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

Deadline for manuscript submissions: closed (30 November 2024) | Viewed by 33681

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Prof. Dr. Mario Muñoz Organero

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Telecommunications Engineering, Carlos III University of Madrid, 28911 Leganes, Spain
Interests: neural networks; artificial intelligence; computer supported learning; sensor-based applications
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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

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Keywords

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

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Published Papers (9 papers)

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22 pages, 286 KiB

Open AccessArticle

SHAP Informed Neural Network

by Jarrod Graham and Victor S. Sheng

Mathematics 2025, 13(5), 849; https://doi.org/10.3390/math13050849 - 4 Mar 2025

Viewed by 756

Abstract

In the context of neural network optimization, this study explores the performance and computational efficiency of learning rate adjustment strategies applied with Adam and SGD optimizers. Methods evaluated include exponential annealing, step decay, and SHAP-informed adjustments across three datasets: Breast Cancer, Diabetes, and California Housing. The SHAP-informed adjustments integrate feature importance metrics derived from cooperative game theory, either scaling the global learning rate or directly modifying gradients of first-layer parameters. A comprehensive grid search was conducted to optimize the hyperparameters, and performance was assessed using metrics such as test loss, RMSE, R² score, accuracy, and training time. Results revealed that while step decay consistently delivered strong performance across datasets, SHAP-informed methods often demonstrated even higher accuracy and generalization, such as SHAP achieving the lowest test loss and RMSE on the California Housing dataset. However, the computational overhead of SHAP-based approaches was significant, particularly in targeted gradient adjustments. This study highlights the potential of SHAP-informed methods to guide optimization processes through feature-level insights, offering advantages in data with complex feature interactions. Despite computational challenges, these methods provide a foundation for exploring how feature importance can inform neural network training, presenting promising directions for future research on scalable and efficient optimization techniques. Full article

(This article belongs to the Special Issue Neural Networks and Their Applications)

13 pages, 1843 KiB

Open AccessArticle

Multiple Inputs and Mixed Data for Alzheimer’s Disease Classification Based on 3D Vision Transformer

by Juan A. Castro-Silva, María N. Moreno-García and Diego H. Peluffo-Ordóñez

Mathematics 2024, 12(17), 2720; https://doi.org/10.3390/math12172720 - 31 Aug 2024

Cited by 3 | Viewed by 1978

Abstract

The current methods for diagnosing Alzheimer’s Disease using Magnetic Resonance Imaging (MRI) have significant limitations. Many previous studies used 2D Transformers to analyze individual brain slices independently, potentially losing critical 3D contextual information. Region of interest-based models often focus on only a few brain regions despite Alzheimer’s affecting multiple areas. Additionally, most classification models rely on a single test, whereas diagnosing Alzheimer’s requires a multifaceted approach integrating diverse data sources for a more accurate assessment. This study introduces a novel methodology called the Multiple Inputs and Mixed Data 3D Vision Transformer (MIMD-3DVT). This method processes consecutive slices together to capture the feature dimensions and spatial information, fuses multiple 3D ROI imaging data inputs, and integrates mixed data from demographic factors, cognitive assessments, and brain imaging. The proposed methodology was experimentally evaluated using a combined dataset that included the Alzheimer’s Disease Neuroimaging Initiative (ADNI), the Australian Imaging, Biomarker, and Lifestyle Flagship Study of Ageing (AIBL), and the Open Access Series of Imaging Studies (OASIS). Our MIMD-3DVT, utilizing single or multiple ROIs, achieved an accuracy of 97.14%, outperforming the state-of-the-art methods in distinguishing between Normal Cognition and Alzheimer’s Disease. Full article

(This article belongs to the Special Issue Neural Networks and Their Applications)

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15 pages, 3745 KiB

Open AccessArticle

Oscillator Simulation with Deep Neural Networks

by Jamshaid Ul Rahman, Sana Danish and Dianchen Lu

Mathematics 2024, 12(7), 959; https://doi.org/10.3390/math12070959 - 23 Mar 2024

Cited by 6 | Viewed by 2114

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 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

Open AccessEditor’s ChoiceArticle

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://doi.org/10.3390/math12060788 - 7 Mar 2024

Cited by 2 | Viewed by 3241

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, 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

Open AccessArticle

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://doi.org/10.3390/math11194145 - 30 Sep 2023

Cited by 3 | Viewed by 1932

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 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

Open AccessArticle

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://doi.org/10.3390/math11183904 - 14 Sep 2023

Viewed by 1113

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 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

Open AccessArticle

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://doi.org/10.3390/math11163448 - 9 Aug 2023

Cited by 3 | Viewed by 3891

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 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

Open AccessArticle

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://doi.org/10.3390/math10213957 - 25 Oct 2022

Cited by 3 | Viewed by 3462

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 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 (

R^{2}

) 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

Open AccessReview

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://doi.org/10.3390/math10244730 - 13 Dec 2022

Cited by 39 | Viewed by 13164

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 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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