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Symmetry
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Symmetries in Machine Learning and Artificial Intelligence
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Symmetries in Machine Learning and Artificial Intelligence

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Computer".

Deadline for manuscript submissions: 31 May 2026 | Viewed by 2781

Special Issue Editors

Dr. Rajesh Natarajan

E-Mail Website
Guest Editor
Faculty of Information Technology, College of Computing and Information Sciences, University of Technology and Applied Sciences-Shinas, Shinas 324, Oman
Interests: big data analytics; blockchain technology; machine learning; AI
Prof. Dr. Francesco Flammini

E-Mail Website
Guest Editor
1. Division of Product Realisation, School of Innovation, Design and Engineering, Mälardalen University, 72123 Västerås, Sweden
2. Dalle Molle Institute for Artificial Intelligence, University of Applied Sciences and Arts of Southern Switzerland, 6928 Manno, Switzerland
Interests: resilient cyber‒physical systems; trustworthy artificial intelligence; trustworthy autonomous systems; data science
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Symmetries are crucial in Machine Learning (ML) and Artificial Intelligence (AI), improving model efficiency and generalization. Symmetries in data and models, such as rotational, translational, or scale invariance, allow algorithms to identify patterns regardless of orientation or scale. By incorporating symmetry, AI models prioritize important features, reducing complexity and improving performance. Symmetries are essential in various domains, including image recognition, speech processing, natural language processing, robotics, computer vision, reinforcement learning, neural networks, optimization, pattern recognition, and data mining. Convolutional neural networks (CNNs) utilize spatial invariance for object detection, leading to faster and more accurate results. Understanding symmetry is key to creating efficient, scalable, robust ML and AI systems.

Dr. Rajesh Natarajan
Prof. Dr. Francesco Flammini
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 250 words) can be sent to the Editorial Office for assessment.

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. Symmetry is an international peer-reviewed open access monthly 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 2400 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

  • symmetries
  • machine learning (ML)
  • artificial intelligence (AI)
  • model efficiency
  • generalization
  • pattern recognition
  • feature prioritization
  • complexity reduction
  • performance improvement
  • image recognition
  • speech processing
  • natural language processing (NLP)
  • robotics
  • computer vision
  • convolutional neural networks (CNNs)
  • object detection

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

Published Papers (3 papers)

