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Keywords = kolmogorov-arnold networks

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27 pages, 1488 KiB  
Article
DKWM-XLSTM: A Carbon Trading Price Prediction Model Considering Multiple Influencing Factors
by Yunlong Yu, Xuan Song, Guoxiong Zhou, Lingxi Liu, Meixi Pan and Tianrui Zhao
Entropy 2025, 27(8), 817; https://doi.org/10.3390/e27080817 (registering DOI) - 31 Jul 2025
Abstract
Forestry carbon sinks play a crucial role in mitigating climate change and protecting ecosystems, significantly contributing to the development of carbon trading systems. Remote sensing technology has become increasingly important for monitoring carbon sinks, as it allows for precise measurement of carbon storage [...] Read more.
Forestry carbon sinks play a crucial role in mitigating climate change and protecting ecosystems, significantly contributing to the development of carbon trading systems. Remote sensing technology has become increasingly important for monitoring carbon sinks, as it allows for precise measurement of carbon storage and ecological changes, which are vital for forecasting carbon prices. Carbon prices fluctuate due to the interaction of various factors, exhibiting non-stationary characteristics and inherent uncertainties, making accurate predictions particularly challenging. To address these complexities, this study proposes a method for predicting carbon trading prices influenced by multiple factors. We introduce a Decomposition (DECOMP) module that separates carbon price data and its influencing factors into trend and cyclical components. To manage non-stationarity, we propose the KAN with Multi-Domain Diffusion (KAN-MD) module, which efficiently extracts relevant features. Furthermore, a Wave-MH attention module, based on wavelet transformation, is introduced to minimize interference from uncertainties, thereby enhancing the robustness of the model. Empirical research using data from the Hubei carbon trading market demonstrates that our model achieves superior predictive accuracy and resilience to fluctuations compared to other benchmark methods, with an MSE of 0.204% and an MAE of 0.0277. These results provide reliable support for pricing carbon financial derivatives and managing associated risks. Full article
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20 pages, 3518 KiB  
Article
YOLO-AWK: A Model for Injurious Bird Detection in Complex Farmland Environments
by Xiang Yang, Yongliang Cheng, Minggang Dong and Xiaolan Xie
Symmetry 2025, 17(8), 1210; https://doi.org/10.3390/sym17081210 - 30 Jul 2025
Viewed by 141
Abstract
Injurious birds pose a significant threat to food production and the agricultural economy. To address the challenges posed by their small size, irregular shape, and frequent occlusion in complex farmland environments, this paper proposes YOLO-AWK, an improved bird detection model based on YOLOv11n. [...] Read more.
Injurious birds pose a significant threat to food production and the agricultural economy. To address the challenges posed by their small size, irregular shape, and frequent occlusion in complex farmland environments, this paper proposes YOLO-AWK, an improved bird detection model based on YOLOv11n. Firstly, to improve the ability of the enhanced model to recognize bird targets in complex backgrounds, we introduce the in-scale feature interaction (AIFI) module to replace the original SPPF module. Secondly, to more accurately localize and identify bird targets of different shapes and sizes, we use WIoUv3 as a new loss function. Thirdly, to remove the noise interference and improve the extraction of bird residual features, we introduce the Kolmogorov–Arnold network (KAN) module. Finally, to improve the model’s detection accuracy for small bird targets, we add a small target detection head. The experimental results show that the detection performance of YOLO-AWK on the farmland bird dataset is significantly improved, and the final precision, recall, mAP@0.5, and mAP@0.5:0.95 reach 93.9%, 91.2%, 95.8%, and 75.3%, respectively, which outperforms the original model by 2.7, 2.3, 1.6, and 3.0 percentage points, respectively. These results demonstrate that the proposed method offers a reliable and efficient technical solution for farmland injurious bird monitoring. Full article
(This article belongs to the Special Issue Symmetry and Its Applications in Image Processing)
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9 pages, 1552 KiB  
Proceeding Paper
Kolmogorov–Arnold Networks for System Identification of First- and Second-Order Dynamic Systems
by Lily Chiparova and Vasil Popov
Eng. Proc. 2025, 100(1), 100059; https://doi.org/10.3390/engproc2025100059 - 30 Jul 2025
Viewed by 113
Abstract
System identification—originating in the 1950s from statistical theory—has since developed a wealth of algorithms, insights, and practical expertise. We introduce Kolmogorov–Arnold neural networks (KANs) as an interpretable alternative for model discovery. Leveraging KANs’ inherent property to approximate data and interpret it by employing [...] Read more.
