from 2014 to 2023 show that EvoGame-CAKNet achieves the most advanced performance, with an average absolute percentage error (MAPE) reduced by 18.3% to 31.6% compared to the best base model. Abandonment studies confirm that each component works collaboratively, with the prior knowledge of EGT having the most significant impact during the regulatory transition period. CAKNet not only provides theoretical progress in multi-agent market modeling but also offers practical decision support for stakeholders in the carbon market. Full article
(This article belongs to the Section C: Mathematical Analysis)
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21 pages, 6772 KB  
Article
A Preliminary Analysis of a Physics-Informed Neural Network for the Forward Problem in EEG
by Athanassios S. Fokas, Alireza Afzal Aghaei and Parham Hashemzadeh
BioMedInformatics 2026, 6(4), 42; https://doi.org/10.3390/biomedinformatics6040042 - 9 Jul 2026
Viewed by 192
Abstract
The distributed inverse source problem in electroencephalography (EEG) requires the determination of a current-independent, geometry-dependent auxiliary function, which is defined by a Poisson partial differential equation (PDE), where its solution is referred to as the forward problem. In this study, we investigate the [...] Read more.
The distributed inverse source problem in electroencephalography (EEG) requires the determination of a current-independent, geometry-dependent auxiliary function, which is defined by a Poisson partial differential equation (PDE), where its solution is referred to as the forward problem. In this study, we investigate the feasibility of employing a mesh-free Physics-Informed Neural Network (PINN) for obtaining this auxiliary function. The proposed architecture integrates Kolmogorov–Arnold Networks (KANs) into an extended PINN (XPINN) framework augmented with Multi-scale Fourier feature mappings to capture potential field discontinuities across piecewise-homogeneous tissue interfaces. The PINN loss functional incorporates the governing PDE, Neumann boundary conditions, flux continuity and reference data for specific neuronal source and electrode configurations. Numerical experiments on a three-layer spherical head model demonstrate that the XPIKAN surrogate achieves a relative L2 error below 1% on unseen sensor coordinates. Factorial sensitivity analyses confirm stable model generalization across varying source-sensor configurations without the need for dense volumetric meshes. As a result, XPIKAN provides a meshless, continuous, and differentiable solution that offers faster inference time compared to classical solvers like finite element or boundary element methods and enables exact gradient computation for inverse source localization. Full article
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49 pages, 1304 KB  
Article
Uncertainty-Aware Continual TinyML Driver Fatigue Detection with Kolmogorov–Arnold Networks at the IoT Edge
by Chaymae Yahyati, Ismail Lamaakal, Yassine Maleh, Khalid El Makkaoui and Ibrahim Ouahbi
Appl. Syst. Innov. 2026, 9(7), 147; https://doi.org/10.3390/asi9070147 - 8 Jul 2026
Viewed by 350
Abstract
Driver fatigue is a major cause of road accidents, and in-cabin monitoring is increasingly embedded into the Internet-of-Things (IoT) ecosystem of modern vehicles. Deploying such monitoring directly on microcontroller-class devices is challenging: models must fit tight memory and compute budgets, provide reliable confidence [...] Read more.
Driver fatigue is a major cause of road accidents, and in-cabin monitoring is increasingly embedded into the Internet-of-Things (IoT) ecosystem of modern vehicles. Deploying such monitoring directly on microcontroller-class devices is challenging: models must fit tight memory and compute budgets, provide reliable confidence estimates, and adapt online to new drivers and conditions. We propose KAN-CLUE, an uncertainty-aware continual TinyML framework for driver fatigue detection from near-infrared periocular images at the IoT edge. KAN-CLUE combines a compact convolutional backbone with a Kolmogorov–Arnold Network (KAN) classification head that outputs Dirichlet-distributed class probabilities and a principled predictive uncertainty measure. A lightweight activation-histogram mechanism provides an additional out-of-distribution (OOD) score, and both signals drive an on-device continual learning scheme that selectively updates a small subset of parameters under a KAN-specific EWC-style regularization. On the ULg DROZY drowsiness database, the quantized KAN-CLUE model uses roughly 167k parameters (about 165 kB in Flash), requires on the order of 106 MACs, and achieves around 3.1 ms latency on a Cortex-M–class microcontroller, while reaching 97.7% test accuracy with improved calibration and OOD detection compared with softmax-based TinyML baselines. Full article
(This article belongs to the Special Issue Deep Visual Recognition for Intelligent Systems and Applications)
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41 pages, 22101 KB  
Article
SPPSFormer: High-Quality Superpoint-Based Transformer for Roof Plane Instance Segmentation from Point Clouds
by Cheng Zeng, Xiatian Qi, Huifan Wang, Kai Sun, Pengcheng Zhong, Qiao Xu, Yan Meng, Yangjie Sun and Yuxuan Liu
Remote Sens. 2026, 18(13), 2144; https://doi.org/10.3390/rs18132144 - 2 Jul 2026
Viewed by 347
Abstract
Superpoint Transformers use superpoints as the basic processing units, thereby significantly reducing the number of tokens processed by Transformers. However, they have been seldom employed in point cloud roof plane instance segmentation, and existing superpoint Transformers suffer from limited performance due to the [...] Read more.
