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Mathematics
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Neural Networks and Their Applications
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Neural Networks and Their Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Network Science".

Deadline for manuscript submissions: 30 June 2024 | Viewed by 15770

Special Issue Editor

Prof. Dr. Mario Muñoz Organero

E-Mail Website
Guest Editor
Telecommunications Engineering, Carlos III University of Madrid, 28911 Leganes, Spain
Interests: neural networks; artificial intelligence; computer supported learning; sensor-based applications
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Neural-network-based models have experienced continuous growth in complexity over the last few decades. The combination of high-performance computing resources (incorporating FPGAs and GPUs), distributed architectures and cloud computing, the availability of big data sources and datasets, and the increasing interest in the research community have created an unprecedented ecosystem to train complex models and apply them to solve many different real-life problems. From personal health recommenders, autonomous vehicles, and market sentiment analyses to natural language recognition or image recognition, different neural-network-based models are able to solve complex classification and regression problems. Deep neural networks have been developed to increase the ability to learn patterns from all kinds of data sources. Attention mechanisms have been able to go further in accuracy in combination with deep neural network based machine learning models.

This Special Issue aims to collect publications that will showcase the power and diversity of novel neural networks and how they can be applied to solve real cases. The application of neural networks in different domains will open the door for new scenarios and encourage their adoption and use by both the research community and the industry. The Special Issue welcomes high-quality papers both from a theoretical perspective and from a practical and experimental approach. The major challenges linked to the use of artificial neural networks to solve real problems will be tackled, and papers are expected to propose solutions to them using neural-network-based models.

Prof. Dr. Mario Muñoz Organero
Guest Editor

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

  • Neural networks
  • High-performance computing
  • Complexity
  • Complex models
  • Machine learning
  • Big data

Published Papers (7 papers)