System identification—originating in the 1950s from statistical theory—has since developed a wealth of algorithms, insights, and practical expertise. We introduce Kolmogorov–Arnold neural networks (KANs) as an interpretable alternative for model discovery. Leveraging KANs’ inherent property to approximate data and interpret it by employing learnable activation functions and decomposition of multivariate mappings into univariate transforms, we test its ability to recover the step responses of first- and second-order systems both numerically and symbolically. We employ synthetic datasets, both noise-free and with Gaussian noise, and find that KANs can achieve very low RMSE and parameter error with simple architectures. Our results demonstrate that KANs combine ease of implementation with symbolic transparency, positioning them as a compelling bridge between classical identification and modern machine learning. Full article
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25 pages, 27219 KiB  
Article
KCUNET: Multi-Focus Image Fusion via the Parallel Integration of KAN and Convolutional Layers
by Jing Fang, Ruxian Wang, Xinglin Ning, Ruiqing Wang, Shuyun Teng, Xuran Liu, Zhipeng Zhang, Wenfeng Lu, Shaohai Hu and Jingjing Wang
Entropy 2025, 27(8), 785; https://doi.org/10.3390/e27080785 - 24 Jul 2025
Viewed by 163
Abstract
Multi-focus image fusion (MFIF) is an image-processing method that aims to generate fully focused images by integrating source images from different focal planes. However, the defocus spread effect (DSE) often leads to blurred or jagged focus/defocus boundaries in fused images, which affects the [...] Read more.
Multi-focus image fusion (MFIF) is an image-processing method that aims to generate fully focused images by integrating source images from different focal planes. However, the defocus spread effect (DSE) often leads to blurred or jagged focus/defocus boundaries in fused images, which affects the quality of the image. To address this issue, this paper proposes a novel model that embeds the Kolmogorov–Arnold network with convolutional layers in parallel within the U-Net architecture (KCUNet). This model keeps the spatial dimensions of the feature map constant to maintain high-resolution details while progressively increasing the number of channels to capture multi-level features at the encoding stage. In addition, KCUNet incorporates a content-guided attention mechanism to enhance edge information processing, which is crucial for DSE reduction and edge preservation. The model’s performance is optimized through a hybrid loss function that evaluates in several aspects, including edge alignment, mask prediction, and image quality. Finally, comparative evaluations against 15 state-of-the-art methods demonstrate KCUNet’s superior performance in both qualitative and quantitative analyses. Full article
(This article belongs to the Section Signal and Data Analysis)
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25 pages, 16941 KiB  
Article
KAN-Sense: Keypad Input Recognition via CSI Feature Clustering and KAN-Based Classifier
by Minseok Koo and Jaesung Park
Electronics 2025, 14(15), 2965; https://doi.org/10.3390/electronics14152965 - 24 Jul 2025
Viewed by 254
Abstract
Wi-Fi sensing leverages variations in CSI (channel state information) to infer human activities in a contactless and low-cost manner, with growing applications in smart homes, healthcare, and security. While deep learning has advanced macro-motion sensing tasks, micro-motion sensing such as keypad stroke recognition [...] Read more.