Superpoint Transformers use superpoints as the basic processing units, thereby significantly reducing the number of tokens processed by Transformers. However, they have been seldom employed in point cloud roof plane instance segmentation, and existing superpoint Transformers suffer from limited performance due to the use of low-quality superpoints. To address this challenge, we establish a set of criteria that high-quality superpoints for Transformers should satisfy and introduce a corresponding two-stage superpoint generation process. The superpoints generated by our method not only have accurate boundaries, but also exhibit consistent geometric sizes and shapes, which greatly benefit the feature learning of superpoint Transformers. To compensate for the limitations of deep learning features when the training set size is limited, we incorporate multidimensional handcrafted features into the model. Additionally, we design a decoder that combines a Kolmogorov–Arnold Network with a Transformer module to improve instance prediction and mask extraction. Finally, our network’s predictions are refined using traditional algorithm-based post-processing. For evaluation, we annotated a real-world dataset and corrected annotation errors in the existing RoofN3D dataset. Experimental results show that our method achieves state-of-the-art performance on our dataset, as well as both the original and corrected RoofN3D datasets. Our model also shows significant advantages over existing methods when handling data with low point density, large density variations, or low 3D point precision. Moreover, it is not sensitive to plane boundary annotations during training, significantly reducing the annotation burden. We will release our code, trained models, and datasets. Full article
(This article belongs to the Section Urban Remote Sensing)
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25 pages, 20405 KB  
Article
Deformable Medical Image Registration with KAN-Based Implicit Neural Representations
by Nikita A. Drozdov, Marat O. Zinovev and Dmitry V. Sorokin
Mach. Learn. Knowl. Extr. 2026, 8(7), 184; https://doi.org/10.3390/make8070184 - 1 Jul 2026
Viewed by 208
Abstract
Deformable image registration (DIR) is central to medical image analysis, supporting spatial alignment for longitudinal studies and multi-modal fusion. Learning-based methods such as CNNs and transformers provide rapid inference but often require large training datasets and can underperform classical iterative methods for specific [...] Read more.
Deformable image registration (DIR) is central to medical image analysis, supporting spatial alignment for longitudinal studies and multi-modal fusion. Learning-based methods such as CNNs and transformers provide rapid inference but often require large training datasets and can underperform classical iterative methods for specific anatomies or modalities. Implicit neural representations (INRs) offer a data-efficient alternative by modeling deformation fields as continuous coordinate-to-displacement mappings, yet their per-pair optimization makes runtime efficiency and robustness to initialization essential. We introduce KAN-IDIR and RandKAN-IDIR, the first Kolmogorov–Arnold network (KAN)-based INR framework for pairwise-optimized, resolution-independent DIR, designed to improve seed stability and resource efficiency without requiring a large training dataset. KANs use learnable activation functions that are well suited to continuous, physically structured deformation fields. RandKAN-IDIR further reduces cost through randomized basis sampling, preserving registration quality with fewer basis functions. We evaluate the methods on lung CT, brain MRI, and cardiac MRI datasets against pairwise-optimized neural approaches, dataset-trained deep models, and classical baselines. KAN-IDIR and RandKAN-IDIR provide the strongest overall performance among pairwise-optimized neural registration methods across all three datasets, with low computational overhead and superior stability across random initializations. On ACDC, KAN-IDIR also achieves the highest DSC and best deformation regularity among all compared methods. RandKAN-IDIR slightly outperforms adaptive basis selection variants while avoiding their additional training-time complexity. This makes the approach practical for reproducible clinical research use. Source code is publicly available. Full article
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20 pages, 5640 KB  
Article
A 24 GHz-Optimized Up-Conversion Mixer for Beyond-5G: A Combined ComGAPSO and ImGKAN Approach
by Unal Aras, Tahesin Samira Delwar, Khizra Tariq, Mangal Singh, Sayak Mukhopadhyay, Yangwon Lee and Jee-Youl Ryu
Micromachines 2026, 17(7), 794; https://doi.org/10.3390/mi17070794 - 29 Jun 2026
Viewed by 246
Abstract
An optimal CMOS up-conversion mixer is designed using a novel combination of genetic algorithms and particle swarm optimization (ComGAPSO) and improved-Kolmogorov–Arnold networks (ImGKAN) for 5G communication. The proposed ImGKAN, trained with ComGAPSO, enhances optimization through [...] Read more.
