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Mathematics
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Machine Learning Methods and Mathematical Modeling with Applications
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Machine Learning Methods and Mathematical Modeling with Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: 30 September 2025 | Viewed by 8179

Special Issue Editors

Prof. Dr. Jian Luo

E-Mail Website
Guest Editor
International Business School, Hainan University, Haikou 570228, China
Interests: machine learning methods with applications to operations management; energy forecasting; financial risk assessment and other fields; forecasting theories and methods; nonlinear optimization; data mining and artificial intelligence
Dr. Zheming Gao

E-Mail Website
Guest Editor
College of Information Science and Engineering, Northeastern University, Shenyang 110819, China
Interests: machine learning; optimization theory; healthcare
Dr. Xin Yan

E-Mail Website
Guest Editor
School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai 201620, China
Interests: machine learning; optimization methods with applications

Special Issue Information

Dear Colleagues,

Machine learning methods (including support vector machine, deep learning and ensemble learning) and mathematical modeling have attracted much attention in recent years. In particular, many machine learning models are formulated as nonlinear optimization models, and mathematical modeling methods have employed machine learning to gain outstanding results. For handling large-scaled real-world data, it is also necessary to develop optimization algorithms for implementing well-known and emerging machine learning methods. Moreover, machine learning methods and mathematical modeling exhibit impressive performances in various real-world applications, including demand and price forecasting, electric load forecasting, scheduling optimization for emergency materials, etc. To this end, this Special Issue focuses on the application of current advances in machine learning and optimization methods for real-world problems, especially for industrial engineering and management science. This Special Issue will provide a platform for researchers from academia and industry to present their novel and unpublished work in the domain of machine learning and mathematical modeling, allowing us to foster future interesting research in related emerging fields.

Prof. Dr. Jian Luo
Dr. Zheming Gao
Dr. Xin Yan
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • machine learning
  • mathematical modeling
  • industrial engineering
  • forecasting methods
  • management science

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Published Papers (10 papers)