Wi-Fi sensing leverages variations in CSI (channel state information) to infer human activities in a contactless and low-cost manner, with growing applications in smart homes, healthcare, and security. While deep learning has advanced macro-motion sensing tasks, micro-motion sensing such as keypad stroke recognition remains underexplored due to subtle inter-class CSI variations and significant intra-class variance. These challenges make it difficult for existing deep learning models typically relying on fully connected MLPs to accurately recognize keypad inputs. To address the issue, we propose a novel approach that combines a discriminative feature extractor with a Kolmogorov–Arnold Network (KAN)-based classifier. The combined model is trained to reduce intra-class variability by clustering features around class-specific centers. The KAN classifier learns nonlinear spline functions to efficiently delineate the complex decision boundaries between different keypad inputs with fewer parameters. To validate our method, we collect a CSI dataset with low-cost Wi-Fi devices (ESP8266 and Raspberry Pi 4) in a real-world keypad sensing environment. Experimental results verify the effectiveness and practicality of our method for keypad input sensing applications in that it outperforms existing approaches in sensing accuracy while requiring fewer parameters. Full article
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18 pages, 5806 KiB  
Article
Optical Flow Magnification and Cosine Similarity Feature Fusion Network for Micro-Expression Recognition
by Heyou Chang, Jiazheng Yang, Kai Huang, Wei Xu, Jian Zhang and Hao Zheng
Mathematics 2025, 13(15), 2330; https://doi.org/10.3390/math13152330 - 22 Jul 2025
Viewed by 226
Abstract
Recent advances in deep learning have significantly advanced micro-expression recognition, yet most existing methods process the entire facial region holistically, struggling to capture subtle variations in facial action units, which limits recognition performance. To address this challenge, we propose the Optical Flow Magnification [...] Read more.
Recent advances in deep learning have significantly advanced micro-expression recognition, yet most existing methods process the entire facial region holistically, struggling to capture subtle variations in facial action units, which limits recognition performance. To address this challenge, we propose the Optical Flow Magnification and Cosine Similarity Feature Fusion Network (MCNet). MCNet introduces a multi-facial action optical flow estimation module that integrates global motion-amplified optical flow with localized optical flow from the eye and mouth–nose regions, enabling precise capture of facial expression nuances. Additionally, an enhanced MobileNetV3-based feature extraction module, incorporating Kolmogorov–Arnold networks and convolutional attention mechanisms, effectively captures both global and local features from optical flow images. A novel multi-channel feature fusion module leverages cosine similarity between Query and Key token sequences to optimize feature integration. Extensive evaluations on four public datasets—CASME II, SAMM, SMIC-HS, and MMEW—demonstrate MCNet’s superior performance, achieving state-of-the-art results with 92.88% UF1 and 86.30% UAR on the composite dataset, surpassing the best prior method by 1.77% in UF1 and 6.0% in UAR. Full article
(This article belongs to the Special Issue Representation Learning for Computer Vision and Pattern Recognition)
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29 pages, 3930 KiB  
Article
KAN-Based Tool Wear Modeling with Adaptive Complexity and Symbolic Interpretability in CNC Turning Processes
by Zhongyuan Che, Chong Peng, Jikun Wang, Rui Zhang, Chi Wang and Xinyu Sun
Appl. Sci. 2025, 15(14), 8035; https://doi.org/10.3390/app15148035 - 18 Jul 2025
Viewed by 298
Abstract
Tool wear modeling in CNC turning processes is critical for proactive maintenance and process optimization in intelligent manufacturing. However, traditional physics-based models lack adaptability, while machine learning approaches are often limited by poor interpretability. This study develops Kolmogorov–Arnold Networks (KANs) to address the [...] Read more.