An optimal CMOS up-conversion mixer is designed using a novel combination of genetic algorithms and particle swarm optimization (ComGAPSO) and improved-Kolmogorov–Arnold networks (ImGKAN) for 5G communication. The proposed ImGKAN, trained with ComGAPSO, enhances optimization through social interactions and private cognition through social interactions. The proposed hybrid approach enables accurate parameter determination due to the effective modeling and compensation of nonlinearities in the up-conversion mixer. The proposed optimized mixer incorporates an enhanced linearity boosting technique (LBT) along with a tunable capacitive feedback common-source (TCF-CS) structure. This combination effectively suppresses third-order nonlinear distortion while compensating for parasitic capacitances to improve gain performance and enhance circuit stability. The proposed design achieves a peak conversion gain (CG) of approximately 4.2 dB near 24 GHz. In terms of isolation characteristics, the LO-IF isolation reaches about −44 dB. Additionally, the RF-IF isolation is around −30 dB, ensuring minimal undesired coupling between the input and output paths, while the LO-RF isolation is maintained near −39 dB. The optimized mixer exhibits an output 1 dB compression point (OP1dB) of 5.1 dBm and an input 1 dB compression point (IP1dB) of −1.1 dBm. The RF port shows a return loss of approximately −24 dB near 24 GHz. The LO port exhibits a return loss in the range of −3 to −5 dB, with improved matching observed over the operating band. Meanwhile, the IF port demonstrates strong matching at lower frequencies, with return loss values dropping below −20 dB. Furthermore, the measured optimized design achieves a minimum noise figure (NF) of approximately 3.8 dB at 24 GHz. Full article
(This article belongs to the Special Issue Advances in CMOS Integrated Sensors and Biosensors)
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19 pages, 12243 KB  
Article
Visible Light Positioning for Accurate 3D Indoor Localization
by Arman Nikraftar Khiabani, Nobby Stevens, Tom Dhaene and Ivo Couckuyt
Photonics 2026, 13(7), 613; https://doi.org/10.3390/photonics13070613 - 26 Jun 2026
Viewed by 379
Abstract
Visible light positioning (VLP) based on received signal strength (RSS) offers a low-cost solution for indoor localization, being easily implemented in a warehouse based on existing infrastructure. However, RSS-based VLP remains challenging in 3D and yields subpar performance compared to 2D due to [...] Read more.
Visible light positioning (VLP) based on received signal strength (RSS) offers a low-cost solution for indoor localization, being easily implemented in a warehouse based on existing infrastructure. However, RSS-based VLP remains challenging in 3D and yields subpar performance compared to 2D due to the larger localization space, as well as the presence of dark spots where many LEDs are not bright enough. This limits the practical use cases of RSS-based VLP in industrial applications. We study the performance of RSS-based VLP on a 3D simulated environment by training various machine learning models, including Gaussian processes and Kolmogorov–Arnold networks on different representations of RSS data. Our findings show that the use of Gaussian processes for predicting distances to LEDs coupled with a logarithmic transformation and multilateration leads to both high-accuracy and high-precision predictions under thermal noise (p95 localization error of 10 cm under 50 dB SNR). With this technique, RSS-based VLP reaches levels of accuracy in our simulated 3D environment that are comparable to those reported for 2D applications, supporting the extension of RSS-based VLP to height-varying industrial use cases. Full article
(This article belongs to the Section Data-Science Based Techniques in Photonics)
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29 pages, 3391 KB  
Article
CNN–Transformer–KAN: A Hybrid Deep-Learning Framework with an Inspectable KAN Classification Head for Industrial Process Fault Diagnosis
by Yujie Wu, Maoyu Zhang, Aoxuan Ding, Yu Hua, Zhehao Jin and Yiyang Dai
Information 2026, 17(7), 626; https://doi.org/10.3390/info17070626 - 24 Jun 2026
Viewed by 374
Abstract
Detecting and identifying faults in industrial chemical plants is essential for safe and stable operation, and modern monitoring systems increasingly rely on deep learning to classify faults from multivariate sensor data. A practical obstacle to adoption is trust: most deep-learning diagnosers reach their [...] Read more.