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Research

19 pages, 6775 KiB  
Article
Multi-Scale TsMixer: A Novel Time-Series Architecture for Predicting A-Share Stock Index Futures
by Zhiyuan Pei, Jianqi Yan, Jin Yan, Bailing Yang and Xin Liu
Mathematics 2025, 13(9), 1415; https://doi.org/10.3390/math13091415 - 25 Apr 2025
Viewed by 137
Abstract
With the advancement of deep learning, its application in financial market forecasting has become a research hotspot. This paper proposes an innovative Multi-Scale TsMixer model for predicting stock index futures in the A-share market, covering SSE50, CSI300, and CSI500. By integrating Multi-Scale time-series [...] Read more.
With the advancement of deep learning, its application in financial market forecasting has become a research hotspot. This paper proposes an innovative Multi-Scale TsMixer model for predicting stock index futures in the A-share market, covering SSE50, CSI300, and CSI500. By integrating Multi-Scale time-series features across the short, medium, and long term, the model effectively captures market fluctuations and trends. Moreover, since stock index futures reflect the collective movement of their constituent stocks, we introduce a novel approach: predicting individual constituent stocks and merging their forecasts using three fusion strategies (average fusion, weighted fusion, and weighted decay fusion). Experimental results demonstrate that the weighted decay fusion method significantly improves the prediction accuracy and stability, validating the effectiveness of Multi-Scale TsMixer. Full article
(This article belongs to the Special Issue Machine Learning Methods and Mathematical Modeling with Applications)
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20 pages, 1581 KiB  
Article
Heterogeneous Spillover Networks and Spatial–Temporal Dynamics of Systemic Risk Transmission: Evidence from G20 Financial Risk Stress Index
by Xing Wang, Jiahui Zhang, Xiaolong Chen, Hongfeng Zhang, Cora Un In Wong and Thomas Chan
Mathematics 2025, 13(8), 1353; https://doi.org/10.3390/math13081353 - 21 Apr 2025
Viewed by 159
Abstract
With the continuous integration of globalization and financial markets, the linkage of global financial risks has increased significantly. This study examines the risk spillover effects and transmission dynamics among the financial markets in G20 countries, which together represent over 80% of global GDP. [...] Read more.
With the continuous integration of globalization and financial markets, the linkage of global financial risks has increased significantly. This study examines the risk spillover effects and transmission dynamics among the financial markets in G20 countries, which together represent over 80% of global GDP. With increasing globalization and the interconnectedness of financial markets, understanding risk transmission mechanisms has become critical for effective risk management. Previous research has primarily focused on price volatility to measure financial risks, often overlooking other critical dimensions such as liquidity, credit, and operational risks. This paper addresses this gap by utilizing the vector autoregressive (VAR) model to explore the spillover effects and the temporal and spatial characteristics of risk transmission. Specifically, we employ global and local Moran indices to analyze spatial dependencies across markets. Our findings reveal that the risk linkages among the G20 financial markets exhibit significant time-varying characteristics, with spatial risk distribution showing weaker dispersion. By constructing a comprehensive financial risk index system and applying a network-based spillover analysis, this study enhances the measurement of financial market risk and uncovers the complex transmission pathways between sub-markets and countries. These results not only deepen our understanding of global financial market dynamics but also provide valuable insights for the design of effective cross-border financial regulatory policies. The study’s contributions lie in enriching the empirical literature on multi-dimensional financial risks, advancing policy formulation by identifying key risk transmission channels, and supporting international risk management strategies through the detection and mitigation of potential contagion effects. Full article
(This article belongs to the Special Issue Machine Learning Methods and Mathematical Modeling with Applications)
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23 pages, 3160 KiB  
Article
CLA-BERT: A Hybrid Model for Accurate Encrypted Traffic Classification by Combining Packet and Byte-Level Features
by Hong Huang, Yinghang Zhou and Feng Jiang
Mathematics 2025, 13(6), 973; https://doi.org/10.3390/math13060973 - 15 Mar 2025
Viewed by 449
Abstract
Encrypted traffic classification is crucial for network security and management, enabling applications like QoS control and malware detection. However, the emergence of new encryption protocols, particularly TLS 1.3, poses challenges for traditional methods. To address this, we propose CLA-BERT, which integrates packet-level and [...] Read more.
