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22 pages, 5221 KB  
Article
Hybrid Deep Neural Network with Natural Language Processing Techniques to Analyze Customer Satisfaction with Delivery Platform Manager Responses
by Salihah Alotaibi
Appl. Sci. 2026, 16(9), 4359; https://doi.org/10.3390/app16094359 - 29 Apr 2026
Abstract
Delivery services have drawn much attention and become of topmost significance in urban areas by presenting online food delivery selections for a diversity of dishes from a wide range of restaurants, decreasing both travel and waiting times. Customer data analysis acts as a [...] Read more.
Delivery services have drawn much attention and become of topmost significance in urban areas by presenting online food delivery selections for a diversity of dishes from a wide range of restaurants, decreasing both travel and waiting times. Customer data analysis acts as a cornerstone in corporate strategy, allowing enterprises to gather and interpret user feedback and helping them to make informed decisions that drive future business development. However, major knowledge gaps remain due to the scarcity of literature review studies on these delivery services, hindering a complete understanding of customer satisfaction in this sector. Furthermore, there has been little systematic research on managerial response tactics to online consumer complaints and negative reviews. Researchers have contributed by applying artificial intelligence, including deep learning and machine learning models, to analyze customer sentiment and understand customer brand perceptions. This study presents a Hybrid Deep Neural Network Model for Customer Satisfaction Analysis (HDNNM-CSA), with the aim of developing an efficient model which is capable of accurately classifying customer satisfaction levels in delivery apps based on textual responses provided by customer experience managers. To achieve this, the model initially pre-processes text data using text cleaning, emoji removal, normalization, tokenization, stop word removal, and stemming to clean and standardize the unstructured text data for further analysis. Following this, term frequency–inverse document frequency-based word embedding is utilized to transform the pre-processed text into meaningful feature representations. Lastly, an ensemble architecture involving bidirectional long short-term memory, temporal convolutional, and graph convolutional networks is deployed to classify customer satisfaction levels with managers’ responses. A series of experimental analyses are performed, and the results are examined for numerous features. A comparative analysis demonstrates the enhanced performance of the HDNNM-CSA technique with respect to existing approaches. Full article
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23 pages, 1944 KB  
Article
Intelligent Localization of Cross-Sectional Structural Damage in Molten Salt Receiver Tubes Using Mel Spectrograms and TSA-Optimized 2D-CNN
by Peiran Leng, Man Liang, Weihong Sun, Tiefeng Shao, Luowei Cao and Sunting Yan
Sensors 2026, 26(9), 2780; https://doi.org/10.3390/s26092780 - 29 Apr 2026
Abstract
In this paper, an intelligent localization framework based on deep learning is proposed to address the limitations of insufficient accuracy and robustness in defect identification and localization during the ultrasonic guided-wave non-destructive testing (NDT) of receiver tubes in tower-type molten salt Concentrated Solar [...] Read more.