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Research

22 pages, 22314 KB  
Article
A Novel Two-Level Entropy-Weighted Fuzzy C-Means Algorithm and Its Application for Classifying Urban Patterns by Residential Building Characteristics
by Rosa Cafaro, Barbara Cardone and Ferdinando Di Martino
Symmetry 2026, 18(5), 807; https://doi.org/10.3390/sym18050807 - 8 May 2026
Viewed by 143
Abstract
In this work, a novel entropy-weighted fuzzy c-means variation, referred to as Group-based Entropy Weighted Fuzzy C-Means (GEWFCM), is proposed. This variation introduces a semantic level of partitioning of features into groups. This approach enables the provision of optimal semantic meaning to the [...] Read more.
In this work, a novel entropy-weighted fuzzy c-means variation, referred to as Group-based Entropy Weighted Fuzzy C-Means (GEWFCM), is proposed. This variation introduces a semantic level of partitioning of features into groups. This approach enables the provision of optimal semantic meaning to the clusters, thereby capturing the intrinsic structure of the features, which are naturally grouped into homogeneous semantic sets; the weights are independent of the clusters. The cluster weights provide a direct measure of the importance of each group, determining which dimensions of the phenomenon are relevant, and the intragroup weights determine the most relevant features within a group. Additionally, GEWFCM is computationally more efficient than other cluster-specific weighted fuzzy clustering algorithms, due to the independence of the weights from the clusters. The efficacy of the method was assessed by evaluating census data from 16 Italian cities, with the objective of partitioning urban settlements based on characteristics of residential buildings, including construction technique, period, number of floors, and state of conservation. The findings suggest that the proposed algorithm effectively captures the semantic meaning of clusters. In addition, a comparative analysis between GEWFCM and the well-known Entropy Weighted Fuzzy C-Means (EWFCM) algorithm showed that, although both algorithms provide high similarity of results for all case studies, GEWFCM is significantly faster. Full article
(This article belongs to the Special Issue Symmetries in Machine Learning and Artificial Intelligence)
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29 pages, 5479 KB  
Article
Hybrid Machine Learning for Optimal Design of Piezoelectric Diaphragm Energy Harvesters Using Modified Grey Wolf Optimization
by Nitin Yadav, Govind Vashishtha, Sumika Chauhan and Rajesh Kumar
Symmetry 2026, 18(4), 608; https://doi.org/10.3390/sym18040608 - 3 Apr 2026
Viewed by 421
Abstract
This study addresses the critical need for sustainable energy by optimizing diaphragm-type piezoelectric elements for efficient waste vibration energy harvesting. Traditional experimental optimization of complex, non-linear design parameters including applied load, tapper diameter, and support structures is often resource-intensive and time-consuming. To overcome [...] Read more.
This study addresses the critical need for sustainable energy by optimizing diaphragm-type piezoelectric elements for efficient waste vibration energy harvesting. Traditional experimental optimization of complex, non-linear design parameters including applied load, tapper diameter, and support structures is often resource-intensive and time-consuming. To overcome these limitations, we developed a novel hybrid machine learning framework that seamlessly integrates an Artificial Neural Network (ANN) with a Modified Grey Wolf Optimization (mGWO) algorithm. The ANN was rigorously trained on experimental data using Bayesian Regularization, establishing itself as a robust and high-fidelity surrogate model capable of accurately predicting voltage output based on diverse input parameters, evidenced by an R-value close to 1. This predictive model subsequently served as the fitness function for the mGWO algorithm, which incorporated a non-linear control parameter to efficiently explore the multi-dimensional design space and effectively balance exploration with exploitation. The framework successfully identified the optimal configuration for maximizing voltage output, predicting a theoretical maximum of approximately 70.67 V. This optimal setup notably involved a high applied load of 100 N, the 6CA multi-pointed tapper configuration, and the three-support boundary condition, which is consistent with the experimentally validated results. The computational findings demonstrated excellent agreement with empirical results while providing significantly higher resolution for design insights. This validated, predictive tool offers a substantial advancement for the future scaling and design optimization of piezoelectric energy harvesters, minimizing the need for extensive physical prototyping and ensuring efficient stress transfer without mechanical failure. Full article
(This article belongs to the Special Issue Symmetries in Machine Learning and Artificial Intelligence)
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43 pages, 4725 KB  
Article
Graph-FEM/ML Framework for Inverse Load Identification in Thick-Walled Hyperelastic Pressure Vessels
by Nasser Firouzi, Ramy M. Hafez, Kareem N. Salloomi, Mohamed A. Abdelkawy and Raja Rizwan Hussain
Symmetry 2025, 17(12), 2021; https://doi.org/10.3390/sym17122021 - 23 Nov 2025
Cited by 3 | Viewed by 1246
Abstract
The accurate identification of internal and external pressures in thick-walled hyperelastic vessels is a challenging inverse problem with significant implications for structural health monitoring, biomedical devices, and soft robotics. Conventional analytical and numerical approaches address the forward problem effectively but offer limited means [...] Read more.
The accurate identification of internal and external pressures in thick-walled hyperelastic vessels is a challenging inverse problem with significant implications for structural health monitoring, biomedical devices, and soft robotics. Conventional analytical and numerical approaches address the forward problem effectively but offer limited means for recovering unknown load conditions from observable deformations. In this study, we introduce a Graph-FEM/ML framework that couples high-fidelity finite element simulations with machine learning models to infer normalized internal and external pressures from measurable boundary deformations. A dataset of 1386 valid samples was generated through Latin Hypercube Sampling of geometric and loading parameters and simulated using finite element analysis with a Neo-Hookean constitutive model. Two complementary neural architectures were explored: graph neural networks (GNNs), which operate directly on resampled and feature-enriched boundary data, and convolutional neural networks (CNNs), which process image-based representations of undeformed and deformed cross-sections. The GNN models consistently achieved low root-mean-square errors (≈0.021) and stable correlations across training, validation, and test sets, particularly when augmented with displacement and directional features. In contrast, CNN models exhibited limited predictive accuracy: quarter-section inputs regressed toward mean values, while full-ring and filled-section inputs improved after Bayesian optimization but remained inferior to GNNs, with higher RMSEs (0.023–0.030) and modest correlations (R2). To the best of our knowledge, this is the first work to combine boundary deformation observations with graph-based learning for inverse load identification in hyperelastic vessels. The results highlight the advantages of boundary-informed GNNs over CNNs and establish a reproducible dataset and methodology for future investigations. This framework represents an initial step toward a new direction in mechanics-informed machine learning, with the expectation that future research will refine and extend the approach to improve accuracy, robustness, and applicability in broader engineering and biomedical contexts. Full article
(This article belongs to the Special Issue Symmetries in Machine Learning and Artificial Intelligence)
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