Tool wear modeling in CNC turning processes is critical for proactive maintenance and process optimization in intelligent manufacturing. However, traditional physics-based models lack adaptability, while machine learning approaches are often limited by poor interpretability. This study develops Kolmogorov–Arnold Networks (KANs) to address the trade-off between accuracy and interpretability in lathe tool wear modeling. Three KAN variants (KAN-A, KAN-B, and KAN-C) with varying complexities are proposed, using feed rate, depth of cut, and cutting speed as input variables to model flank wear. The proposed KAN-based framework generates interpretable mathematical expressions for tool wear, enabling transparent decision-making. To evaluate the performance of KANs, this research systematically compares prediction errors, topological evolutions, and mathematical interpretations of derived symbolic formulas. For benchmarking purposes, MLP-A, MLP-B, and MLP-C models are developed based on the architectures of their KAN counterparts. A comparative analysis between KAN and MLP frameworks is conducted to assess differences in modeling performance, with particular focus on the impact of network depth, width, and parameter configurations. Theoretical analyses, grounded in the Kolmogorov–Arnold representation theorem and Cybenko’s theorem, explain KANs’ ability to approximate complex functions with fewer nodes. The experimental results demonstrate that KANs exhibit two key advantages: (1) superior accuracy with fewer parameters compared to traditional MLPs, and (2) the ability to generate white-box mathematical expressions. Thus, this work bridges the gap between empirical models and black-box machine learning in manufacturing applications. KANs uniquely combine the adaptability of data-driven methods with the interpretability of physics-based models, offering actionable insights for researchers and practitioners. Full article
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20 pages, 9135 KiB  
Article
Kolmogorov–Arnold Networks for Interpretable Crop Yield Prediction Across the U.S. Corn Belt
by Mustafa Serkan Isik, Ozan Ozturk and Mehmet Furkan Celik
Remote Sens. 2025, 17(14), 2500; https://doi.org/10.3390/rs17142500 - 18 Jul 2025
Viewed by 645
Abstract
Accurate crop yield prediction is essential for stabilizing food supply chains and reducing the uncertainties in financial risks related to agricultural production. Yet, it is even more essential to understand how crop yield models make predictions depending on their relationship to Earth Observation [...] Read more.
Accurate crop yield prediction is essential for stabilizing food supply chains and reducing the uncertainties in financial risks related to agricultural production. Yet, it is even more essential to understand how crop yield models make predictions depending on their relationship to Earth Observation (EO) indicators. This study presents a state-of-the-art explainable artificial intelligence (XAI) method to estimate corn yield prediction over the Corn Belt in the continental United States (CONUS). We utilize the recently introduced Kolmogorov–Arnold Network (KAN) architecture, which offers an interpretable alternative to the traditional Multi-Layer Perceptron (MLP) approach by utilizing learnable spline-based activation functions instead of fixed ones. By including a KAN in our crop yield prediction framework, we are able to achieve high prediction accuracy and identify the temporal drivers behind crop yield variability. We create a multi-source dataset that includes biophysical parameters along the crop phenology, as well as meteorological, topographic, and soil parameters to perform end-of-season and in-season predictions of county-level corn yields between 2016–2023. The performance of the KAN model is compared with the commonly used traditional machine learning (ML) models and its architecture-wise equivalent MLP. The KAN-based crop yield model outperforms the other models, achieving an R2 of 0.85, an RMSE of 0.84 t/ha, and an MAE of 0.62 t/ha (compared to MLP: R2 = 0.81, RMSE = 0.95 t/ha, and MAE = 0.71 t/ha). In addition to end-of-season predictions, the KAN model also proves effective for in-season yield forecasting. Notably, even three months prior to harvest, the KAN model demonstrates strong performance in in-season yield forecasting, achieving an R2 of 0.82, an MAE of 0.74 t/ha, and an RMSE of 0.98 t/ha. These results indicate that the model maintains a high level of explanatory power relative to its final performance. Overall, these findings highlight the potential of the KAN model as a reliable tool for early yield estimation, offering valuable insights for agricultural planning and decision-making. Full article
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24 pages, 890 KiB  
Article
MCTGNet: A Multi-Scale Convolution and Hybrid Attention Network for Robust Motor Imagery EEG Decoding
by Huangtao Zhan, Xinhui Li, Xun Song, Zhao Lv and Ping Li
Bioengineering 2025, 12(7), 775; https://doi.org/10.3390/bioengineering12070775 - 17 Jul 2025
Viewed by 345
Abstract
Motor imagery (MI) EEG decoding is a key application in brain–computer interface (BCI) research. In cross-session scenarios, the generalization and robustness of decoding models are particularly challenging due to the complex nonlinear dynamics of MI-EEG signals in both temporal and frequency domains, as [...] Read more.