In this paper, an intelligent localization framework based on deep learning is proposed to address the limitations of insufficient accuracy and robustness in defect identification and localization during the ultrasonic guided-wave non-destructive testing (NDT) of receiver tubes in tower-type molten salt Concentrated Solar Power (CSP) stations. In the proposed method, a 1D convolutional neural network (1D-CNN) initially processes raw time-series-guided wave signals, achieving coarse identification and preliminary localization of defective segments. Then, Mel spectrograms are employed to exploit multi-dimensional features in the time–frequency domain and transform 1D signals into 2D representations, thereby enriching feature diversity. A regression-based 2D-CNN was designed to predict the start and end points of defect segments, enabling precise interval localization. Furthermore, the Tree Seed Algorithm (TSA) was integrated to jointly optimize key hyperparameters, enhancing training efficiency and prediction accuracy. Experimental validation on a dataset of ultrasonic guided-wave signals from molten salt receiver tubes demonstrates that the TSA-optimized Mel+2D-CNN model achieves superior performance, with a Mean Absolute Error (MAE) of 75.11 sampling points and a Coefficient of Determination (R2) of 0.90. At an Intersection over Union (IoU) threshold of 0.3, the model achieves a hit rate of 89.21%, exhibiting significantly higher localization accuracy and stability compared to the 1D-CNN baseline model. These findings indicate that the proposed method effectively enhances the accuracy and robustness of guided wave-based defect localization in slender structures. While promising, the model’s generalization capability remains dependent on the data distribution and operating conditions; future work will focus on validating its engineering applicability across diverse, multi-scenario industrial environments. Full article
(This article belongs to the Special Issue Ultrasonic Sensors and Ultrasonic Signal Processing)
37 pages, 13630 KB  
Article
Data-Driven Probabilistic Forecasting of Voltage Quality in Distribution Transformers Using Gaussian Processes
by Efraín Mondragón-García, Ángel Marroquín de Jesús, Raúl García-García, Yuri Salazar-Flores, Adán Díaz-Hernández and Emmanuel Vallejo-Castañeda
Energies 2026, 19(9), 2133; https://doi.org/10.3390/en19092133 - 29 Apr 2026
Abstract
A probabilistic data-driven framework for voltage quality forecasting in distribution transformers based on Gaussian process regression and high-resolution field measurements is presented. Voltage time series acquired under real operating conditions were modeled using composite covariance functions designed to capture long-term trends and stochastic [...] Read more.
A probabilistic data-driven framework for voltage quality forecasting in distribution transformers based on Gaussian process regression and high-resolution field measurements is presented. Voltage time series acquired under real operating conditions were modeled using composite covariance functions designed to capture long-term trends and stochastic multi-scale fluctuations. The proposed approach enables simultaneous prediction and uncertainty quantification, allowing direct compliance assessment with voltage quality standards. The additive Gaussian process models achieved coefficients of determination above 0.75 and produced statistically uncorrelated residuals, indicating an adequate representation of the intrinsic temporal structure. However, the predictive intervals exhibit a certain level of undercoverage, indicating that, while uncertainty is effectively quantified, there is still room for improvement in calibration. The selected kernel structures revealed distinct physical regimes in the voltage dynamics, including smooth steady operation, moderately irregular behavior associated with localized disturbances, and multi-scale stochastic variability. For benchmarking purposes, results were compared with those obtained from a stochastic damped harmonic oscillator with restoring force, a naive model, a seasonal naive model and an Autoregressive Integrated Moving Average model. The oscillator model, the naive model, the seasonal naive model, and the Autoregressive Integrated Moving Average model generated strongly autocorrelated residuals, whereas the Gaussian process models yielded consistent white-noise residuals that outperformed all the other models. These findings demonstrate that probabilistic Gaussian process modeling provides an interpretable, scalable, and uncertainty-aware alternative for predictive voltage quality assessment in modern distribution systems. Full article
(This article belongs to the Section F1: Electrical Power System)
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23 pages, 3967 KB  
Article
PULSE-KAN: Price-Aware Unified Linear-Attention and Smoothed-Trend Encoder with Kolmogorov–Arnold Network Head for Stock Movement Prediction
by Xingwang Zhang and Jiabo Li
Mathematics 2026, 14(9), 1494; https://doi.org/10.3390/math14091494 - 29 Apr 2026
Abstract
Accurate prediction of binary stock price movements remains a challenging task due to the coexistence of short-term noise and medium-term trend dynamics in financial time series. Existing recurrent models typically encode raw price sequences within a single representation stream and aggregate temporal information [...] Read more.
