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29 pages, 1928 KB  
Article
Denoising Stock Price Time Series with Singular Spectrum Analysis for Enhanced Deep Learning Forecasting
by Carol Anne Hargreaves and Zixian Fan
Analytics 2026, 5(1), 9; https://doi.org/10.3390/analytics5010009 (registering DOI) - 27 Jan 2026
Abstract
Aim: Stock price prediction remains a highly challenging task due to the complex and nonlinear nature of financial time series data. While deep learning (DL) has shown promise in capturing these nonlinear patterns, its effectiveness is often hindered by the low signal-to-noise ratio [...] Read more.
Aim: Stock price prediction remains a highly challenging task due to the complex and nonlinear nature of financial time series data. While deep learning (DL) has shown promise in capturing these nonlinear patterns, its effectiveness is often hindered by the low signal-to-noise ratio inherent in market data. This study aims to enhance the stock predictive performance and trading outcomes by integrating Singular Spectrum Analysis (SSA) with deep learning models for stock price forecasting and strategy development on the Australian Securities Exchange (ASX)50 index. Method: The proposed framework begins by applying SSA to decompose raw stock price time series into interpretable components, effectively isolating meaningful trends and eliminating noise. The denoised sequences are then used to train a suite of deep learning architectures, including Convolutional Neural Networks (CNN), Long Short-Term Memory (LSTM), and hybrid CNN-LSTM models. These models are evaluated based on their forecasting accuracy and the profitability of the trading strategies derived from their predictions. Results: Experimental results demonstrated that the SSA-DL framework significantly improved the prediction accuracy and trading performance compared to baseline DL models trained on raw data. The best-performing model, SSA-CNN-LSTM, achieved a Sharpe Ratio of 1.88 and a return on investment (ROI) of 67%, indicating robust risk-adjusted returns and effective exploitation of the underlying market conditions. Conclusions: The integration of Singular Spectrum Analysis with deep learning offers a powerful approach to stock price prediction in noisy financial environments. By denoising input data prior to model training, the SSA-DL framework enhanced signal clarity, improved forecast reliability, and enabled the construction of profitable trading strategies. These findings suggested a strong potential for SSA-based preprocessing in financial time series modeling. Full article
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23 pages, 2976 KB  
Article
Transfer Learning-Based Piezoelectric Actuators Feedforward Control with GRU-CNN
by Yaqian Hu, Herong Jin, Xiangcheng Chu and Yali Yi
Appl. Sci. 2026, 16(3), 1305; https://doi.org/10.3390/app16031305 - 27 Jan 2026
Abstract
To compensate for hysteresis, low damping vibration, and their coupling effects, this paper proposes a gated recurrent unit and convolutional neural network (GRU-CNN) model as a feedforward control model that maps desired displacement trajectories to driving voltages. The GRU-CNN integrates a gated recurrent [...] Read more.
To compensate for hysteresis, low damping vibration, and their coupling effects, this paper proposes a gated recurrent unit and convolutional neural network (GRU-CNN) model as a feedforward control model that maps desired displacement trajectories to driving voltages. The GRU-CNN integrates a gated recurrent unit (GRU) layer to capture long-term temporal dependencies, a multi-layer convolutional neural network (CNN) to extract local data features, and residual connections to mitigate information distortion. The GRU-CNN is then combined with transfer learning (TL) for feedforward control of cross-batch and cross-type piezoelectric actuators (PEAs), so as to reduce reliance on training datasets. The analysis focuses on the impacts of target PEA data volume and source-target similarity on transfer learning strategies. The GRU-CNN trained on PEA #1 achieves high control accuracy, with a mean absolute error (MAE) of 0.077, a root mean square error (RMSE) of 0.129, and a coefficient of determination (R2) of 0.997. When transferred to cross-batch PEA #2 and cross-type PEA #3, the GRU-CNN feedforward controller still delivers favorable performance; R2 values all exceed 0.98, representing at least a 27% improvement compared to training from scratch. These results indicate that the proposed transfer learning-based feedforward control method can effectively reduce retraining effort, suggesting its potential applicability to batch production scenarios. Full article
19 pages, 16026 KB  
Article
CIR-SSM: A Cross and Inter Resolution State-Space Model for Underwater Image Enhancement
by Fengxian Liu, Ning Ye and Haitao Wang
Appl. Sci. 2026, 16(3), 1297; https://doi.org/10.3390/app16031297 - 27 Jan 2026
Abstract
Underwater images often suffer from strong color casts, low contrast, and blurred textures. It is observed that low resolution can provide globally correct color, so low-resolution priors can guide high-resolution correction. While many recent methods combine Transformer and CNN components, Mamba offers an [...] Read more.
