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Applied Sciences
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Advances and Applications of Numerical Analysis and Intelligent Computing
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Advances and Applications of Numerical Analysis and Intelligent Computing

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Computing and Artificial Intelligence".

Deadline for manuscript submissions: 20 June 2024 | Viewed by 3020

Special Issue Editor

Dr. Francesca Pelosi

E-Mail Website
Guest Editor
Department of Information Engineering and Mathematical Sciences, University of Siena, 53100 Siena, Italy
Interests: numerical analysis and intelligent computing

Special Issue Information

Dear Colleagues,

Machine learning and intelligent computing in general are becoming increasingly relied upon to make computers learn data. The collection of large amounts of data produced by a wide variety of users has been a fact of life for many years. In addition, the use of intelligent computing has revolutionized several areas, including the numerical analysis of partial differential equations (PDEs), inverse problems and compressed detection. On the other hand, numerical analysis forms the basis of many machine learning algorithms. The use of existing methods and the adjustment of their parameters still gives very interesting results for the problems dealt with. Aiming to go further in solving existing or new, increasingly difficult problems, scientists must study, analyze and process the numerical analysis used in machine learning in order to research and create new, stable and accurate methods.

In this Special Issue, we invite our colleagues to submit articles that use numerical analysis methods to address problems in the field of intelligent computing, presenting both theoretical and experimental results. Areas of interest arise from inverse problems, imaging, optimal control, approximation theory and applied harmonic analysis. Possible topics range from network architectures; neural operators for PDEs; deep generative models and real-world applications, from machine learning to the biomedical, engineering and physical sciences.

Dr. Francesca Pelosi
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. Applied Sciences 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 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

  • intelligent computing
  • machine learning for PDEs
  • applied harmonic analysis
  • analysis of neural networks
  • approximation theory
  • image processing

Published Papers (4 papers)