Motor imagery (MI) EEG decoding is a key application in brain–computer interface (BCI) research. In cross-session scenarios, the generalization and robustness of decoding models are particularly challenging due to the complex nonlinear dynamics of MI-EEG signals in both temporal and frequency domains, as well as distributional shifts across different recording sessions. While multi-scale feature extraction is a promising approach for generalized and robust MI decoding, conventional classifiers (e.g., multilayer perceptrons) struggle to perform accurate classification when confronted with high-order, nonstationary feature distributions, which have become a major bottleneck for improving decoding performance. To address this issue, we propose an end-to-end decoding framework, MCTGNet, whose core idea is to formulate the classification process as a high-order function approximation task that jointly models both task labels and feature structures. By introducing a group rational Kolmogorov–Arnold Network (GR-KAN), the system enhances generalization and robustness under cross-session conditions. Experiments on the BCI Competition IV 2a and 2b datasets demonstrate that MCTGNet achieves average classification accuracies of 88.93% and 91.42%, respectively, outperforming state-of-the-art methods by 3.32% and 1.83%. Full article
(This article belongs to the Special Issue Brain Computer Interfaces for Motor Control and Motor Learning)
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20 pages, 8094 KiB  
Article
Deep Learning-Based Method for Operation Dispatch Strategy Generation of Virtual Power Plants
by Jie Li, Wenteng Liang, Yuheng Liu, Nan Zhou, Tao Qian and Qinran Hu
Processes 2025, 13(7), 2213; https://doi.org/10.3390/pr13072213 - 10 Jul 2025
Viewed by 305
Abstract
Centralized and distributed optimization methods used by traditional virtual power plants (VPPs) in power system dispatching face issues such as high computational complexity, difficulties in privacy protection, and slow iterative convergence. There is an urgent need to propose an accurate and efficient acceleration [...] Read more.
Centralized and distributed optimization methods used by traditional virtual power plants (VPPs) in power system dispatching face issues such as high computational complexity, difficulties in privacy protection, and slow iterative convergence. There is an urgent need to propose an accurate and efficient acceleration method for generating VPP operational dispatching strategies. This paper proposes a deep learning-based acceleration method for generating VPP operational dispatching strategies. By using the equivalent projection method to solve the operation feasible region of the VPP, the objective function and constraints of the VPP are transformed into constraints of coordination variables and submitted to the system dispatching center for optimization, thereby avoiding the slow convergence problem of iterative computation methods. The Kolmogorov–Arnold Network (KAN) is employed to predict the batch operation feasible regions of the VPP, addressing the inefficiency of individually calculating feasible regions. Tests on a 13,659-node system show that the proposed method reduces solution time by 64.40% while increasing the objective function value by only 4.74%, verifying its accuracy and speed. Full article
(This article belongs to the Section Energy Systems)
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28 pages, 2047 KiB  
Article
Multimodal-Based Non-Contact High Intraocular Pressure Detection Method
by Zibo Lan, Ying Hu, Shuang Yang, Jiayun Ren and He Zhang
Sensors 2025, 25(14), 4258; https://doi.org/10.3390/s25144258 - 8 Jul 2025
Viewed by 334
Abstract
This study proposes a deep learning-based, non-contact method for detecting elevated intraocular pressure (IOP) by integrating Scheimpflug images with corneal biomechanical features. Glaucoma, the leading cause of irreversible blindness worldwide, requires accurate IOP monitoring for early diagnosis and effective treatment. Traditional IOP measurements [...] Read more.