Accurate prediction of binary stock price movements remains a challenging task due to the coexistence of short-term noise and medium-term trend dynamics in financial time series. Existing recurrent models typically encode raw price sequences within a single representation stream and aggregate temporal information using softmax-based attention, which often entangles noisy fluctuations with underlying trends and limits nonlinear expressiveness in the final classification stage. In this paper, we propose PULSE-KAN (Price-aware Unified Linear-attention and Smoothed-trend Encoder with Kolmogorov–Arnold Network Head), a modular neural architecture designed to enhance binary stock movement prediction. The proposed framework introduces three plug-and-play components designed for LSTM-based pipelines as demonstrated here within the Adv-ALSTM framework. First, the P-EMA Trend Bridge constructs an explicit smoothed trend representation via a parameterized exponential moving average and fuses it with the raw price stream to improve trend awareness. Second, the Pola Pulse Router performs efficient temporal aggregation using linear-complexity polarized attention combined with local convolutional priors, enabling better capture of multi-scale temporal dependencies. Third, the KAN Signal Refiner replaces the conventional linear prediction head with learnable Chebyshev-polynomial activations, providing enhanced nonlinear modeling capacity for decision boundaries. Extensive experiments on two public benchmark datasets demonstrate that PULSE-KAN consistently outperforms strong recurrent and attention-based baselines in terms of both classification accuracy and the Matthews Correlation Coefficient. Further ablation studies verify that each proposed component contributes independently and significantly to the overall performance improvement. Full article
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22 pages, 16582 KB  
Article
Temporal Convolutional Network–Transformer Hybrid Architecture with Hippo Optimization for Lithium Battery SOC Estimation
by Long Wu, Yang Wang and Likun Xing
World Electr. Veh. J. 2026, 17(5), 236; https://doi.org/10.3390/wevj17050236 - 29 Apr 2026
Abstract
As an important state parameter in battery management systems, accurate state of charge (SOC) estimation is of great significance for the safe and reliable use of batteries. In this paper, a Temporal Convolutional Network–Transformer (TCN–Transformer) model is proposed for achieving accurate estimation of [...] Read more.
As an important state parameter in battery management systems, accurate state of charge (SOC) estimation is of great significance for the safe and reliable use of batteries. In this paper, a Temporal Convolutional Network–Transformer (TCN–Transformer) model is proposed for achieving accurate estimation of SOC. First, the TCN is integrated in series with the Transformer model. This integration not only extracts the local characteristics of time-series data but also captures broader spatiotemporal correlations, thereby enhancing the feature representation and achieving highly accurate estimation. However, since the hyperparameter settings of neural networks have a significant impact on model performance, this study employs the advanced hippo optimization (HO) algorithm to determine the optimal values for the number of filters, filter size, number of residual blocks, and number of encoder layers, ultimately improving the model’s stability and efficiency. Finally, the proposed model was tested under various dynamic driving conditions at different temperatures. Experimental validation on the CALCE dataset demonstrates that the proposed HO–TCN–Transformer achieves RMSE and MAE both under 0.7%, representing an approximately 50% overall error reduction compared to the standalone TCN. Cross-validation across five folds confirms robust performance with <7% standard deviation. Full article
(This article belongs to the Section Storage Systems)
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25 pages, 3306 KB  
Article
Unsupervised Driving Behavior Primitive Inference via Hierarchical Segmentation and Context-Aware Clustering
by Lu Zhang, Tao Li, Xuelian Zheng, Wenyu Kang and Yuhan Fu
Sensors 2026, 26(9), 2744; https://doi.org/10.3390/s26092744 - 29 Apr 2026
Abstract
Driving behavior primitives serve as fundamental building blocks for modeling and semantically interpreting time-series driving behavior. Extracting behavior primitives is challenging due to the high dimensionality and complex interdependencies among behavioral variables, as well as the rich temporal dynamics of real-world driving maneuvers. [...] Read more.