Detecting and identifying faults in industrial chemical plants is essential for safe and stable operation, and modern monitoring systems increasingly rely on deep learning to classify faults from multivariate sensor data. A practical obstacle to adoption is trust: most deep-learning diagnosers reach their decisions through a classification layer that operators cannot inspect, making it hard to see how the model maps process signals to a particular fault. This study targets fault diagnosis on the Tennessee Eastman (TE) process, a standard benchmark of simulated chemical-plant sensor data, and asks whether this final decision stage can be made directly inspectable without sacrificing accuracy. We propose CNN–Transformer–KAN (CTKAN), a hybrid model that learns local temporal patterns with a one-dimensional convolutional encoder, captures global inter-time-step dependencies with a Transformer encoder, and classifies faults with a Kolmogorov–Arnold Network (KAN) head whose learnable B-spline activations can be plotted and examined individually, in place of a conventional multi-layer perceptron (MLP). On the TE benchmark, CTKAN attains a Macro-F1 of 91.38 ± 0.26% over ten independent runs, comparable to a CNN + Transformer + MLP ablation (91.21 ± 0.32%) and a capacity-matched MLP-head variant (91.43 ± 0.37%) within seed-to-seed variability. The main finding is therefore not a higher score: at matched capacity the KAN and MLP heads are statistically indistinguishable in accuracy, so the KAN head’s value is to add a directly inspectable view of the classification stage at no measurable accuracy cost, helping process engineers sanity-check how the diagnoser separates faults in safety-critical settings. Full article
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23 pages, 11196 KB  
Article
An End-to-End Fault Diagnosis Model for Rolling Bearings Based on Multi-Scale Convolution and the Kolmogorov–Arnold Network
by Donghua Yu, Zhenyu Wang, Jia Liu, Huan Liu and Changtian Ying
Sensors 2026, 26(13), 4005; https://doi.org/10.3390/s26134005 - 24 Jun 2026
Viewed by 178
Abstract
Rolling bearings, as core components of rotating machinery, are prone to failure under harsh working conditions, and their fault diagnosis is crucial for the safe operation of industrial systems. Aiming at resolving the problems of weak fault feature representation, poor model generalization ability [...] Read more.
Rolling bearings, as core components of rotating machinery, are prone to failure under harsh working conditions, and their fault diagnosis is crucial for the safe operation of industrial systems. Aiming at resolving the problems of weak fault feature representation, poor model generalization ability and high dependence on manual preprocessing in traditional bearing fault diagnosis methods, an end-to-end fault diagnosis model named KanMSConv is proposed for one-dimensional raw vibration signals. The model abandons complex time–frequency transformation and manual feature engineering, and constructs a multi-scale feature extraction module based on depthwise separable convolution to capture local impulsive components and global modulation characteristics of fault signals simultaneously. The SE channel attention mechanism is integrated to adaptively enhance fault-related critical features and reduce redundant channel responses. Residual connection is introduced to alleviate the gradient degradation problem of deep networks and improve feature reuse capability. On this basis, the Kolmogorov–Arnold Network (KAN) is used to replace the traditional fully connected layer, which enhances the model’s ability to fit complex nonlinear mapping relationships and distinguish fault classification boundaries. Experimental verification is carried out on three representative rolling bearing datasets (CWRU, PU, SDUST) under multi-load, multi-class and cross-platform conditions. The results show that the KanMSConv model achieves 100% accuracy on the CWRU dataset, 99.93% on the PU dataset and 99.80% on the SDUST dataset, which is significantly superior to the existing mainstream fault diagnosis models in terms of Accuracy, Precision, Recall and F1-Score. And the ablation and computational cost analyses further support this conclusion. Full article
(This article belongs to the Section Fault Diagnosis & Sensors)
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30 pages, 15842 KB  
Article
Aircraft Surface Flow-Field Prediction with Variable-Geometry Unification Using a Hybrid KM-GAT Surrogate Network
by Kunze Du, Tianrun Wang, Ji Chen, Bin Liu, Meilian Liu, Haisheng Li and Nan Li
Aerospace 2026, 13(6), 562; https://doi.org/10.3390/aerospace13060562 - 20 Jun 2026
Viewed by 299
Abstract
High-fidelity computational fluid dynamics (CFD) remains computationally expensive for steady aerodynamic prediction under multi-condition and variable-geometry configurations, which limits rapid design iteration. To address this issue, this study proposes a data-driven surrogate framework for aircraft surface flow-field prediction on irregular meshes. The framework [...] Read more.
