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Mathematics
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Advances in Computational Science and Its Applications
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Advances in Computational Science and Its Applications

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

Deadline for manuscript submissions: 31 May 2024 | Viewed by 7846

Special Issue Editors

Dr. Haojie Lian

E-Mail Website
Guest Editor
Key Laboratory of In-situ Property-improving Mining of Ministry of Education, Taiyuan University of Technology, Taiyuan 030024, China
Interests: computational science; artificial intelligence; renewable energy
Special Issues, Collections and Topics in MDPI journals
Dr. Chensen Ding

E-Mail Website
Guest Editor
Institute of Data Science and Artificial Intelligence, University of Exeter, Exeter EX4 4PY, UK
Interests: data-driven; machine learning; uncertainty quantification; computational mechanics (numerical methods), e.g., FEM, SFEM, BEM and IGA; structural fast analysis/optimization; composite
Special Issues, Collections and Topics in MDPI journals
Dr. Leilei Chen

E-Mail Website
Guest Editor
College of Architecture and Engineering, Huanghuai University, Zhumadian 463000, China
Interests: isogeometric analysis; boundary element analysis; coupled finite element and boundary element; structural optimization; topology optimization; stochastic analysis; deep learning engineering computation; fracture mechanics
Dr. Xiao Lin

E-Mail Website
Guest Editor
School for Business and Society, University of York, York YO10 5ZF, UK
Interests: sustainability transition; sustainable transportation; operations research
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Computational science is a discipline concerned with the development of numerical methods to model, simulate and analyse scientific problems. As a highly interdisciplinary area, computational sciences bring together applied mathematics, statistics, computer science, mechanics etc. Computational science is rapidly growing, and finds important applications in a wide range of fields. For example, it plays a fundamental role in engineering, chemistry, and physics. It also has many branches in social science, such as computational economics, computational sociology, cliodynamics and culturomics. For this Special Issue, we invite original research articles and survey papers on the state-of-the-art theoretical research and applications of computational science. Manuscripts that address the industrial and societal problems associated with COVID-19 are particularly welcome.

Dr. Haojie Lian
Dr. Chensen Ding
Dr. Leilei Chen
Dr. Xiao Lin
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 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

  • numerical analysis
  • data-driven methods
  • machine learning
  • optimization and inverse problems
  • uncertainty qualification
  • operations research
  • computational social science
  • error estimation
  • software development

Published Papers (5 papers)