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Research

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15 pages, 3745 KiB  
Article
Oscillator Simulation with Deep Neural Networks
by Jamshaid Ul Rahman, Sana Danish and Dianchen Lu
Mathematics 2024, 12(7), 959; https://0-doi-org.brum.beds.ac.uk/10.3390/math12070959 - 23 Mar 2024
Viewed by 614
Abstract
The motivation behind this study is to overcome the complex mathematical formulation and time-consuming nature of traditional numerical methods used in solving differential equations. It seeks an alternative approach for more efficient and simplified solutions. A Deep Neural Network (DNN) is utilized to [...] Read more.
The motivation behind this study is to overcome the complex mathematical formulation and time-consuming nature of traditional numerical methods used in solving differential equations. It seeks an alternative approach for more efficient and simplified solutions. A Deep Neural Network (DNN) is utilized to understand the intricate correlations between the oscillator’s variables and to precisely capture their dynamics by being trained on a dataset of known oscillator behaviors. In this work, we discuss the main challenge of predicting the behavior of oscillators without depending on complex strategies or time-consuming simulations. The present work proposes a favorable modified form of neural structure to improve the strategy for simulating linear and nonlinear harmonic oscillators from mechanical systems by formulating an ANN as a DNN via an appropriate oscillating activation function. The proposed methodology provides the solutions of linear and nonlinear differential equations (DEs) in differentiable form and is a more accurate approximation as compared to the traditional numerical method. The Van der Pol equation with parametric damping and the Mathieu equation are adopted as illustrations. Experimental analysis shows that our proposed scheme outperforms other numerical methods in terms of accuracy and computational cost. We provide a comparative analysis of the outcomes obtained through our proposed approach and those derived from the LSODA algorithm, utilizing numerical techniques, Adams–Bashforth, and the Backward Differentiation Formula (BDF). The results of this research provide insightful information for engineering applications, facilitating improvements in energy efficiency, and scientific innovation. Full article
(This article belongs to the Special Issue Neural Networks and Their Applications)
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28 pages, 844 KiB  
Article
Sparse Bayesian Neural Networks: Bridging Model and Parameter Uncertainty through Scalable Variational Inference
by Aliaksandr Hubin and Geir Storvik
Mathematics 2024, 12(6), 788; https://0-doi-org.brum.beds.ac.uk/10.3390/math12060788 - 07 Mar 2024
Viewed by 1388
Abstract
Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a Bayesian approach: parameter and prediction uncertainties become easily available, [...] Read more.
Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a Bayesian approach: parameter and prediction uncertainties become easily available, facilitating more rigorous statistical analysis. Furthermore, prior knowledge can be incorporated. However, the construction of scalable techniques that combine both structural and parameter uncertainty remains a challenge. In this paper, we apply the concept of model uncertainty as a framework for structural learning in BNNs and, hence, make inferences in the joint space of structures/models and parameters. Moreover, we suggest an adaptation of a scalable variational inference approach with reparametrization of marginal inclusion probabilities to incorporate the model space constraints. Experimental results on a range of benchmark datasets show that we obtain comparable accuracy results with the competing models, but based on methods that are much more sparse than ordinary BNNs. Full article
(This article belongs to the Special Issue Neural Networks and Their Applications)
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22 pages, 5982 KiB  
Article
Predicting PM10 Concentrations Using Evolutionary Deep Neural Network and Satellite-Derived Aerosol Optical Depth
by Yasser Ebrahimian Ghajari, Mehrdad Kaveh and Diego Martín
Mathematics 2023, 11(19), 4145; https://0-doi-org.brum.beds.ac.uk/10.3390/math11194145 - 30 Sep 2023
Cited by 1 | Viewed by 940
Abstract
Predicting particulate matter with a diameter of 10 μm (PM10) is crucial due to its impact on human health and the environment. Today, aerosol optical depth (AOD) offers high resolution and wide coverage, making it a viable way to estimate PM concentrations. Recent [...] Read more.
Predicting particulate matter with a diameter of 10 μm (PM10) is crucial due to its impact on human health and the environment. Today, aerosol optical depth (AOD) offers high resolution and wide coverage, making it a viable way to estimate PM concentrations. Recent years have also witnessed in-creasing promise in refining air quality predictions via deep neural network (DNN) models, out-performing other techniques. However, learning the weights and biases of the DNN is a task classified as an NP-hard problem. Current approaches such as gradient-based methods exhibit significant limitations, such as the risk of becoming ensnared in local minimal within multi-objective loss functions, substantial computational requirements, and the requirement for continuous objective functions. To tackle these challenges, this paper introduces a novel approach that combines the binary gray wolf optimizer (BGWO) with DNN to improve the optimization of models for air pollution prediction. The BGWO algorithm, inspired by the behavior of gray wolves, is used to optimize both the weight and bias of the DNN. In the proposed BGWO, a novel sigmoid function is proposed as a transfer function to adjust the position of the wolves. This study gathers meteorological data, topographic information, PM10 pollution data, and satellite images. Data preparation includes tasks such as noise removal and handling missing data. The proposed approach is evaluated through cross-validation using metrics such as correlation rate, R square, root-mean-square error (RMSE), and accuracy. The effectiveness of the BGWO-DNN framework is compared to seven other machine learning (ML) models. The experimental evaluation of the BGWO-DNN method using air pollution data shows its superior performance compared with traditional ML techniques. The BGWO-DNN, CapSA-DNN, and BBO-DNN models achieved the lowest RMSE values of 16.28, 19.26, and 20.74, respectively. Conversely, the SVM-Linear and GBM algorithms displayed the highest levels of error, yielding RMSE values of 36.82 and 32.50, respectively. The BGWO-DNN algorithm secured the highest R2 (88.21%) and accuracy (93.17%) values, signifying its superior performance compared with other models. Additionally, the correlation between predicted and actual values shows that the proposed model surpasses the performance of other ML techniques. This paper also observes relatively stable pollution levels during spring and summer, contrasting with significant fluctuations during autumn and winter. Full article
(This article belongs to the Special Issue Neural Networks and Their Applications)
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23 pages, 6677 KiB  
Article
Using Traffic Sensors in Smart Cities to Enhance a Spatio-Temporal Deep Learning Model for COVID-19 Forecasting
by Mario Muñoz-Organero
Mathematics 2023, 11(18), 3904; https://0-doi-org.brum.beds.ac.uk/10.3390/math11183904 - 14 Sep 2023
Viewed by 609
Abstract
Respiratory viruses, such as COVID-19, are spread over time and space based on human-to-human interactions. Human mobility plays a key role in the propagation of the virus. Different types of sensors in smart cities are able to continuously monitor traffic-related human mobility, showing [...] Read more.
Respiratory viruses, such as COVID-19, are spread over time and space based on human-to-human interactions. Human mobility plays a key role in the propagation of the virus. Different types of sensors in smart cities are able to continuously monitor traffic-related human mobility, showing the impact of COVID-19 on traffic volumes and patterns. In a similar way, traffic volumes measured by smart traffic sensors provide a proxy variable to capture human mobility, which is expected to have an impact on new COVID-19 infections. Adding traffic data from smart city sensors to machine learning models designed to estimate upcoming COVID-19 incidence values should provide optimized results compared to models based on COVID-19 data alone. This paper proposes a novel model to extract spatio-temporal patterns in the spread of the COVID-19 virus for short-term predictions by organizing COVID-19 incidence and traffic data as interrelated temporal sequences of spatial images. The model is trained and validated with real data from the city of Madrid in Spain for 84 weeks, combining information from 4372 traffic measuring points and 143 COVID-19 PCR test centers. The results are compared with a baseline model designed for the extraction of spatio-temporal patterns from COVID-19-only sequences of images, showing that using traffic information enhances the results when forecasting a new wave of infections (MSE values are reduced by a 70% factor). The information that traffic data has on the spread of the COVID-19 virus is also analyzed, showing that traffic data alone is not sufficient for accurate COVID-19 forecasting. Full article
(This article belongs to the Special Issue Neural Networks and Their Applications)
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18 pages, 672 KiB  
Article
Threat Hunting System for Protecting Critical Infrastructures Using a Machine Learning Approach
by Mario Aragonés Lozano, Israel Pérez Llopis and Manuel Esteve Domingo
Mathematics 2023, 11(16), 3448; https://0-doi-org.brum.beds.ac.uk/10.3390/math11163448 - 09 Aug 2023
Cited by 1 | Viewed by 1984
Abstract
Cyberattacks are increasing in number and diversity in nature daily, and the tendency for them is to escalate dramatically in the forseeable future, with critical infrastructures (CI) assets and networks not being an exception to this trend. As time goes by, cyberattacks are [...] Read more.
Cyberattacks are increasing in number and diversity in nature daily, and the tendency for them is to escalate dramatically in the forseeable future, with critical infrastructures (CI) assets and networks not being an exception to this trend. As time goes by, cyberattacks are more complex than before and unknown until they spawn, being very difficult to detect and remediate. To be reactive against those cyberattacks, usually defined as zero-day attacks, cyber-security specialists known as threat hunters must be in organizations’ security departments. All the data generated by the organization’s users must be processed by those threat hunters (which are mainly benign and repetitive and follow predictable patterns) in short periods to detect unusual behaviors. The application of artificial intelligence, specifically machine learning (ML) techniques (for instance NLP, C-RNN-GAN, or GNN), can remarkably impact the real-time analysis of those data and help to discriminate between harmless data and malicious data, but not every technique is helpful in every circumstance; as a consequence, those specialists must know which techniques fit the best at every specific moment. The main goal of the present work is to design a distributed and scalable system for threat hunting based on ML, and with a special focus on critical infrastructure needs and characteristics. Full article
(This article belongs to the Special Issue Neural Networks and Their Applications)
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17 pages, 1708 KiB  
Article
Neural Network Approaches for Computation of Soil Thermal Conductivity
by Zarghaam Haider Rizvi, Syed Jawad Akhtar, Syed Mohammad Baqir Husain, Mohiuddeen Khan, Hasan Haider, Sakina Naqvi, Vineet Tirth and Frank Wuttke
Mathematics 2022, 10(21), 3957; https://0-doi-org.brum.beds.ac.uk/10.3390/math10213957 - 25 Oct 2022
Cited by 2 | Viewed by 2158
Abstract
The effective thermal conductivity (ETC) of soil is an essential parameter for the design and unhindered operation of underground energy transportation and storage systems. Various experimental, empirical, semi-empirical, mathematical, and numerical methods have been tried in the past, but lack either accuracy or [...] Read more.
The effective thermal conductivity (ETC) of soil is an essential parameter for the design and unhindered operation of underground energy transportation and storage systems. Various experimental, empirical, semi-empirical, mathematical, and numerical methods have been tried in the past, but lack either accuracy or are computationally cumbersome. The recent developments in computer science provided a new computational approach, the neural networks, which are easy to implement, faster, versatile, and reasonably accurate. In this study, we present three classes of neural networks based on different network constructions, learning and computational strategies to predict the ETC of the soil. A total of 384 data points are collected from literature, and the three networks, Artificial neural network (ANN), group method of data handling (GMDH) and gene expression programming (GEP), are constructed and trained. The best accuracy of each network is measured with the coefficient of determination (R2) and found to be 91.6, 83.2 and 80.5 for ANN, GMDH and GEP, respectively. Furthermore, two sands with 80% and 99% quartz content are measured, and the best performing network from each class of ANN, GMDH and GEP is independently validated. The GEP model provided the best estimate for 99% quartz sand and GMDH with 80%. Full article
(This article belongs to the Special Issue Neural Networks and Their Applications)
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Review