Driving behavior primitives serve as fundamental building blocks for modeling and semantically interpreting time-series driving behavior. Extracting behavior primitives is challenging due to the high dimensionality and complex interdependencies among behavioral variables, as well as the rich temporal dynamics of real-world driving maneuvers. This paper proposes an unsupervised two-stage framework that optimizes time-series segmentation and segment clustering to yield interpretable and context-aware behavior primitives. First, a Hierarchical Bayesian Model-based Agglomerative Sequence Segmentation (H-BMASS) method is introduced that decouples longitudinal and lateral driving behaviors and performs hierarchical segmentation. This design mitigates under-segmentation by ensuring that change points reflect genuine behavioral transitions. Second, to cluster driving segments of varying durations into a finite set of primitive types, an Integrating Numerical and Trend Discretization Latent Dirichlet Allocation (INT-LDA) model is developed. The model combines variables’ temporal trend discretization with numerical discretization to create symbolic representations of driving data, thereby preserving the essential time dependency of driving behavior and improving segment clustering accuracy. Evaluated on naturalistic driving data collected from a high-fidelity simulator, the proposed framework identifies five distinct behavior primitives with clear physical interpretations. The resulting primitives provide a compact, semantically rich representation of driving behavior, facilitating driver modeling, decision prediction, and scenario-based testing for autonomous vehicles. Full article
(This article belongs to the Section Vehicular Sensing)
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21 pages, 548 KB  
Article
Sheffer-Type General-λ-Matrix Polynomials and Their Structural Properties
by Ghazala Yasmin, Aditi Sharma, Georgia Irina Oros and Shahid Ahmad Wani
Symmetry 2026, 18(5), 760; https://doi.org/10.3390/sym18050760 - 28 Apr 2026
Abstract
In this paper, a new class of special polynomials, called the Sheffer-type general-λ-matrix polynomials, is introduced within the framework of the monomiality principle. This family is obtained by combining the structure of Sheffer sequences with the theory of general-λ matrix [...] Read more.
In this paper, a new class of special polynomials, called the Sheffer-type general-λ-matrix polynomials, is introduced within the framework of the monomiality principle. This family is obtained by combining the structure of Sheffer sequences with the theory of general-λ matrix polynomials, which leads to a unified formulation encompassing several polynomial families. Fundamental properties of the proposed polynomials are established, including their generating function, explicit series representation, summation formulas, quasi-monomial structure, differential relations, and determinant representation. The proposed framework addresses an important problem in the theory of special functions: the systematic construction of matrix-valued polynomial families that simultaneously generalize both classical scalar polynomials and existing matrix polynomial hierarchies. Such a unified structure is of broad significance, with applications in quantum mechanics (wave function expansions), mathematical physics (matrix differential equations and spectral problems), approximation theory, and the study of special functions in the matrix domain. Several hybrid forms of the proposed family are derived through appropriate choices of the defining functions, which yield polynomial subclasses related to classical families such as Hermite, Laguerre, Bessel, and Poisson–Charlier polynomials. These subclasses illustrate how the proposed framework provides a systematic approach for constructing and studying generalized polynomial structures. In each case, the matrix parameter L introduces a new layer of structural richness not present in the scalar setting, enabling the modelling of phenomena governed by matrix-valued spectral data. Furthermore, a numerical and graphical investigation of selected hybrid forms is carried out using Mathematica(version 14.3, 2025; Wolfram Research, Inc.). Surface plots, distributions of complex zeros, and real-zero patterns are presented for different parameter values, highlighting the influence of the parameters on the behavior and structural characteristics of the polynomials. Full article
17 pages, 2618 KB  
Article
Improving Coastal Bottom Dissolved Oxygen Forecasting Using Tide-Derived Features with an LSTM-Based Model
by Eun-Joo Lee, Sung-Eun Park, Junmo Jo, Jong-Hong Kim, Chung-Sook Kim, Jiyoung Lee and Wol-Ae Lim
Water 2026, 18(9), 1045; https://doi.org/10.3390/w18091045 - 28 Apr 2026
Abstract
Coastal bottom dissolved oxygen (DO) depletion poses a serious threat to marine ecosystems and aquaculture, and hypoxic events in the semi-enclosed Jinhae Bay, Korea, repeatedly cause large-scale damage to fish farms. Accurate DO prediction models are therefore crucial for ecosystem management and loss [...] Read more.
