Recent Advances of Computational and Mathematical Applications in Deep Learning

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (30 July 2024) | Viewed by 3160

Special Issue Editors


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Guest Editor
Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000 Novi Sad, Serbia
Interests: artificial intelligence; machine learning; deep learning; speech recognition; human–computer interaction

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Guest Editor
Mathematical Institute of the Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11001 Belgrade, Serbia
Interests: fractional calculus; machine learning; pattern recognition; image processing

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Guest Editor
Faculty of Information Technology, Alfa BK University, Palmira Toljatija 3, 11070 Novi Beograd, Serbia
Interests: computer vision; shape descriptors; image processing; E-learning

Special Issue Information

Dear Colleagues,

The Special Issue is aimed toward recent theoretical advances and practical computational and mathematical applications in deep learning. The editors would like to provide an opportunity to present state-of-the-art research on the development of cutting-edge neural network model architectures, the understanding, explainability, and interpretability of deep learning models, their mathematical bias and fairness, robustness,  and ethical and societal regulations and considerations, including but not limited to subjects such as image recognition, retrieval, generation and processing, speech, speaker and emotion recognition and synthesis, style translation, generative adversarial models, reinforcement learning, transfer learning, natural language processing, attention mechanisms, transformer-based networks, sequence modelling, data augmentation, time series analysis, biomedical and agricultural applications, computer vision, etc. The Special Issue will address the following non-exhaustive list of topics (however, we also encourage other ideas in the scope of this issue): 

deep learning theory and applications; computational and mathematical applications (information theory; optimization algorithms; probability and statistics; functional analysis; signal processing; graph theory; medical; pharmaceutical; agricultural; automotive; educational; and financial applications; genomic sequence analysis; gaming; etc.); convolutional neural networks; recurrent neural networks; long short-term memory networks; reinforcement learning; transfer learning; autoencoders; attention mechanisms; generative models; transformers; natural language processing; speech and audio processing; object recognition; style transform; scene understanding; classification and clustering; unsupervised; semi-supervised; supervised; and self-supervised learning; explainable AI. 

We hope that the initiative will be attractive to deep learning researchers and experts in mathematical and computational deep learning applications, and we highly encourage you to submit your current research for peer review before the deadline.

Dr. Branislav Popovic
Dr. Marko Janev
Dr. Lazar Kopanja
Guest Editors

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Keywords

  • deep learning
  • neural networks
  • generative models
  • autoencoders
  • reinforcement learning
  • transfer learning
  • style translation
  • object recognition
  • signal processing
  • optimization

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Published Papers (3 papers)

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Research

18 pages, 1135 KiB  
Article
Applications of Fuzzy Logic and Probabilistic Neural Networks in E-Service for Malware Detection
by Kristijan Kuk, Aleksandar Stanojević, Petar Čisar, Brankica Popović, Mihailo Jovanović, Zoran Stanković and Olivera Pronić-Rančić
Axioms 2024, 13(9), 624; https://doi.org/10.3390/axioms13090624 - 12 Sep 2024
Viewed by 484
Abstract
The key point in the process of agent-based management in e-service for malware detection (according to accuracy criteria) is a decision-making process. To determine the optimal e-service for malware detection, two concepts were investigated: Fuzzy Logic (FL) and Probabilistic Neural Networks (PNN). In [...] Read more.
The key point in the process of agent-based management in e-service for malware detection (according to accuracy criteria) is a decision-making process. To determine the optimal e-service for malware detection, two concepts were investigated: Fuzzy Logic (FL) and Probabilistic Neural Networks (PNN). In this study, three evolutionary variants of fuzzy partitioning, including regular, hierarchical fuzzy partitioning, and k-means, were used to automatically process the design of the fuzzy partition. Also, this study demonstrates the application of a feature selection method to reduce the dimensionality of the data by removing irrelevant features to create fuzzy logic in a dataset. The behaviors of malware are analyzed by fuzzifying relevant features for pattern recognition. The Apriori algorithm was applied to the fuzzified features to find the fuzzy-based rules, and these rules were used for predicting the output of malware detection e-services. Probabilistic neural networks were also used to find the ideal agent-based model for numerous classification problems. The numerical results show that the agent-based management performances trained with the clustering method achieve an accuracy of 100% with the PNN-MCD model. This is followed by the FL model, which classifies on the basis of linguistic variables and achieves an average accuracy of 82%. Full article
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20 pages, 17123 KiB  
Article
A Physics-Informed Neural Network Based on the Boltzmann Equation with Multiple-Relaxation-Time Collision Operators
by Zhixiang Liu, Chenkai Zhang, Wenhao Zhu and Dongmei Huang
Axioms 2024, 13(9), 588; https://doi.org/10.3390/axioms13090588 - 29 Aug 2024
Viewed by 547
Abstract
The Boltzmann equation with multiple-relaxation-time (MRT) collision operators has been widely employed in kinetic theory to describe the behavior of gases and liquids at the macro-level. Given the successful development of deep learning and the availability of data analytic tools, it is a [...] Read more.
The Boltzmann equation with multiple-relaxation-time (MRT) collision operators has been widely employed in kinetic theory to describe the behavior of gases and liquids at the macro-level. Given the successful development of deep learning and the availability of data analytic tools, it is a feasible idea to try to solve the Boltzmann-MRT equation using a neural network-based method. Based on the canonical polyadic decomposition, a new physics-informed neural network describing the Boltzmann-MRT equation, named the network for MRT collision (NMRT), is proposed in this paper for solving the Boltzmann-MRT equation. The method of tensor decomposition in the Boltzmann-MRT equation is utilized to combine the collision matrix with discrete distribution functions within the moment space. Multiscale modeling is adopted to accelerate the convergence of high frequencies for the equations. The micro–macro decomposition method is applied to improve learning efficiency. The problem-dependent loss function is proposed to balance the weight of the function for different conditions at different velocities. These strategies will greatly improve the accuracy of the network. The numerical experiments are tested, including the advection–diffusion problem and the wave propagation problem. The results of the numerical simulation show that the network-based method can obtain a measure of accuracy at O103. Full article
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21 pages, 731 KiB  
Article
Computing Transiting Exoplanet Parameters with 1D Convolutional Neural Networks
by Santiago Iglesias Álvarez, Enrique Díez Alonso, María Luisa Sánchez Rodríguez, Javier Rodríguez Rodríguez, Saúl Pérez Fernández and Francisco Javier de Cos Juez
Axioms 2024, 13(2), 83; https://doi.org/10.3390/axioms13020083 - 26 Jan 2024
Cited by 1 | Viewed by 1334
Abstract
The transit method allows the detection and characterization of planetary systems by analyzing stellar light curves. Convolutional neural networks appear to offer a viable solution for automating these analyses. In this research, two 1D convolutional neural network models, which work with simulated light [...] Read more.
The transit method allows the detection and characterization of planetary systems by analyzing stellar light curves. Convolutional neural networks appear to offer a viable solution for automating these analyses. In this research, two 1D convolutional neural network models, which work with simulated light curves in which transit-like signals were injected, are presented. One model operates on complete light curves and estimates the orbital period, and the other one operates on phase-folded light curves and estimates the semimajor axis of the orbit and the square of the planet-to-star radius ratio. Both models were tested on real data from TESS light curves with confirmed planets to ensure that they are able to work with real data. The results obtained show that 1D CNNs are able to characterize transiting exoplanets from their host star’s detrended light curve and, furthermore, reducing both the required time and computational costs compared with the current detection and characterization algorithms. Full article
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