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Research

17 pages, 1926 KiB  
Article
Modeling Error and Nonuniqueness of the Continuous-Time Models Learned via Runge–Kutta Methods
by Shunpei Terakawa and Takaharu Yaguchi
Mathematics 2024, 12(8), 1190; https://0-doi-org.brum.beds.ac.uk/10.3390/math12081190 - 16 Apr 2024
Viewed by 221
Abstract
In the present study, we consider continuous-time modeling of dynamics using observed data and formulate the modeling error caused by the discretization method used in the process. In the formulation, a class of linearized dynamics called Dahlquist’s test equations is used as representative [...] Read more.
In the present study, we consider continuous-time modeling of dynamics using observed data and formulate the modeling error caused by the discretization method used in the process. In the formulation, a class of linearized dynamics called Dahlquist’s test equations is used as representative of the target dynamics, and the characteristics of each discretization method for various dynamics are taken into account. The family of explicit Runge–Kutta methods is analyzed as a specific discretization method using the proposed framework. As a result, equations for predicting the modeling error are derived, and it is found that there can be multiple possible models obtained when using these methods. Several learning experiments using a simple neural network exhibited consistent results with theoretical predictions, including the nonuniqueness of the resulting model. Full article
(This article belongs to the Special Issue Advances in Computational Science and Its Applications)
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12 pages, 401 KiB  
Article
Parameter Estimation for Nonlinear Diffusion Problems by the Constrained Homotopy Method
by Tao Liu, Zijian Ding, Jiayuan Yu and Wenwen Zhang
Mathematics 2023, 11(12), 2642; https://0-doi-org.brum.beds.ac.uk/10.3390/math11122642 - 09 Jun 2023
Cited by 5 | Viewed by 861
Abstract
This paper studies a parameter estimation problem for the non-linear diffusion equation within multiphase porous media flow, which has important applications in the field of oil reservoir simulation. First, the given problem is transformed into an optimization problem by using optimal control framework [...] Read more.
This paper studies a parameter estimation problem for the non-linear diffusion equation within multiphase porous media flow, which has important applications in the field of oil reservoir simulation. First, the given problem is transformed into an optimization problem by using optimal control framework and the constraints such as well logs, which can restrain noise and improve the quality of inversion, are introduced. Then we propose the widely convergent homotopy method, which makes natural use of constraints and incorporates Tikhonov regularization. The effectiveness of the proposed approach is demonstrated on illustrative examples. Full article
(This article belongs to the Special Issue Advances in Computational Science and Its Applications)
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20 pages, 3710 KiB  
Article
An Improved Arithmetic Optimization Algorithm and Its Application to Determine the Parameters of Support Vector Machine
by Heping Fang, Xiaopeng Fu, Zhiyong Zeng, Kunhua Zhong and Shuguang Liu
Mathematics 2022, 10(16), 2875; https://0-doi-org.brum.beds.ac.uk/10.3390/math10162875 - 11 Aug 2022
Cited by 11 | Viewed by 2348
Abstract
The arithmetic optimization algorithm (AOA) is a new metaheuristic algorithm inspired by arithmetic operators (addition, subtraction, multiplication, and division) to solve arithmetic problems. The algorithm is characterized by simple principles, fewer parameter settings, and easy implementation, and has been widely used in many [...] Read more.
The arithmetic optimization algorithm (AOA) is a new metaheuristic algorithm inspired by arithmetic operators (addition, subtraction, multiplication, and division) to solve arithmetic problems. The algorithm is characterized by simple principles, fewer parameter settings, and easy implementation, and has been widely used in many fields. However, similar to other meta-heuristic algorithms, AOA suffers from shortcomings, such as slow convergence speed and an easy ability to fall into local optimum. To address the shortcomings of AOA, an improved arithmetic optimization algorithm (IAOA) is proposed. First, dynamic inertia weights are used to improve the algorithm’s exploration and exploitation ability and speed up the algorithm’s convergence speed; second, dynamic mutation probability coefficients and the triangular mutation strategy are introduced to improve the algorithm’s ability to avoid local optimum. In order to verify the effectiveness and practicality of the algorithm in this paper, six benchmark test functions are selected for the optimization search test verification to verify the optimization search ability of IAOA; then, IAOA is used for the parameter optimization of support vector machines to verify the practical ability of IAOA. The experimental results show that IAOA has a strong global search capability, and the optimization-seeking capability is significantly improved, and it shows excellent performance in support vector machine parameter optimization. Full article
(This article belongs to the Special Issue Advances in Computational Science and Its Applications)
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17 pages, 45211 KiB  
Article
Monte Carlo Based Isogeometric Stochastic Finite Element Method for Uncertainty Quantization in Vibration Analysis of Piezoelectric Materials
by Yanming Xu, Haozhi Li, Leilei Chen, Juan Zhao and Xin Zhang
Mathematics 2022, 10(11), 1840; https://0-doi-org.brum.beds.ac.uk/10.3390/math10111840 - 27 May 2022
Cited by 10 | Viewed by 1808
Abstract
In this study, a Monte Carlo simulation (MCs)-based isogeometric stochastic Finite Element Method (FEM) is proposed for uncertainty quantification in the vibration analysis of piezoelectric materials. In this method, deterministic solutions (natural frequencies) of the coupled eigenvalue problem are obtained via isogeometric analysis [...] Read more.
In this study, a Monte Carlo simulation (MCs)-based isogeometric stochastic Finite Element Method (FEM) is proposed for uncertainty quantification in the vibration analysis of piezoelectric materials. In this method, deterministic solutions (natural frequencies) of the coupled eigenvalue problem are obtained via isogeometric analysis (IGA). Moreover, MCs is employed to solve various uncertainty parameters, including separate elastic and piezoelectric constants and their combined cases. Full article
(This article belongs to the Special Issue Advances in Computational Science and Its Applications)
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16 pages, 16852 KiB  
Article
Study on Flow Distribution and Structure Optimization in a Mix Chamber and Diffuser of a CO2 Two-Phase Ejector
by Lixing Zheng, Hongwei Hu, Weibo Wang, Yiyan Zhang and Lingmei Wang
Mathematics 2022, 10(5), 693; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050693 - 23 Feb 2022
Cited by 4 | Viewed by 1263
Abstract
This paper establishes a mathematic model of a CO2 two-phase ejector to investigate flow distribution in the components of a mixing chamber and diffuser. The suction chamber was modeled using the characteristic line method to describe the development process of the supersonic [...] Read more.
This paper establishes a mathematic model of a CO2 two-phase ejector to investigate flow distribution in the components of a mixing chamber and diffuser. The suction chamber was modeled using the characteristic line method to describe the development process of the supersonic expansion wave, and the mixing chamber, as well as diffuser models, were built based on the double-flow model. The reliability of the model was verified by experimental data. The distributions of flow parameters along the axis of the mixing chamber and diffuser were analyzed under different expansion ratios of the ejector. Structure optimizations of the mixing chamber and diffuser were conducted. The results showed that the primary flow temperature gradually increased along the axis of the mixing chamber and diffuser, but the Mach number distribution decreased for a certain ejector expansion ratio. The temperature and Mach number of the secondary flow showed the opposite trend. Moreover, at the initial stage of mixing, the fluid pressure increased rapidly, and the Mach number of the primary flow decreased rapidly. The gas-phase fraction of primary flow increased gradually in the mixing chamber and was stable in the diffuser. When the length–diameter ratio of the mixing chamber was about 10.8–12, it was beneficial to mix uniformity, and when the expansion angle of the diffuser was 4–6°, the ejector had a better ejector efficiency. Full article
(This article belongs to the Special Issue Advances in Computational Science and Its Applications)
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