Encrypted traffic classification is crucial for network security and management, enabling applications like QoS control and malware detection. However, the emergence of new encryption protocols, particularly TLS 1.3, poses challenges for traditional methods. To address this, we propose CLA-BERT, which integrates packet-level and byte-level features. Unlike existing methods, CLA-BERT efficiently fuses these features using a multi-head attention mechanism, enhancing accuracy and robustness. It leverages BERT for packet-level feature extraction, while CNN and BiLSTM capture local and global dependencies in byte-level features. Experimental results show that CLA-BERT is highly robust in small-sample scenarios, achieving F1 scores of 93.51%, 94.79%, 97.10%, 97.78%, and 98.09% under varying data sizes. Moreover, CLA-BERT demonstrates outstanding performance across three encrypted traffic classification tasks, attaining F1 scores of 99.02%, 99.49%, and 97.78% for VPN service classification, VPN application classification, and TLS 1.3 application classification, respectively. Notably, in TLS 1.3 classification, it surpasses state-of-the-art methods with a 0.47% improvement in F1 score. These results confirm CLA-bert’s effectiveness and generalization capability, making it well-suited for encrypted traffic classification. Full article
(This article belongs to the Special Issue Machine Learning Methods and Mathematical Modeling with Applications)
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16 pages, 3560 KiB  
Article
PRNet: A Priori Embedded Network for Real-World Blind Micro-Expression Recognition
by Xin Liu, Fugang Wang, Hui Zeng, Yile Chen, Liang Zheng and Junming Chen
Mathematics 2025, 13(5), 749; https://doi.org/10.3390/math13050749 - 25 Feb 2025
Viewed by 347
Abstract
Micro-expressions, fleeting and often unnoticed facial cues, hold the key to uncovering concealed emotions, offering significant implications for understanding emotions, cognition, and psychological processes. However, micro-expression information capture presents challenges due to its instantaneous and subtle nature. Furthermore, it is affected by unpredictable [...] Read more.
Micro-expressions, fleeting and often unnoticed facial cues, hold the key to uncovering concealed emotions, offering significant implications for understanding emotions, cognition, and psychological processes. However, micro-expression information capture presents challenges due to its instantaneous and subtle nature. Furthermore, it is affected by unpredictable degradation factors such as device performance and weather, and model degradation issues persist in real scenarios, and directly training deep networks or introducing image restoration networks yields unsatisfactory results, hindering the development of micro-expression recognition in real-world applications. This study aims to develop an advanced micro-expression recognition algorithm to promote the research of micro-expression applications in psychology. Firstly, Generative Adversarial Networks (GANs) are employed to build high-quality micro-expression generation models, which are then used as prior decoders to model micro-expression features. Subsequently, the GAN priors of deep neural networks are fine-tuned using low-quality facial micro-expression images. The designed micro-expression GAN module ensures that the generation of latent codes and noise inputs suitable for micro-expression GAN blocks from the deep and shallow features of deep neural networks. This approach controls the reconstruction of facial structure, local details, and accurate expressions to enhance the stability of subsequent recognition networks. Additionally, a Multi-Scale Dynamic Cross-Domain (MSCD) module is proposed to dynamically adjust the input of reconstructed features to different task representation layers. Doing so effectively integrates reconstructed features and improves the micro-expression recognition performance. Experimental results demonstrate that our method consistently achieves superior performance on multiple datasets, achieving particularly significant performance improvements in micro-expression recognition for severely degraded facial images in real scenarios. Full article
(This article belongs to the Special Issue Machine Learning Methods and Mathematical Modeling with Applications)
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29 pages, 10754 KiB  
Article
IPM-AgriGPT: A Large Language Model for Pest and Disease Management with a G-EA Framework and Agricultural Contextual Reasoning
by Yuqin Zhang, Qijie Fan, Xuan Chen, Min Li, Zeying Zhao, Fuzhong Li and Leifeng Guo
Mathematics 2025, 13(4), 566; https://doi.org/10.3390/math13040566 - 8 Feb 2025
Viewed by 966
Abstract
Traditional pest and disease management methods are inefficient, relying on agricultural experts or static resources, making it difficult to respond quickly to large-scale outbreaks and meet local needs. Although deep learning technologies have been applied in pest and disease management, challenges remain, such [...] Read more.
Traditional pest and disease management methods are inefficient, relying on agricultural experts or static resources, making it difficult to respond quickly to large-scale outbreaks and meet local needs. Although deep learning technologies have been applied in pest and disease management, challenges remain, such as the dependence on large amounts of manually labeled data and the limitations of dynamic reasoning. To address these challenges, this study proposes IPM-AgriGPT (Integrated Pest Management—Agricultural Generative Pre-Trained Transformer), a Chinese large language model specifically designed for pest and disease knowledge. The proposed Generation-Evaluation Adversarial (G-EA) framework is used to generate high-quality question–answer corpora and combined with Agricultural Contextual Reasoning Chain-of-Thought Distillation (ACR-CoTD) and low-rank adaptation (LoRA) techniques further optimizes the base model to build IPM-AgriGPT. During the evaluation phase, this study designed a specialized benchmark for the agricultural pest and disease domain, comprehensively assessing the performance of IPM-AgriGPT in pest management tasks. Experimental results show that IPM-AgriGPT achieved excellent evaluation scores in multiple tasks, demonstrating its great potential in agricultural intelligence and pest management. Full article