Coastal bottom dissolved oxygen (DO) depletion poses a serious threat to marine ecosystems and aquaculture, and hypoxic events in the semi-enclosed Jinhae Bay, Korea, repeatedly cause large-scale damage to fish farms. Accurate DO prediction models are therefore crucial for ecosystem management and loss mitigation. This study analyzes how different tidal input representations affect the performance of data-driven DO prediction models in a tide-dominated coastal environment. Using time-series data of oceanographic and meteorological variables from nearby observation sites, we develop an long short-term memory (LSTM)-based neural network ensemble model with four experimental configurations. These include not only water level but also tidal envelope, tidal-intensity proxy, and temporal differences in water level and DO (Δtide, ΔDO) as additional inputs. Compared with the baseline configuration, the full tide-informed input case reduced the 72 h mean root mean square error (RMSE) from 1.16 to 1.12 and increased the Pearson correlation coefficient from 0.873 to 0.883. It also improved the representation of intraday variability and prediction stability. These results show that tide-derived variables help the model more effectively capture tidal-phase-locked DO fluctuations, while temporal-difference inputs further strengthen short-term variability and sensitivity to DO changes. These results indicate that properly representing tidal forcing is essential for learning the temporal structure and variability of coastal bottom DO. Full article
(This article belongs to the Section Oceans and Coastal Zones)
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14 pages, 2063 KB  
Article
Pseudodifferential Phase-Space Dynamics for SU(1,1) Systems and Numerical Evaluation Using Oscillatory Integrals
by Rodrigo D. Aceves, Iván F. Valtierra and Andrés García Sandoval
Mathematics 2026, 14(9), 1477; https://doi.org/10.3390/math14091477 - 28 Apr 2026
Abstract
We study the phase-space dynamics of quantum systems with SU(1,1) group symmetry using coherent-state representations on the Poincaré disk. The resulting evolution equation combines transport terms with nonlocal contributions generated with the spectral functions of the Casimir operator, [...] Read more.
We study the phase-space dynamics of quantum systems with SU(1,1) group symmetry using coherent-state representations on the Poincaré disk. The resulting evolution equation combines transport terms with nonlocal contributions generated with the spectral functions of the Casimir operator, which admit a natural interpretation as pseudodifferential operators associated with the hyperbolic Laplace–Beltrami operator. Using this pseudodifferential structure, we classify the phase-space generators according to the type of the underlying PDE: compact quadratic dynamics (H^K^02) yield a degenerate hyperbolic operator of the transport type, and noncompact dynamics (H^K^22) give rise to a mixed-order differential–pseudodifferential operator. For numerical evaluation, we reformulate the propagator as an oscillatory integral and develop two complementary strategies: a Fourier-series reduction exploiting the periodicity of compact orbits and a Levin-type spectral collocation method for the noncompact case. Both approaches are stable, accurate, and free of the stiffness issues that afflict direct PDE evolution on the Poincaré disk. Full article
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23 pages, 3999 KB  
Article
ProAdapt: A Meta-Incremental Learning Framework with Spectral-Temporal Representation Learning and Online EWC for Stock Trend Forecasting
by Lele Gao, Yafei Bai, Wenjie Yao, Nan Li, Yilun Wang and Yong Hu
Electronics 2026, 15(9), 1858; https://doi.org/10.3390/electronics15091858 - 28 Apr 2026
Abstract
Stock trend forecasting remains challenging in real financial markets because data distributions evolve over time, and models trained under static settings often degrade during online deployment. Recent studies have introduced incremental and meta-incremental learning into stock forecasting, yet effective sequential adaptation remains constrained [...] Read more.