Underwater images often suffer from strong color casts, low contrast, and blurred textures. It is observed that low resolution can provide globally correct color, so low-resolution priors can guide high-resolution correction. While many recent methods combine Transformer and CNN components, Mamba offers an efficient alternative for global dependency modeling. Motivated by these insights, this paper proposes a cross- and inter-resolution state-space model for underwater image enhancement (CIR-SSM). The method consists of three sub-networks at full, 1/2, and 1/4 resolutions, each stacking color–texture Mamba modules. Each module includes a color Mamba block, a texture Mamba block, and a color–texture fusion Mamba block. The color Mamba block injects low-resolution color priors into the state-space trajectory to steer global color reconstruction in the high-resolution branch. In parallel, the texture Mamba block operates at the native resolution to capture fine-grained structural dependencies for texture restoration. The fusion Mamba block adaptively merges the enhanced color and texture representations within the state-space framework to produce the restored image. Comprehensive quantitative assessments on both the UIEB and SQUID benchmarks show that the proposed framework achieves the highest evaluated scores, outperforming several representative state-of-the-art methods. Full article
(This article belongs to the Special Issue Computational Imaging: Algorithms, Technologies, and Applications)
15 pages, 1396 KB  
Article
Intelligent Fault-Tolerant Control for Wave Compensation Systems Considering Unmodeled Dynamics and Dead-Zone
by Zhiqiang Xu, Xiaoning Zhao, Zhixin Shen, Yingjia Guo and Yougang Sun
J. Mar. Sci. Eng. 2026, 14(3), 265; https://doi.org/10.3390/jmse14030265 - 27 Jan 2026
Abstract
For marine development in harsh sea states, floating-body salvage equipment serves as critical support infrastructure. Aiming at the challenges of nonlinear dead-zone, model uncertainty, and actuator failures in the wave compensation systems of such equipment, this paper proposes an intelligent fault-tolerant control method [...] Read more.
For marine development in harsh sea states, floating-body salvage equipment serves as critical support infrastructure. Aiming at the challenges of nonlinear dead-zone, model uncertainty, and actuator failures in the wave compensation systems of such equipment, this paper proposes an intelligent fault-tolerant control method based on neural networks. First, the dead-zone nonlinearity of the hydraulic system is compensated using an inverse model approach. Then, neural networks are employed to online learn unmodeled dynamics, while adaptive laws are designed to handle partial actuator failures and Lyapunov theory is used to prove the global stability of the closed-loop system, effectively enhancing the robustness and fault-tolerance of the wave compensation system under complex sea conditions. Unlike existing studies that rely on accurate system models, the proposed method integrates data-driven learning with model-based compensation. This integration enables adaptive handling of wave disturbances, model uncertainties, and actuator faults, thereby overcoming the strong model dependence and complex observer design inherent in traditional sliding-mode fault-tolerant control. Simulation and experiment results show that the method ensures high-precision dynamic tracking and compensation performance under various sea conditions. Full article
(This article belongs to the Section Ocean Engineering)
20 pages, 10210 KB  
Article
300-GHz Photonics-Aided Wireless 2 × 2 MIMO Transmission over 200 m Using GMM-Enhanced Duobinary Unsupervised Adaptive CNN
by Luhan Jiang, Jianjun Yu, Qiutong Zhang, Wen Zhou and Min Zhu
Sensors 2026, 26(3), 842; https://doi.org/10.3390/s26030842 - 27 Jan 2026
Abstract
Terahertz wireless communication offers ultra-high bandwidth, enabling an extremely high data rate for next-generation networks. However, it faces challenges including severe propagation loss and atmospheric absorption, which limits the transmission rate and transmission distance. To address the problem, polarization division multiplexing (PDM) and [...] Read more.
