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Mathematics
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Advances in Machine Learning and Graph Neural Networks
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Advances in Machine Learning and Graph Neural Networks

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 31 January 2026 | Viewed by 1758

Special Issue Editors

Prof. Dr. Marco Antonio Aceves-Fernández

E-Mail Website
Guest Editor
Facultad de Ingeniería, Universidad Autónoma de Querétaro, Querétaro 76010, Mexico
Interests: artificial intelligence; machine learning; data processing; data science; time series forecasting
Prof. Dr. Jesus Carlos Pedraza-Ortega

E-Mail Website
Guest Editor
Facultad de Ingeniería, Universidad Autónoma de Querétaro, Querétaro 76010, Mexico
Interests: image processing; 3D reconstruction; medical image processing; machine learning; deep learning
Dr. Sebastián Salazar-Colores

E-Mail Website
Guest Editor
Centro de Investigaciones en Óptica (CIO), León 37150, Mexico
Interests: artificial intelligence; machine learning; computer vision; medical signal processing; convolutional neural networks

Special Issue Information

Dear Colleagues,

We are delighted to invite you to participate in our Special Issue, which is exclusively dedicated to exploring cutting-edge developments in Machine Learning (ML) and Graph Neural Networks (GNNs), particularly in comprehensive engineering solutions. This issue explores how these advanced technologies, especially ML models and GNNs, are revolutionizing the engineering sector by enabling sophisticated predictions and decision-making processes and enhancing visual analysis through pattern detection.

Integrating ML and GNNs into engineering practices has yielded remarkable outcomes in today’s technologically saturated world. These advancements have paved the way for creating holistic solutions by optimizing processes, refining the design and functionality of electrical and electronic systems, and ultimately enhancing various engineering disciplines. ML and GNNs’ influence spans critical engineering domains, including but not limited to health-related engineering such as biomedical applications, energy system efficiencies, and more. Our Special Issue seeks to assemble the latest research, case studies, and innovative projects that underscore the transformative role of ML and GNNs in engineering solutions.

We encourage submissions demonstrating ML and GNNs’ innovative potential in addressing complex engineering problems. Your contributions will play a crucial role in shaping the future of engineering through the lens of these advanced technologies.

Prof. Dr. Marco Antonio Aceves-Fernández
Prof. Dr. Jesus Carlos Pedraza-Ortega
Dr. Sebastián Salazar-Colores
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 (ML)
  • graph neural networks (GNNs)
  • engineering solutions
  • optimization
  • biomedical applications
  • decision-making processes
  • visual analysis
  • pattern detection
  • electrical systems
  • energy system efficiencies