Stock trend forecasting remains challenging in real financial markets because data distributions evolve over time, and models trained under static settings often degrade during online deployment. Recent studies have introduced incremental and meta-incremental learning into stock forecasting, yet effective sequential adaptation remains constrained by two issues: financial multivariate time series require stronger representation modeling before downstream prediction, and repeated online updates may lead to forgetting and parameter drift. To address these issues, we propose ProAdapt, a bi-level meta-incremental learning framework for stock trend forecasting in non-stationary markets. ProAdapt contains two key components. The first is a Structural Spectral-Temporal Feature Adapter (SSTFA), which enhances financial time series representations by modeling non-uniform temporal importance and selective cross-factor interactions through adaptive soft window temporal encoding, frequency-domain structure modeling, and feature refinement. The second is online Elastic Weight Consolidation (EWC), which is incorporated into the outer-loop optimization to regularize sequential parameter updates and improve the balance between adaptation and stability. We evaluate ProAdapt on the CSI300 and CSI500 benchmarks under an incremental forecasting setting with sequential task updates. Experimental results across multiple backbones show that ProAdapt generally achieves favorable forecasting results relative to the compared baselines, with relatively clearer gains on CSI500. Additional ablation and analysis results further support the effectiveness of SSTFA and online EWC. Overall, the results suggest that combining explicit representation enhancement with stability-aware sequential updating is beneficial for incremental stock forecasting in evolving market environments. Full article
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33 pages, 5127 KB  
Article
Fractional-Order Algebraic Parameter Estimation for Disturbed Differentially Flat Systems
by Alexis Castelan-Perez, Francisco Beltran-Carbajal, David Marcos-Andrade, Ivan Rivas-Cambero, Clementina Rueda-German and Hugo Yañez-Badillo
Mathematics 2026, 14(9), 1468; https://doi.org/10.3390/math14091468 - 27 Apr 2026
Viewed by 57
Abstract
Disturbances in dynamical systems pose a major challenge for parameter identification, particularly in the presence of unknown initial conditions and uncertain external influences. To address this issue, this paper proposes an algebraic parameter estimation methodology that incorporates fractional-order calculus in the Laplace domain [...] Read more.
Disturbances in dynamical systems pose a major challenge for parameter identification, particularly in the presence of unknown initial conditions and uncertain external influences. To address this issue, this paper proposes an algebraic parameter estimation methodology that incorporates fractional-order calculus in the Laplace domain for controlled linear engineering systems. The proposed approach eliminates the influence of unknown initial conditions and considers external disturbances that admit a local polynomial representation through Taylor series expansions over sufficiently small time intervals, while avoiding explicit numerical differentiation in the time domain. The manuscript includes analytical, numerical, and experimental validations to highlight the benefits of incorporating fractional-order differentiation in the derivation of algebraic estimators for online parameter estimation. The method is experimentally validated on two linear differentially flat electrical circuits, whose flat representations enable the proposed algebraic formulation under distinct disturbance signals. The results demonstrate that the fractional differentiation order acts as an additional tuning parameter, and that appropriately selected fractional orders can improve estimation accuracy, yielding parameter estimates consistently closer to their true values when compared with the conventional integer-order algebraic formulation. Full article
(This article belongs to the Special Issue Fractional Calculus: Advances and Applications)
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22 pages, 11494 KB  
Article
Wind-Radiation Data-Driven Modelling Using Derivative Transform, Deep-LSTM, and Stochastic Tree AI Learning in 2-Layer Meteo-Patterns
by Ladislav Zjavka
Modelling 2026, 7(3), 82; https://doi.org/10.3390/modelling7030082 - 27 Apr 2026
Viewed by 103
Abstract
Self-contained local forecasting of wind and solar series can improve operational planning of wind farms and photovoltaic (PV) plant day-cycles in addition to numerical models, which are mostly behind time due to high simulation costs. Unstable electricity production requires balancing the availability of [...] Read more.