Terahertz wireless communication offers ultra-high bandwidth, enabling an extremely high data rate for next-generation networks. However, it faces challenges including severe propagation loss and atmospheric absorption, which limits the transmission rate and transmission distance. To address the problem, polarization division multiplexing (PDM) and antenna diversity techniques are utilized in this work to increase system capacity without changing the bandwidth of transmitted signals. Meanwhile, duobinary shaping is used to solve the problem of bandwidth limitation of components in the system, and the final duobinary signals are recovered by maximum likelihood sequence detection (MLSD). A Gaussian mixture model (GMM)-enhanced duobinary unsupervised adaptive convolutional neural network (DB-UACNN) is proposed, to further deal with channel noise. Based on the technologies above, a 2 × 2 multiple-input multiple-output (MIMO) photonic-aided terahertz wireless transmission system at 300 GHz is demonstrated. Experimental results have proved that the signal-to-noise ratio (SNR) gain of duobinary shaping is up to 1.87 dB and 1.70 dB in X-polarization and Y-polarization. The proposed GMM-enhanced DB-UACNN also shows extra SNR gain of up to 2.59 dB and 2.63 dB in X-polarization and Y-polarization, compared to the conventional duobinary filter. The high transmission rate of 100 Gbit/s over the distance of 200 m is finally realized under a 7% hard-decision forward error correction (HD-FEC) threshold. Full article
19 pages, 5729 KB  
Article
AI-Driven Hybrid Architecture for Secure, Reconstruction-Resistant Multi-Cloud Storage
by Munir Ahmed and Jiann-Shiun Yuan
Future Internet 2026, 18(2), 70; https://doi.org/10.3390/fi18020070 - 27 Jan 2026
Abstract
Cloud storage continues to experience recurring provider-side breaches, raising concerns about the confidentiality and recoverability of user data. This study addresses this challenge by introducing an Artificial Intelligence (AI)-driven hybrid architecture for secure, reconstruction-resistant multi-cloud storage. The system applies telemetry-guided fragmentation, where fragment [...] Read more.
Cloud storage continues to experience recurring provider-side breaches, raising concerns about the confidentiality and recoverability of user data. This study addresses this challenge by introducing an Artificial Intelligence (AI)-driven hybrid architecture for secure, reconstruction-resistant multi-cloud storage. The system applies telemetry-guided fragmentation, where fragment sizes are dynamically predicted from real-time bandwidth, latency, memory availability and disk I/O, eliminating the predictability of fixed-size fragmentation. All payloads are compressed, encrypted with AES-128 and dispersed across independent cloud providers, while two encrypted fragments are retained within a VeraCrypt-protected local vault to enforce a distributed trust threshold that prevents cloud-only reconstruction. Synthetic telemetry was first used to evaluate model feasibility and scalability, followed by hybrid telemetry integrating real Microsoft system traces and Cisco network metrics to validate generalization under realistic variability. Across all evaluations, XGBoost and Random Forest achieved the highest predictive accuracy, while Neural Network and Linear Regression models provided moderate performance. Security validation confirmed that partial-access and cloud-only attack scenarios cannot yield reconstruction without the local vault fragments and the encryption key. These findings demonstrate that telemetry-driven adaptive fragmentation enhances predictive reliability and establishes a resilient, zero-trust framework for secure multi-cloud storage. Full article
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17 pages, 1437 KB  
Article
Traffic Flow Prediction in Complex Transportation Networks via a Spatiotemporal Causal–Trend Network
by Xingyu Feng, Lina Sheng, Linglong Zhu, Yishan Feng, Chen Wei, Xudong Xiao and Haochen Wang
Mathematics 2026, 14(3), 443; https://doi.org/10.3390/math14030443 - 27 Jan 2026
Abstract
Traffic systems are quintessential complex systems, characterized by nonlinear interactions, multiscale dynamics, and emergent spatiotemporal patterns over complex networks. These properties make traffic prediction highly challenging, as it requires jointly modeling stable global topology and time-varying local dependencies. Existing graph neural networks often [...] Read more.