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Research

24 pages, 10168 KiB  
Article
Comprehensive Evaluation of Lateral Performance of Innovative Post in Sand
by Abdelrahman Abouzaid, Mohamed Hesham El Naggar and Osama Drbe
Appl. Sci. 2024, 14(6), 2442; https://doi.org/10.3390/app14062442 - 14 Mar 2024
Viewed by 530
Abstract
Under environmental loads such as wind and earthquakes, piles are subjected to large lateral loads. A foundation system denoted Innovative Post (IP) that is composed of an H-pile shaft and one or two steel plates (paddles) welded to its flanges, has been developed [...] Read more.
Under environmental loads such as wind and earthquakes, piles are subjected to large lateral loads. A foundation system denoted Innovative Post (IP) that is composed of an H-pile shaft and one or two steel plates (paddles) welded to its flanges, has been developed to resist large lateral loads on sound wall systems. The present study evaluates the performance of IP installed in layered cohesionless soils through a comprehensive full-scale lateral load testing program and finite element (FE) analysis considering various pile and plate configurations. The developed FE model was validated employing the field test data and was then employed to conduct a parametric study to evaluate the performance of IP considering different paddles geometry (i.e., number of paddles, single or double, width, and length). The results demonstrated that adding the plates significantly increased the lateral capacity of H-piles. A positive relationship was identified between paddle’s width and length and the load efficiency. Optimal parameter values for paddles are established based on the experimental and numerical results proposed. Full article
(This article belongs to the Special Issue Advances and Applications of Numerical Analysis and Intelligent Computing)
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29 pages, 1327 KiB  
Article
Q-Analogues of Parallel Numerical Scheme Based on Neural Networks and Their Engineering Applications
by Mudassir Shams and Bruno Carpentieri
Appl. Sci. 2024, 14(4), 1540; https://doi.org/10.3390/app14041540 - 14 Feb 2024
Viewed by 488
Abstract
Quantum calculus can provide new insights into the nonlinear behaviour of functions and equations, addressing problems that may be difficult to tackle by classical calculus due to high nonlinearity. Iterative methods for solving nonlinear equations can benefit greatly from the mathematical theory and [...] Read more.
Quantum calculus can provide new insights into the nonlinear behaviour of functions and equations, addressing problems that may be difficult to tackle by classical calculus due to high nonlinearity. Iterative methods for solving nonlinear equations can benefit greatly from the mathematical theory and tools provided by quantum calculus, e.g., using the concept of q-derivatives, which extends beyond classical derivatives. In this paper, we develop parallel numerical root-finding algorithms that approximate all distinct roots of nonlinear equations by utilizing q-analogies of the function derivative. Furthermore, we utilize neural networks to accelerate the convergence rate by providing accurate initial guesses for our parallel schemes. The global convergence of the q-parallel numerical techniques is demonstrated using random initial approximations on selected biomedical applications, and the efficiency, stability, and consistency of the proposed hybrid numerical schemes are analyzed. Full article
(This article belongs to the Special Issue Advances and Applications of Numerical Analysis and Intelligent Computing)
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13 pages, 2050 KiB  
Article
Inverse Problem Protocol to Estimate Horizontal Groundwater Velocity from Temperature–Depth Profiles in a 2D Aquifer
by Francisco Alhama, José Antonio Jiménez-Valera and Iván Alhama
Appl. Sci. 2024, 14(2), 922; https://doi.org/10.3390/app14020922 - 22 Jan 2024
Viewed by 466
Abstract
A general and precise protocol that follows the standards of an inverse problem in engineering is proposed to estimate groundwater velocity from experimental lectures of temperature vertical profiles in a 2D aquifer. Several values of error in the temperature measurements are assumed. Since [...] Read more.
A general and precise protocol that follows the standards of an inverse problem in engineering is proposed to estimate groundwater velocity from experimental lectures of temperature vertical profiles in a 2D aquifer. Several values of error in the temperature measurements are assumed. Since a large quantity of parameters and initial conditions influence the solution of this process, the protocol is very complex and needs to be tested to ensure its reliability. The studied scenario takes into account the input temperature of the water as well as the isothermal conditions at the surface and bottom of the aquifer. The existence of an input region, in which profiles develop to become linear, allows us to eliminate experimental measurements beyond such a region. Once the protocol is developed and tested, it is successfully applied to estimate the regional (lateral) groundwater velocity of the real aquifer and the result compared with estimations coming from the piezometric map. Full article
(This article belongs to the Special Issue Advances and Applications of Numerical Analysis and Intelligent Computing)
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21 pages, 8355 KiB  
Article
A Hard-Constraint Wide-Body Physics-Informed Neural Network Model for Solving Multiple Cases in Forward Problems for Partial Differential Equations
by Simin Chen, Zhixiang Liu, Wenbo Zhang and Jinkun Yang
Appl. Sci. 2024, 14(1), 189; https://doi.org/10.3390/app14010189 - 25 Dec 2023
Viewed by 1093
Abstract
In the fields of physics and engineering, it is crucial to understand phase transition dynamics. This field involves fundamental partial differential equations (PDEs) such as the Allen–Cahn, Burgers, and two-dimensional (2D) wave equations. In alloys, the evolution of the phase transition interface is [...] Read more.
In the fields of physics and engineering, it is crucial to understand phase transition dynamics. This field involves fundamental partial differential equations (PDEs) such as the Allen–Cahn, Burgers, and two-dimensional (2D) wave equations. In alloys, the evolution of the phase transition interface is described by the Allen–Cahn equation. Vibrational and wave phenomena during phase transitions are modeled using the Burgers and 2D wave equations. The combination of these equations gives comprehensive information about the dynamic behavior during a phase transition. Numerical modeling methods such as finite difference method (FDM), finite volume method (FVM) and finite element method (FEM) are often applied to solve phase transition problems that involve many partial differential equations (PDEs). However, physical problems can lead to computational complexity, increasing computational costs dramatically. Physics-informed neural networks (PINNs), as new neural network algorithms, can integrate physical law constraints with neural network algorithms to solve partial differential equations (PDEs), providing a new way to solve PDEs in addition to the traditional numerical modeling methods. In this paper, a hard-constraint wide-body PINN (HWPINN) model based on PINN is proposed. This model improves the effectiveness of the approximation by adding a wide-body structure to the approximation neural network part of the PINN architecture. A hard constraint is used in the physically driven part instead of the traditional practice of PINN constituting a residual network with boundary or initial conditions. The high accuracy of HWPINN for solving PDEs is verified through numerical experiments. One-dimensional (1D) Allen–Cahn, one-dimensional Burgers, and two-dimensional wave equation cases are set up for numerical experiments. The properties of the HWPINN model are inferred from the experimental data. The solution predicted by the model is compared with the FDM solution for evaluating the experimental error in the numerical experiments. HWPINN shows great potential for solving the PDE forward problem and provides a new approach for solving PDEs. Full article
(This article belongs to the Special Issue Advances and Applications of Numerical Analysis and Intelligent Computing)
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