Self-contained local forecasting of wind and solar series can improve operational planning of wind farms and photovoltaic (PV) plant day-cycles in addition to numerical models, which are mostly behind time due to high simulation costs. Unstable electricity production requires balancing the availability of renewable energy (RE) with unpredictable user consumption to achieve effective usage. Artificial intelligence (AI) predictive modelling can minimise the intermittent uncertainty in wind and solar resources by trying to eliminate specific problems in RE-detached system reliability and optimal utilisation. The proposed 24 h day-training and prediction scheme comprises the starting detection and the following similarity re-assessment of sampling day-series intervals. Two-point professional weather stations record standard meteorological variables, of which the most relevant are selected as optimal model inputs. Automatic two-layer altitude observation captures key relationships between hill- and lowland-level data, which comply with pattern progress. New biologically inspired differential learning (DfL) is designed and developed to integrate adaptive neurocomputing (evolving node tree components) with customised numerical procedures of operator calculus (OC) based on derivative transforms. DfL enables the representation of uncertain dynamics related to local weather patterns. Angular and frequency data (wind azimuth, temperature, irradiation) are processed together with the amplitudes to solve simple 2-variable partial differential equations (PDEs) in binomial nodes. Differentiated data provide the fruitful information necessary to model upcoming changes in mid-term day horizons. Additional PDE components in periodic form improve the modelling of hidden complex patterns in cycle data. The DfL efficiency was proved in statistical experiments, compared to a variety of elaborated AI techniques, enhanced by selective difference input preprocessing. Successful LSTM-deep and stochastic tree learning shows little inferior model performances, notably in day-ahead estimation of chaotic 24 h wind series, and slightly better approximation of alterative 8 h solar cycles. Free parametric C++ software with the applied archive data is available for additional comparative and reproducible experiments. Full article
(This article belongs to the Section Modelling in Artificial Intelligence)
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22 pages, 19401 KB  
Article
Explainable Combined Spatial Representations for ECG Arrhythmia Classification
by Iulia Onică and Iulian B. Ciocoiu
Mach. Learn. Knowl. Extr. 2026, 8(5), 114; https://doi.org/10.3390/make8050114 - 25 Apr 2026
Viewed by 176
Abstract
The paper addresses ECG arrhythmia classification using a novel input fusion strategy that combines spatial representations of ECG time series recordings. Four distinct time series-to-image transformations are considered, namely classical spectrograms, Gramian Angular Field (GAF), Recursive Plot (RP), and the S-Transform (ST). Classification [...] Read more.
The paper addresses ECG arrhythmia classification using a novel input fusion strategy that combines spatial representations of ECG time series recordings. Four distinct time series-to-image transformations are considered, namely classical spectrograms, Gramian Angular Field (GAF), Recursive Plot (RP), and the S-Transform (ST). Classification of combined 2 × 2 images generated from single-lead ECG recordings is performed using both custom and ResNet-50 deep learning architectures. Finally, several distinct explainability algorithms are used to identify the relevant regions in the input images that mainly influence the classification decisions. Experiments performed on the MIT-BIH and Chapman–Shaoxing arrhythmia datasets revealed performance comparable to more sophisticated approaches in terms of accuracy (99%), F1-score (98.6%), and AUC (0.999) values. Full article
(This article belongs to the Section Data)
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19 pages, 4750 KB  
Article
Research on Vehicle Operating Condition Prediction and Optimization Method Based on LSTM-LSSVM-CC
by Mengjie Li, Yongbao Liu and Xing He
Electronics 2026, 15(9), 1785; https://doi.org/10.3390/electronics15091785 - 22 Apr 2026
Viewed by 227
Abstract
To address the limited accuracy of power demand prediction for hybrid electric vehicles under complex and dynamic driving conditions, this paper proposes a hybrid prediction approach based on the cascade correction of Long Short-Term Memory networks and Least Squares Support Vector Machines (LSTM-LSSVM-CC). [...] Read more.