Traffic systems are quintessential complex systems, characterized by nonlinear interactions, multiscale dynamics, and emergent spatiotemporal patterns over complex networks. These properties make traffic prediction highly challenging, as it requires jointly modeling stable global topology and time-varying local dependencies. Existing graph neural networks often rely on predefined or static learnable graphs, overlooking hidden dynamic structures, while most RNN- or CNN-based approaches struggle with long-range temporal dependencies. This paper proposes a Spatiotemporal Causal–Trend Network (SCTN) tailored to complex transportation networks. First, we introduce a dual-path adaptive graph learning scheme: a static graph that captures global, topology-aligned dependencies of the complex network, and a dynamic graph that adapts to localized, time-varying interactions. Second, we design a Gated Temporal Attention Module (GTAM) with a causal–trend attention mechanism that integrates 1D and causal convolutions to reinforce temporal causality and local trend awareness while maintaining long-range attention. Extensive experiments on two real-world PeMS traffic flow datasets demonstrate that SCTN consistently achieves superior accuracy compared to strong baselines, reducing by 3.5–4.5% over the best-performing existing methods, highlighting its effectiveness for modeling the intrinsic complexity of urban traffic systems. Full article
(This article belongs to the Special Issue Advanced Machine Learning Research in Complex System)
29 pages, 614 KB  
Article
A Privacy-Preserving Classification Framework for Multi-Class Imbalanced Data Using Geometric Oversampling and Homomorphic Encryption
by Shoulei Lu, Jun Ye, Fanglin An and Zhengqi Zhang
Appl. Sci. 2026, 16(3), 1283; https://doi.org/10.3390/app16031283 - 27 Jan 2026
Abstract
Data classification tasks based on deep neural networks and machine learning are increasingly used in different fields, such as medicine, finance, and data circulation. However, in these applications, the accuracy of predictions must be guaranteed, and the privacy and security of prediction data [...] Read more.
Data classification tasks based on deep neural networks and machine learning are increasingly used in different fields, such as medicine, finance, and data circulation. However, in these applications, the accuracy of predictions must be guaranteed, and the privacy and security of prediction data and models must be guaranteed. In an unsafe cloud environment, cloud users are reluctant to use the classification prediction tasks provided by the cloud. To solve these problems, this paper researches the data oversampling method and proposes the G-MSMOTE method, which can solve the oversampling problem of multiple minority classes in the data set, generate more diverse data, and solve the data imbalance problem. By improving the traditional FV and using CRT technology to improve coding efficiency, the cloud receives the user’s encrypted ciphertext, and the neural network completes the data prediction task in the ciphertext, thereby providing confidentiality for user data and model parameters under the semi-honest adversarial model, assuming the security of the underlying fully homomorphic encryption scheme and accepting the leakage of model architecture and ciphertext sizes. The feasibility of our method was demonstrated through experimental comparative analysis. We created unbalanced cases based on the MNIST dataset and performed comparative analysis in plain and ciphertext. In the balanced dataset, the model’s prediction accuracy in ciphertext reached 93.44%. In the unbalanced case, after preprocessing with our improved G-MSMOTE algorithm, the model’s prediction accuracy in ciphertext increased by at least 10%. These results show that our scheme can efficiently, accurately, and securely (under the semi-honest model) complete the data classification prediction task. Full article
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31 pages, 901 KB  
Article
Neutral, Leakage, and Mixed Delays in Quaternion-Valued Neural Networks on Time Scales: Stability and Synchronization Analysis
by Călin-Adrian Popa
Mathematics 2026, 14(3), 440; https://doi.org/10.3390/math14030440 - 27 Jan 2026
Abstract
Quaternion-valued neural networks (QVNNs) that have multiple types of delays (leakage, time-varying, distributed, and neutral) and defined on time scales are discussed in this paper. Quaternions form a 4D normed division algebra and allow for a better representation of 3D and 4D data. [...] Read more.