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46 pages, 715 KiB  
Review
Perceptron: Learning, Generalization, Model Selection, Fault Tolerance, and Role in the Deep Learning Era
by Ke-Lin Du, Chi-Sing Leung, Wai Ho Mow and M. N. S. Swamy
Mathematics 2022, 10(24), 4730; https://0-doi-org.brum.beds.ac.uk/10.3390/math10244730 - 13 Dec 2022
Cited by 11 | Viewed by 6947
Abstract
The single-layer perceptron, introduced by Rosenblatt in 1958, is one of the earliest and simplest neural network models. However, it is incapable of classifying linearly inseparable patterns. A new era of neural network research started in 1986, when the backpropagation (BP) algorithm was [...] Read more.
The single-layer perceptron, introduced by Rosenblatt in 1958, is one of the earliest and simplest neural network models. However, it is incapable of classifying linearly inseparable patterns. A new era of neural network research started in 1986, when the backpropagation (BP) algorithm was rediscovered for training the multilayer perceptron (MLP) model. An MLP with a large number of hidden nodes can function as a universal approximator. To date, the MLP model is the most fundamental and important neural network model. It is also the most investigated neural network model. Even in this AI or deep learning era, the MLP is still among the few most investigated and used neural network models. Numerous new results have been obtained in the past three decades. This survey paper gives a comprehensive and state-of-the-art introduction to the perceptron model, with emphasis on learning, generalization, model selection and fault tolerance. The role of the perceptron model in the deep learning era is also described. This paper provides a concluding survey of perceptron learning, and it covers all the major achievements in the past seven decades. It also serves a tutorial for perceptron learning. Full article
(This article belongs to the Special Issue Neural Networks and Their Applications)
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