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

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37 pages, 1654 KiB  
Article
CISMN: A Chaos-Integrated Synaptic-Memory Network with Multi-Compartment Chaotic Dynamics for Robust Nonlinear Regression
by Yaser Shahbazi, Mohsen Mokhtari Kashavar, Abbas Ghaffari, Mohammad Fotouhi and Siamak Pedrammehr
Mathematics 2025, 13(9), 1513; https://doi.org/10.3390/math13091513 - 4 May 2025
Viewed by 317
Abstract
Modeling complex, non-stationary dynamics remains challenging for deterministic neural networks. We present the Chaos-Integrated Synaptic-Memory Network (CISMN), which embeds controlled chaos across four modules—Chaotic Memory Cells, Chaotic Plasticity Layers, Chaotic Synapse Layers, and a Chaotic Attention Mechanism—supplemented by a logistic-map learning-rate schedule. Rigorous [...] Read more.
Modeling complex, non-stationary dynamics remains challenging for deterministic neural networks. We present the Chaos-Integrated Synaptic-Memory Network (CISMN), which embeds controlled chaos across four modules—Chaotic Memory Cells, Chaotic Plasticity Layers, Chaotic Synapse Layers, and a Chaotic Attention Mechanism—supplemented by a logistic-map learning-rate schedule. Rigorous stability analyses (Lyapunov exponents, boundedness proofs) and gradient-preservation guarantees underpin our design. In experiments, CISMN-1 on a synthetic acoustical regression dataset (541 samples, 22 features) achieved R2 = 0.791 and RMSE = 0.059, outpacing physics-informed and attention-augmented baselines. CISMN-4 on the PMLB sonar benchmark (208 samples, 60 bands) attained R2 = 0.424 and RMSE = 0.380, surpassing LSTM, memristive, and reservoir models. Across seven standard regression tasks with 5-fold cross-validation, CISMN led on diabetes (R2 = 0.483 ± 0.073) and excelled in high-dimensional, low-sample regimes. Ablations reveal a scalability–efficiency trade-off: lightweight variants train in <10 s with >95% peak accuracy, while deeper configurations yield marginal gains. CISMN sustains gradient norms (~2300) versus LSTM collapse (<3), and fixed-seed protocols ensure <1.2% MAE variation. Interpretability remains challenging (feature-attribution entropy ≈ 2.58 bits), motivating future hybrid explanation methods. CISMN recasts chaos as a computational asset for robust, generalizable modeling across scientific, financial, and engineering domains. Full article
(This article belongs to the Special Issue Advances in Machine Learning and Graph Neural Networks)
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22 pages, 1432 KiB  
Article
An Improved Summary–Explanation Method for Promoting Trust Through Greater Support with Application to Credit Evaluation Systems
by Chen Peng and Tianci He
Mathematics 2025, 13(8), 1305; https://doi.org/10.3390/math13081305 - 16 Apr 2025
Viewed by 176
Abstract
Decision support systems are being increasingly applied in critical decision-making domains such as healthcare and criminal justice. Trust in these systems requires transparency and explainability. Among the forms of explanation, globally consistent summary–explanation (SE) is a rule-based local explanation offering useful global information [...] Read more.
Decision support systems are being increasingly applied in critical decision-making domains such as healthcare and criminal justice. Trust in these systems requires transparency and explainability. Among the forms of explanation, globally consistent summary–explanation (SE) is a rule-based local explanation offering useful global information and 100% dataset consistency. However, globally consistent SEs with limited complexity often have a small amount of support, making them unconvincing. To improve the support of SEs, this paper introduces the q-consistent SE, trading slightly lower consistency for greater support. The challenge is solving the maximizing support with the q-consistency (MSqC) problem, which is more complex than maximizing support for global consistency, leading to extended solution times using standard solvers. To enhance efficiency, the paper proposes a weighted column sampling (WCS) method, using simplified increase support (SIS) scores to create and solve smaller problem instances. Experiments on credit evaluation scenarios confirm that the SIS-based WCS method on MSqC problems improves scalability and yields SEs with greater support and better global extrapolation effectiveness. Full article
(This article belongs to the Special Issue Advances in Machine Learning and Graph Neural Networks)
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32 pages, 4118 KiB  
Article
Mutual-Energy Inner Product Optimization Method for Constructing Feature Coordinates and Image Classification in Machine Learning
by Yuanxiu Wang
Mathematics 2024, 12(23), 3872; https://doi.org/10.3390/math12233872 - 9 Dec 2024
Viewed by 885
Abstract
As a key task in machine learning, data classification is essential to find a suitable coordinate system to represent the data features of different classes of samples. This paper proposes the mutual-energy inner product optimization method for constructing a feature coordinate system. First, [...] Read more.
As a key task in machine learning, data classification is essential to find a suitable coordinate system to represent the data features of different classes of samples. This paper proposes the mutual-energy inner product optimization method for constructing a feature coordinate system. First, by analyzing the solution space and eigenfunctions of the partial differential equations describing a non-uniform membrane, the mutual-energy inner product is defined. Second, by expressing the mutual-energy inner product as a series of eigenfunctions, it shows the significant advantage of enhancing low-frequency features and suppressing high-frequency noise, compared to the Euclidean inner product. And then, a mutual-energy inner product optimization model is built to extract the data features, and the convexity and concavity properties of its objective function are discussed. Next, by combining the finite element method, a stable and efficient sequential linearization algorithm is constructed to solve the optimization model. This algorithm only solves positive definite symmetric matrix equations and linear programming with a few constraints, and its vectorized implementation is discussed. Finally, the mutual-energy inner product optimization method is used to construct feature coordinates, and multi-class Gaussian classifiers are trained on the MINST training set. Good prediction results of the Gaussian classifiers are achieved on the MINST test set. Full article
(This article belongs to the Special Issue Advances in Machine Learning and Graph Neural Networks)
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