Quaternion-valued neural networks (QVNNs) that have multiple types of delays (leakage, time-varying, distributed, and neutral) and defined on time scales are discussed in this paper. Quaternions form a 4D normed division algebra and allow for a better representation of 3D and 4D data. QVNNs have been proposed and applications have appeared lately. Time-scale calculus was developed to allow the joint treatment of systems, or any hybrid mixing of them, and was also applied with success to the analysis of dynamic properties for neural networks (NNs). Because of its generality, encompassing the common properties of discrete-time (DT) and continuous-time (CT) NNs, time-scale NNs dynamics research does not benefit from a fully-developed Lyapunov theory. So, Halanay-type inequalities have to be used instead. To this end, we provide a novel generalization of inequalities of Halanay-type on time scales specifically suited for neutral systems, i.e., systems with neutral delays. Then, this new lemma is employed to obtain sufficient conditions presented both as linear matrix inequalities (LMIs) and as algebraic inequalities for the exponential stability and exponential synchronization of QVNNs on time scales with the mentioned delay types. The model put forward in this paper has a generality which is appealing for practical applications, in which both DT and CT dynamics are interesting, and all the discussed types of delays appear. For both the DT and CT scenarios, four numerical applications are used to illustrate the four theorems put forward in this research. Full article
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12 pages, 2668 KB  
Article
Spatial-Frequency Fusion Tiny-Transformer for Efficient Image Super-Resolution
by Qiaoyue Man
Appl. Sci. 2026, 16(3), 1284; https://doi.org/10.3390/app16031284 - 27 Jan 2026
Abstract
In image super-resolution tasks, methods based on Generative Adversarial Networks (GANs), Transformer models, and diffusion models demonstrate robust global modeling capabilities and outstanding performance. However, their computational costs remain prohibitively high, limiting deployment on resource-constrained devices. Meanwhile, frequency-domain approaches based on convolutional neural [...] Read more.
In image super-resolution tasks, methods based on Generative Adversarial Networks (GANs), Transformer models, and diffusion models demonstrate robust global modeling capabilities and outstanding performance. However, their computational costs remain prohibitively high, limiting deployment on resource-constrained devices. Meanwhile, frequency-domain approaches based on convolutional neural networks (CNNs) capture complementary structural information but lack long-range dependencies, resulting in suboptimal perceptual image quality. To overcome these limitations, we propose a micro-Transformer-based architecture. This framework enriches high-frequency image information through wavelet transform-based frequency-domain features, integrates spatio-temporal and frequency-domain cross-feature fusion, and incorporates a discriminator constraint to achieve image super-resolution. Extensive experiments demonstrate that this approach achieves competitive PSNR/SSIM performance while maintaining reasonable computational complexity. Its visual quality and efficiency outperform most existing SR methods. Full article
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25 pages, 969 KB  
Article
H-CLAS: A Hybrid Continual Learning Framework for Adaptive Fault Detection and Self-Healing in IoT-Enabled Smart Grids
by Tina Babu, Rekha R. Nair, Balamurugan Balusamy and Sumendra Yogarayan
IoT 2026, 7(1), 12; https://doi.org/10.3390/iot7010012 - 27 Jan 2026
Abstract
The rapid expansion of Internet of Things (IoT)-enabled smart grids has intensified the need for reliable fault detection and autonomous self-healing under non-stationary operating conditions characterized by frequent concept drift. To address the limitations of static and single-strategy adaptive models, this paper proposes [...] Read more.
The rapid expansion of Internet of Things (IoT)-enabled smart grids has intensified the need for reliable fault detection and autonomous self-healing under non-stationary operating conditions characterized by frequent concept drift. To address the limitations of static and single-strategy adaptive models, this paper proposes H-CLAS, a novel Hybrid Continual Learning for Adaptive Self-healing framework that unifies regularization-based, memory-based, architectural, and meta-learning strategies within a single adaptive pipeline. The framework integrates convolutional neural networks (CNNs) for fault detection, graph neural networks for topology-aware fault localization, reinforcement learning for self-healing control, and a hybrid drift detection mechanism combining ADWIN and Page–Hinkley tests. Continual adaptation is achieved through the synergistic use of Elastic Weight Consolidation, memory-augmented replay, progressive neural network expansion, and Model-Agnostic Meta-Learning for rapid adaptation to emerging drifts. Extensive experiments conducted on the Smart City Air Quality and Network Intrusion Detection Dataset (NSL-KDD) demonstrate that H-CLAS achieves accuracy improvements of 12–15% over baseline methods, reduces false positives by over 50%, and enables 2–3× faster recovery after drift events. By enhancing resilience, reliability, and autonomy in critical IoT-driven infrastructures, the proposed framework contributes to improved grid stability, reduced downtime, and safer, more sustainable energy and urban monitoring systems, thereby providing significant societal and environmental benefits. Full article
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27 pages, 1633 KB  
Review
Transformer Models, Graph Networks, and Generative AI in Gut Microbiome Research: A Narrative Review
by Yan Zhu, Yiteng Tang, Xin Qi and Xiong Zhu
Bioengineering 2026, 13(2), 144; https://doi.org/10.3390/bioengineering13020144 - 27 Jan 2026
Abstract
Background: The rapid advancement in artificial intelligence (AI) has fundamentally reshaped gut microbiome research by enabling high-resolution analysis of complex, high-dimensional microbial communities and their functional interactions with the human host. Objective: This narrative review aims to synthesize recent methodological advances in AI-driven [...] Read more.