(This article belongs to the Special Issue Machine Learning Methods and Mathematical Modeling with Applications)
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17 pages, 2407 KiB  
Article
Price Prediction for Fresh Agricultural Products Based on a Boosting Ensemble Algorithm
by Nana Zhang, Qi An, Shuai Zhang and Huanhuan Ma
Mathematics 2025, 13(1), 71; https://doi.org/10.3390/math13010071 - 28 Dec 2024
Viewed by 1450
Abstract
The time series of agricultural prices exhibit brevity and considerable volatility. Considering that traditional time series models and machine learning models are facing challenges in making predictions with high accuracy and robustness, this paper proposes a Light gradient boosting machine model based on [...] Read more.
The time series of agricultural prices exhibit brevity and considerable volatility. Considering that traditional time series models and machine learning models are facing challenges in making predictions with high accuracy and robustness, this paper proposes a Light gradient boosting machine model based on the boosting ensemble learning algorithm to predict prices for three representative types of fresh agricultural products (bananas, beef, crucian carp). The prediction performance of the Light gradient boosting machine model is evaluated by comparing it against multiple benchmark models (ARIMA, decision tree, random forest, support vector machine, XGBoost, and artificial neural network) in terms of accuracy, generalizability, and robustness on different datasets and under different time windows. Among these models, the Light gradient boosting machine model is shown to have the highest prediction accuracy and the most stable performance across three different datasets under both long-term and short-term time windows. As the time window length increases, the Light gradient boosting machine model becomes more advantageous for effectively reducing error fluctuation, demonstrating better robustness. Consequently, the model proposed in this paper holds significant potential for forecasting fresh agricultural product prices, thereby facilitating the advancement of precision and sustainable farming practices. Full article
(This article belongs to the Special Issue Machine Learning Methods and Mathematical Modeling with Applications)
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21 pages, 4740 KiB  
Article
Multi-Scale Geometric Feature Extraction and Global Transformer for Real-World Indoor Point Cloud Analysis
by Yisheng Chen, Yu Xiao, Hui Wu, Chongcheng Chen and Ding Lin
Mathematics 2024, 12(23), 3827; https://doi.org/10.3390/math12233827 - 3 Dec 2024
Cited by 1 | Viewed by 1220
Abstract
Indoor point clouds often present significant challenges due to the complexity and variety of structures and high object similarity. The local geometric structure helps the model learn the shape features of objects at the detail level, while the global context provides overall scene [...] Read more.
Indoor point clouds often present significant challenges due to the complexity and variety of structures and high object similarity. The local geometric structure helps the model learn the shape features of objects at the detail level, while the global context provides overall scene semantics and spatial relationship information between objects. To address these challenges, we propose a novel network architecture, PointMSGT, which includes a multi-scale geometric feature extraction (MSGFE) module and a global Transformer (GT) module. The MSGFE module consists of a geometric feature extraction (GFE) module and a multi-scale attention (MSA) module. The GFE module reconstructs triangles through each point’s two neighbors and extracts detailed local geometric relationships by the triangle’s centroid, normal vector, and plane constant. The MSA module extracts features through multi-scale convolutions and adaptively aggregates features, focusing on both local geometric details and global semantic information at different scale levels, enhancing the understanding of complex scenes. The global Transformer employs a self-attention mechanism to capture long-range dependencies across the entire point cloud. The proposed method demonstrates competitive performance in real-world indoor scenarios, with a mIoU of 68.6% in semantic segmentation on S3DIS and OA of 86.4% in classification on ScanObjectNN. Full article
(This article belongs to the Special Issue Machine Learning Methods and Mathematical Modeling with Applications)
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22 pages, 2752 KiB  
Article
A Noisy Sample Selection Framework Based on a Mixup Loss and Recalibration Strategy
by Qian Zhang, De Yu, Xinru Zhou, Hanmeng Gong, Zheng Li, Yiming Liu and Ruirui Shao
Mathematics 2024, 12(15), 2389; https://doi.org/10.3390/math12152389 - 31 Jul 2024
Cited by 2 | Viewed by 1158
Abstract
Deep neural networks (DNNs) have achieved breakthrough progress in various fields, largely owing to the support of large-scale datasets with manually annotated labels. However, obtaining such datasets is costly and time-consuming, making high-quality annotation a challenging task. In this work, we propose an [...] Read more.