This study proposes a deep learning-based, non-contact method for detecting elevated intraocular pressure (IOP) by integrating Scheimpflug images with corneal biomechanical features. Glaucoma, the leading cause of irreversible blindness worldwide, requires accurate IOP monitoring for early diagnosis and effective treatment. Traditional IOP measurements are often influenced by corneal biomechanical variability, leading to inaccurate readings. To address these limitations, we present a multi-modal framework incorporating CycleGAN for data augmentation, Swin Transformer for visual feature extraction, and the Kolmogorov–Arnold Network (KAN) for efficient fusion of heterogeneous data. KAN approximates complex nonlinear relationships with fewer parameters, making it effective in small-sample scenarios with intricate variable dependencies. A diverse dataset was constructed and augmented to alleviate data scarcity and class imbalance. By combining Scheimpflug imaging with clinical parameters, the model effectively integrates multi-source information to improve high IOP prediction accuracy. Experiments on a real-world private hospital dataset show that the model achieves a diagnostic accuracy of 0.91, outperforming traditional approaches. Grad-CAM visualizations identify critical anatomical regions, such as corneal thickness and anterior chamber depth, that correlate with IOP changes. These findings underscore the role of corneal structure in IOP regulation and suggest new directions for non-invasive, biomechanics-informed IOP screening. Full article
(This article belongs to the Collection Medical Image Classification)
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20 pages, 2200 KiB  
Article
Well Production Forecasting in Volve Field Using Kolmogorov–Arnold Networks
by Xingyu Lu, Jing Cao and Jian Zou
Energies 2025, 18(13), 3584; https://doi.org/10.3390/en18133584 - 7 Jul 2025
Viewed by 304
Abstract
Accurate oil production forecasting is essential for optimizing field development and supporting efficient decision-making. However, traditional methods often struggle to capture the complex dynamics of reservoirs, and existing machine learning models rely on large parameter sets, resulting in high computational costs and limited [...] Read more.
Accurate oil production forecasting is essential for optimizing field development and supporting efficient decision-making. However, traditional methods often struggle to capture the complex dynamics of reservoirs, and existing machine learning models rely on large parameter sets, resulting in high computational costs and limited scalability. To address these limitations, we propose the Kolmogorov–Arnold Network (KAN) for oil production forecasting, which replaces traditional weights with spline-based learnable activation functions to enhance nonlinear modeling capabilities without large-scale parameter expansion. This design reduces training costs and enables adaptive scaling. The KAN model was applied to forecast oil production from wells 15/9-F-11 and 15/9-F-14 in the Volve field, Norway. The experimental results demonstrate that, compared to the best-performing baseline model, the KAN reduces the Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) by 78.5% and 89.5% for well 15/9-F-11 and by 80.1% and 91.8% for well 15/9-F-14, respectively. These findings suggest that the KAN is a robust and efficient multivariate forecasting method capable of capturing complex dependencies in oil production data, with strong potential for practical applications in reservoir management and production optimization. Full article
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22 pages, 1291 KiB  
Article
Kolmogorov-Arnold Networks for Interpretable Analysis of Water Quality Time-Series Data
by Ignacio Sánchez-Gendriz, Ivanovitch Silva and Luiz Affonso Guedes
J 2025, 8(3), 24; https://doi.org/10.3390/j8030024 - 6 Jul 2025
Viewed by 245
Abstract
Kolmogorov–Arnold networks (KANs) represent a promising modeling framework for applications requiring interpretability. In this study, we investigate the use of KANs to analyze time series of water quality parameters obtained from a publicly available dataset related to an aquaponic environment. Two water quality [...] Read more.