Background: The rapid advancement in artificial intelligence (AI) has fundamentally reshaped gut microbiome research by enabling high-resolution analysis of complex, high-dimensional microbial communities and their functional interactions with the human host. Objective: This narrative review aims to synthesize recent methodological advances in AI-driven gut microbiome research and to evaluate their translational relevance for therapeutic optimization, personalized nutrition, and precision medicine. Methods: A narrative literature review was conducted using PubMed, Google Scholar, Web of Science, and IEEE Xplore, focusing on peer-reviewed studies published between approximately 2015 and early 2025. Representative articles were selected based on relevance to AI methodologies applied to gut microbiome analysis, including machine learning, deep learning, transformer-based models, graph neural networks, generative AI, and multi-omics integration frameworks. Additional seminal studies were identified through manual screening of reference lists. Results: The reviewed literature demonstrates that AI enables robust identification of diagnostic microbial signatures, prediction of individual responses to microbiome-targeted therapies, and design of personalized nutritional and pharmacological interventions using in silico simulations and digital twin models. AI-driven multi-omics integration—encompassing metagenomics, metatranscriptomics, metabolomics, proteomics, and clinical data—has improved functional interpretation of host–microbiome interactions and enhanced predictive performance across diverse disease contexts. For example, AI-guided personalized nutrition models have achieved AUC exceeding 0.8 for predicting postprandial glycemic responses, while community-scale metabolic modeling frameworks have accurately forecast individualized short-chain fatty acid production. Conclusions: Despite substantial progress, key challenges remain, including data heterogeneity, limited model interpretability, population bias, and barriers to clinical deployment. Future research should prioritize standardized data pipelines, explainable and privacy-preserving AI frameworks, and broader population representation. Collectively, these advances position AI as a cornerstone technology for translating gut microbiome data into actionable insights for diagnostics, therapeutics, and precision nutrition. Full article
(This article belongs to the Special Issue Application of Artificial Intelligence in Complex Diseases)
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18 pages, 2796 KB  
Article
Leveraging Distributional Symmetry in Credit Card Fraud Detection via Conditional Tabular GAN Augmentation and LightGBM
by Cichen Wang, Can Xie and Jialiang Li
Symmetry 2026, 18(2), 224; https://doi.org/10.3390/sym18020224 - 27 Jan 2026
Abstract
Credit card fraud detection remains a major challenge due to extreme class imbalance and evolving attack patterns. This paper proposes a practical hybrid pipeline that combines conditional tabular generative adversarial networks (CTGANs) for targeted minority-class synthesis with Light Gradient Boosting Machine (LightGBM) for [...] Read more.