Deep neural networks (DNNs) have achieved breakthrough progress in various fields, largely owing to the support of large-scale datasets with manually annotated labels. However, obtaining such datasets is costly and time-consuming, making high-quality annotation a challenging task. In this work, we propose an improved noisy sample selection method, termed “sample selection framework”, based on a mixup loss and recalibration strategy (SMR). This framework enhances the robustness and generalization abilities of models. First, we introduce a robust mixup loss function to pre-train two models with identical structures separately. This approach avoids additional hyperparameter adjustments and reduces the need for prior knowledge of noise types. Additionally, we use a Gaussian Mixture Model (GMM) to divide the entire training set into labeled and unlabeled subsets, followed by robust training using semi-supervised learning (SSL) techniques. Furthermore, we propose a recalibration strategy based on cross-entropy (CE) loss to prevent the models from converging to local optima during the SSL process, thus further improving performance. Ablation experiments on CIFAR-10 with 50% symmetric noise and 40% asymmetric noise demonstrate that the two modules introduced in this paper improve the accuracy of the baseline (i.e., DivideMix) by 1.5% and 0.5%, respectively. Moreover, the experimental results on multiple benchmark datasets demonstrate that our proposed method effectively mitigates the impact of noisy labels and significantly enhances the performance of DNNs on noisy datasets. For instance, on the WebVision dataset, our method improves the top-1 accuracy by 0.7% and 2.4% compared to the baseline method. Full article
(This article belongs to the Special Issue Machine Learning Methods and Mathematical Modeling with Applications)
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17 pages, 287 KiB  
Article
Priority-Based Capacity Allocation for Hierarchical Distributors with Limited Production Capacity
by Jun Tong, Xiaotao Zhou and Lei Lei
Mathematics 2024, 12(14), 2237; https://doi.org/10.3390/math12142237 - 18 Jul 2024
Viewed by 944
Abstract
This paper studies the issue of capacity allocation in multi-rank distribution channel management, a topic that has been significantly overlooked in the existing literature. Departing from conventional approaches, hierarchical priority rules are introduced as constraints, and an innovative assignment integer programming model focusing [...] Read more.
This paper studies the issue of capacity allocation in multi-rank distribution channel management, a topic that has been significantly overlooked in the existing literature. Departing from conventional approaches, hierarchical priority rules are introduced as constraints, and an innovative assignment integer programming model focusing on capacity selection is formulated. This model goes beyond merely optimizing profit or cost, aiming instead to enhance the overall business orientation of the firm. We propose a greedy algorithm and a priority-based binary particle swarm optimization (PB-BPSO) algorithm. Our numerical results indicate that both algorithms exhibit strong optimization capabilities and rapid solution speeds, especially in large-scale scenarios. Moreover, the model is validated through empirical tests using real-world data. The results demonstrate that the proposed approaches can provide actionable strategies to operators, in practice. Full article
(This article belongs to the Special Issue Machine Learning Methods and Mathematical Modeling with Applications)
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20 pages, 784 KiB  
Article
Fractional Adaptive Resonance Theory (FRA-ART): An Extension for a Stream Clustering Method with Enhanced Data Representation
by Yingwen Zhu, Ping Li, Qian Zhang, Yi Zhu and Jun Yang
Mathematics 2024, 12(13), 2049; https://doi.org/10.3390/math12132049 - 30 Jun 2024
Viewed by 923
Abstract
Clustering data streams has become a hot topic and has been extensively applied to many real-world applications. Compared with traditional clustering, data stream clustering is more challenging. Adaptive Resonance Theory (ART) is a powerful (online) clustering method, it can automatically adjust to learn [...] Read more.
Clustering data streams has become a hot topic and has been extensively applied to many real-world applications. Compared with traditional clustering, data stream clustering is more challenging. Adaptive Resonance Theory (ART) is a powerful (online) clustering method, it can automatically adjust to learn both abstract and concrete information, and can respond to arbitrarily large non-stationary databases while having fewer parameters, low computational complexity, and less sensitivity to noise, but its limited feature representation hinders its application to complex data streams. In this paper, considering its advantages and disadvantages, we present its flexible extension for stream clustering, called fractional adaptive resonance theory (FRA-ART). FRA-ART enhances data representation by fractionally exponentiating input features using self-interactive basis functions (SIBFs) and incorporating feature interaction through cross-interactive basis functions (CIBFs) at the cost only of introducing an additionally adjustable fractional order. Both SIBFs and CIBFs can be precomputed using existing algorithms, making FRA-ART easily adaptable to any ART variant. Finally, comparative experiments on five data stream datasets, including artificial and real-world datasets, demonstrate FRA-ART’s superior robustness and comparable or improved performance in terms of accuracy, normalized mutual information, rand index, and cluster stability compared to ART and the state-of-the-art G-Stream algorithm. Full article
(This article belongs to the Special Issue Machine Learning Methods and Mathematical Modeling with Applications)
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