Kolmogorov–Arnold networks (KANs) represent a promising modeling framework for applications requiring interpretability. In this study, we investigate the use of KANs to analyze time series of water quality parameters obtained from a publicly available dataset related to an aquaponic environment. Two water quality indices (WQIs) were computed—a linear case based on the weighted average WQI, and a non-linear case using the weighted quadratic mean (WQM) WQI, both derived from three water parameters: pH, total dissolved solids (TDS), and temperature. For each case, KAN models were trained to predict the respective WQI, yielding explicit algebraic expressions with low prediction errors and clear input–output mathematical relationships. Model performance was evaluated using standard regression metrics, with R2 values exceeding 0.96 on the hold-out test set across all cases. Specifically for the non-linear WQM case, we trained 15 classical regressors using the LazyPredict Python library. The top three models were selected based on validation performance. They were then compared against the KAN model and its symbolic expressions using a 5-fold cross-validation protocol on a temporally shifted test set (approximately one month after the training period), without retraining. Results show that KAN slightly outperforms the best tested baseline regressor (multilayer perceptron, MLP), with average R2 scores of 0.998±0.001 and 0.996±0.001, respectively. These findings highlight the potential of KAN in terms of predictive performance, comparable to well-established algorithms. Moreover, the ability of KAN to extract data-driven, interpretable, and lightweight symbolic models makes it a valuable tool for applications where accuracy, transparency, and model simplification are critical. Full article
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33 pages, 2533 KiB  
Article
VBTCKN: A Time Series Forecasting Model Based on Variational Mode Decomposition with Two-Channel Cross-Attention Network
by Zhiguo Xiao, Changgen Li, Huihui Hao, Siwen Liang, Qi Shen and Dongni Li
Symmetry 2025, 17(7), 1063; https://doi.org/10.3390/sym17071063 - 4 Jul 2025
Viewed by 409
Abstract
Time series forecasting serves a critical function in domains such as energy, meteorology, and power systems by leveraging historical data to predict future trends. However, existing methods often prioritize long-term dependencies while neglecting the integration of local features and global patterns, resulting in [...] Read more.
Time series forecasting serves a critical function in domains such as energy, meteorology, and power systems by leveraging historical data to predict future trends. However, existing methods often prioritize long-term dependencies while neglecting the integration of local features and global patterns, resulting in limited accuracy for short-term predictions of non-stationary multivariate sequences. To address these challenges, this paper proposes a time series forecasting model named VBTCKN based on variational mode decomposition and a dual-channel cross-attention network. First, the model employs variational mode decomposition (VMD) to decompose the time series into multiple frequency-complementary modal components, thereby reducing sequence volatility. Subsequently, the BiLSTM channel extracts temporal dependencies between sequences, while the transformer channel captures dynamic correlations between local features and global patterns. The cross-attention mechanism dynamically fuses features from both channels, enhancing complementary information integration. Finally, prediction results are generated through Kolmogorov–Arnold networks (KAN). Experiments conducted on four public datasets demonstrated that VBTCKN outperformed other state-of-the-art methods in both accuracy and robustness. Compared with BiLSTM, VBTCKN reduced RMSE by 63.32%, 68.31%, 57.98%, and 90.76%, respectively. Full article
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16 pages, 2895 KiB  
Article
Flat vs. Curved: Machine Learning Classification of Flexible PV Panel Geometries
by Ahmad Manasrah, Yousef Jaradat, Mohammad Masoud, Mohammad Alia, Khaled Suwais and Piero Bevilacqua
Energies 2025, 18(13), 3529; https://doi.org/10.3390/en18133529 - 4 Jul 2025
Viewed by 323
Abstract
As the global demand for clean and sustainable energy grows, photovoltaics (PVs) have become an important technology in this industry. Thin-film and flexible PV modules offer noticeable advantages for irregular surface mounts and mobile applications. This study investigates the use of four machine [...] Read more.
As the global demand for clean and sustainable energy grows, photovoltaics (PVs) have become an important technology in this industry. Thin-film and flexible PV modules offer noticeable advantages for irregular surface mounts and mobile applications. This study investigates the use of four machine learning models to detect different flexible PV module geometries based on power output data. Three identical flexible PV modules were mounted in flat, concave, and convex configurations and connected to batteries via solar chargers. The experimental results showed that all geometries fully charged their batteries within 6–7 h on a sunny day with the flat, concave-, and convex-shaped modules achieving a peak power of 95 W. On a cloudy day, the concave and convex modules recorded peak outputs of 72 W and 65 W, respectively. Simulation results showed that the XGBoost model delivered the best classification performance, showing 93% precision with the flat-mounted module and 98% recall across all geometries. In comparison, the KAN model recorded the lowest precision (78%) with the curved geometries. A calibration analysis on the ML models showed that Random Forest and XGBoost were well calibrated for the flat-mounted module. However, they also showed overconfidence and underconfidence issues with the curved module geometries. Full article
(This article belongs to the Section A2: Solar Energy and Photovoltaic Systems)
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