Credit card fraud detection remains a major challenge due to extreme class imbalance and evolving attack patterns. This paper proposes a practical hybrid pipeline that combines conditional tabular generative adversarial networks (CTGANs) for targeted minority-class synthesis with Light Gradient Boosting Machine (LightGBM) for classification. Inspired by symmetry principles in machine learning, we leverage the adversarial equilibrium of CTGAN to generate realistic fraudulent transactions that maintain distributional symmetry with real fraud patterns, thereby preserving the structural and statistical balance of the original dataset. Synthetic fraud samples are merged with real data to form augmented training sets that restore the symmetry of class representation. We evaluate Simple Recurrent Neural Network (RNN), Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU) classifiers, and a LightGBM model on a public dataset using stratified 5-fold validation and an independent hold-out test set. Models are compared using sensitivity, precision, F-measure(F1), and area under the precision–recall curve (PR-AUC), which reflects symmetry between detection and false-alarm trade-offs. Results show that CTGAN-based augmentation yields large and consistent gains across architectures. The best-performing configuration, CTGAN + LightGBM, attains sensitivity = 0.986, precision = 0.982, F1 = 0.984, and PR-AUC = 0.918 on the test data, substantially outperforming non-augmented baselines and recent methods. These findings indicate that conditional synthetic augmentation materially improves the detection of rare fraud modes while preserving low false-alarm rates, demonstrating the value of symmetry-aware data synthesis in classification under imbalance. We discuss generation-quality checks, risk of distributional shift, and deployment considerations. Future work will explore alternative generative models with explicit symmetry constraints and time-aware production evaluation. Full article
(This article belongs to the Section Computer)
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16 pages, 2791 KB  
Article
Towards Stable Training of Complex-Valued Physics-Informed Neural Networks: A Holomorphic Initialization Approach
by Andrei-Ionuț Mohuț and Călin-Adrian Popa
Mathematics 2026, 14(3), 435; https://doi.org/10.3390/math14030435 - 27 Jan 2026
Abstract
This work introduces a new initialization scheme for complex-valued layers in physics-informed neural networks that use holomorphic activation functions. The proposed method is derived empirically by estimating the activation and gradient gains specific to complex-valued tanh and sigmoid functions through Monte Carlo simulations. [...] Read more.
This work introduces a new initialization scheme for complex-valued layers in physics-informed neural networks that use holomorphic activation functions. The proposed method is derived empirically by estimating the activation and gradient gains specific to complex-valued tanh and sigmoid functions through Monte Carlo simulations. These estimates are then used to formulate variance-preserving initialization rules. The effectiveness of these formulas is evaluated on several second-order complex-valued ordinary differential equations derived from the Helmholtz equation, a fundamental model in wave theory and theoretical physics. Comparative experiments show that complex-valued neural solvers initialized with the proposed method outperform traditional real-valued physics-informed neural networks in terms of both accuracy and training dynamics. Full article
(This article belongs to the Special Issue Machine Learning: Mathematical Foundations and Applications)
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23 pages, 2393 KB  
Article
Information-Theoretic Intrinsic Motivation for Reinforcement Learning in Combinatorial Routing
by Ruozhang Xi, Yao Ni and Wangyu Wu
Entropy 2026, 28(2), 140; https://doi.org/10.3390/e28020140 - 27 Jan 2026
Abstract
Intrinsic motivation provides a principled mechanism for driving exploration in reinforcement learning when external rewards are sparse or delayed. A central challenge, however, lies in defining meaningful novelty signals in high-dimensional and combinatorial state spaces, where observation-level density estimation and prediction-error heuristics often [...] Read more.
Intrinsic motivation provides a principled mechanism for driving exploration in reinforcement learning when external rewards are sparse or delayed. A central challenge, however, lies in defining meaningful novelty signals in high-dimensional and combinatorial state spaces, where observation-level density estimation and prediction-error heuristics often become unreliable. In this work, we propose an information-theoretic framework for intrinsically motivated reinforcement learning grounded in the Information Bottleneck principle. Our approach learns compact latent state representations by explicitly balancing the compression of observations and the preservation of predictive information about future state transitions. Within this bottlenecked latent space, intrinsic rewards are defined through information-theoretic quantities that characterize the novelty of state–action transitions in terms of mutual information, rather than raw observation dissimilarity. To enable scalable estimation in continuous and high-dimensional settings, we employ neural mutual information estimators that avoid explicit density modeling and contrastive objectives based on the construction of positive–negative pairs. We evaluate the proposed method on two representative combinatorial routing problems, the Travelling Salesman Problem and the Split Delivery Vehicle Routing Problem, formulated as Markov decision processes with sparse terminal rewards. These problems serve as controlled testbeds for studying exploration and representation learning under long-horizon decision making. Experimental results demonstrate that the proposed information bottleneck-driven intrinsic motivation improves exploration efficiency, training stability, and solution quality compared to standard reinforcement learning baselines. Full article
(This article belongs to the Special Issue The Information Bottleneck Method: Theory and Applications)
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