High-fidelity computational fluid dynamics (CFD) remains computationally expensive for steady aerodynamic prediction under multi-condition and variable-geometry configurations, which limits rapid design iteration. To address this issue, this study proposes a data-driven surrogate framework for aircraft surface flow-field prediction on irregular meshes. The framework combines a geometry-unification strategy for variable rudder-deflection configurations with KM-GAT, a hybrid neural architecture that integrates graph attention and KAN-based nonlinear feature transformation. Geometry unification maps the surface flow fields associated with different rudder-deflection states onto a common zero-deflection reference template, thereby establishing consistent mesh correspondence and fixed prediction locations across samples while retaining the rudder angle as an operating-condition variable. The KM-GAT model further combines topology-aware message passing with localized nonlinear refinement, while the Huber loss is adopted to improve training robustness for CFD-derived data. Experiments on the F-22 research model show that the proposed framework achieves lower prediction errors and more concentrated error distributions than baseline MLP and GNN-based models. Qualitative comparisons further indicate that KM-GAT better preserves localized high-gradient structures, including pressure transitions and vortex-dominated regions. These results suggest that the proposed framework provides an effective surrogate modeling strategy for variable-geometry aerodynamic flow field prediction. Full article
(This article belongs to the Section Aeronautics)
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31 pages, 2435 KB  
Article
DEP-TFDualNet: A Dual-Domain Attention Framework with Temporal–Frequency Fusion for Depression Recognition Using Three-Channel Frontal EEG
by Haijun Lin, Jiayi Liu and Dongxu Jiang
Sensors 2026, 26(12), 3861; https://doi.org/10.3390/s26123861 - 17 Jun 2026
Viewed by 330
Abstract
Early depression screening is important for timely intervention, and electroencephalography (EEG) offers an objective and potentially portable sensing modality for computer-aided assessment. However, recognition from fixed three-channel frontal EEG remains difficult because of limited spatial information and incomplete modeling of temporal–frequency characteristics and [...] Read more.
Early depression screening is important for timely intervention, and electroencephalography (EEG) offers an objective and potentially portable sensing modality for computer-aided assessment. However, recognition from fixed three-channel frontal EEG remains difficult because of limited spatial information and incomplete modeling of temporal–frequency characteristics and temporal dependencies. This study proposes DEP-TFDualNet for acquisition-constrained frontal resting-state EEG. The framework integrates multi-scale convolution, dual-domain channel attention, temporal modeling derived from the independent recurrent neural network (IndRNN) architecture, and decision-stage fusion of deep representations with low-order statistical descriptors through a Kolmogorov–Arnold Network (KAN)-based nonlinear projection layer. Experiments were conducted on the publicly available three-channel frontal EEG subset of the MODMA dataset. After additional quality control, 48 subjects were retained (22 patients with major depressive disorder, 26 healthy controls). Under subject-wise stratified five-fold cross-validation, DEP-TFDualNet achieved 85.42% accuracy, 85.26% macro-F1, 81.82% sensitivity, 88.46% specificity, an AUC of 0.82, and a Brier score of 0.121. It achieved the best threshold-based subject-level performance and the lowest Brier score among the evaluated models. These results provide preliminary evidence that simplified frontal EEG sensing may support depression recognition in acquisition-constrained settings, although larger and external validation is still required. Full article
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