To address the limited accuracy of power demand prediction for hybrid electric vehicles under complex and dynamic driving conditions, this paper proposes a hybrid prediction approach based on the cascade correction of Long Short-Term Memory networks and Least Squares Support Vector Machines (LSTM-LSSVM-CC). The proposed method adopts a stage-wise modeling framework that exploits the least-squares optimality of LSSVM for low-frequency steady-state signals and the dynamic compensation capability of LSTM for high-frequency non-stationary residuals, thereby achieving complementary feature representation in the frequency domain. Specifically, an LSSVM is first used to construct a baseline regression model that captures stationary components, followed by an LSTM network that performs deep temporal modeling of the residual sequence to correct nonlinear prediction errors. Extensive experiments conducted on three standard driving cycles—CLTC-P, WLTP, and UDDS—demonstrate that the proposed model consistently outperforms conventional methods including LSSVM, RNN, ELMAN, and Random Forest in multi-step predictions, achieving an average RMSE reduction of 28–52% and maintaining correlation coefficients (R2) between 0.87 and 0.99. Particularly under highly dynamic and abrupt load conditions, the model exhibits superior real-time performance and stability while significantly mitigating cumulative prediction errors. These results demonstrate that the proposed LSTM-LSSVM-CC model achieves robust modeling performance of non-stationary time series while balancing prediction accuracy and computational efficiency, providing an effective technical foundation for hybrid vehicle energy management optimization and offering a transferable theoretical framework for time-series prediction in complex systems. Full article
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29 pages, 1833 KB  
Article
MSTFNet: Multi-Scale Temporal Fusion Network with Frequency-Enhanced Attention for Financial Time Series Forecasting
by Qian Xia and Wenhao Kang
Mathematics 2026, 14(8), 1391; https://doi.org/10.3390/math14081391 - 21 Apr 2026
Viewed by 169
Abstract
Financial time series forecasting remains a persistent challenge due to the non-stationary nature, inherent noise, and multi-scale temporal dependencies present in market data. This paper presents MSTFNet, a multi-scale temporal fusion network that combines dilated causal convolutions with a frequency-enhanced sparse attention mechanism [...] Read more.
Financial time series forecasting remains a persistent challenge due to the non-stationary nature, inherent noise, and multi-scale temporal dependencies present in market data. This paper presents MSTFNet, a multi-scale temporal fusion network that combines dilated causal convolutions with a frequency-enhanced sparse attention mechanism for improved financial prediction. The proposed architecture consists of three core components: a multi-scale dilated causal convolution module that extracts temporal patterns across different time horizons through parallel convolutional branches with varying dilation rates, a frequency-enhanced sparse attention mechanism that leverages Fast Fourier Transform to identify dominant periodic components and modulate attention weights accordingly, and an adaptive scale fusion gate that learns to dynamically combine representations from multiple temporal scales. Extensive experiments conducted on three public financial datasets (S&P 500, CSI 300, and NASDAQ Composite) spanning the period from January 2015 to December 2024 show two key results. First, consistent with near-efficient markets, the random-walk benchmark (y^t+1=yt) outperforms all the data-driven models on level-error metrics (MAE, RMSE, MAPE, and R2), establishing the martingale as the binding lower bound on point-prediction error. Second, MSTFNet achieves the highest directional accuracy (DA) across all three indices—56.3% on the S&P 500 versus 50.0% for the martingale—representing a 6.3 percentage-point improvement that generates positive pre-cost returns in a trading strategy backtest. Among the eight data-driven baselines (LSTM, GRU, TCN, Transformer, Autoformer, FEDformer, PatchTST, and iTransformer), MSTFNet also achieves the lowest MAE, reducing it by 13.6% relative to the strongest data-driven baseline (iTransformer) on the S&P 500. These results confirm that integrating multi-scale temporal modeling with frequency-domain guidance extracts a real, if modest, directional signal from financial time series. Full article
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