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Computation
Special Issues
Applications of Computational Mathematics to Simulation and Data Analysis II
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Applications of Computational Mathematics to Simulation and Data Analysis II

A special issue of Computation (ISSN 2079-3197). This special issue belongs to the section "Computational Engineering".

Deadline for manuscript submissions: closed (1 November 2023) | Viewed by 8881

Special Issue Editors

Dr. Carlos Balsa

E-Mail Website
Guest Editor
Research Centre in Digitalization and Intelligent Robotics (CeDRI), Instituto Politécnico de Bragança, Bragança, Portugal
Interests: mathematical modeling and computational simulation; data analysis; fluid mechanics and heat transfer; weather forecasting; bioinformatics
Special Issues, Collections and Topics in MDPI journals
Dr. Teresa Guarda

E-Mail Website
Guest Editor
CIST Research and Innovation Center, Faculty of Systems and Telecommunications, Santa Elena Provincial State University, La Libertad, Ecuador; ALGORITMI Research Centre of Minho University, Guimarães, Portugal
Interests: pervasive systems; intelligent systems; information science; computer theory; knowledge management; cybersecurity
Special Issues, Collections and Topics in MDPI journals
Dr. Ronan Guivarch

E-Mail Website
Guest Editor
Institut de Recherche en Informatique de Toulouse (IRIT), Université de Toulouse, Toulouse, France
Interests: high performance computing; parallel programming; data analysis; clustering
Special Issues, Collections and Topics in MDPI journals
Dr. Sílvio Gama

E-Mail Website
Guest Editor
Centro de Matemática da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
Interests: turbulence, magnetohydrodynamics, computational fluid dynamics, econophysics, optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue will publish a set of selected papers from ACMaSDA 2022—Applications of Computational Mathematics to Simulation and Data Analysis, integrated in ARTIIS 2022, held on 12–15 September, Santiago de Compostela, Spain. This Special Issue focuses on the applications of computational mathematics to simulation and data analysis in various fields of science and engineering. It seeks to highlight the potential of interdisciplinary interactions as a source of new knowledge.

Contributions with new research results involving computational mathematics, numerical methods, high-performance computing, and their applications in different fields, such as fluid mechanics, mass and heat transfer, energy, weather forecasts, and medical or biological processes are welcome.

The list of topics of interest includes but is not limited to the following:

  • Simulation and data analysis;
  • Computation in earth sciences;
  • Computational mechanics;
  • Computing in healthcare and biosciences;
  • Digital image processing;
  • High-performance computing;
  • Numerical algorithms for computational science;
  • Econophysics;
  • Weather and environment forecast.

Dr. Carlos Balsa
Dr. Teresa Guarda
Dr. Ronan Guivarch
Dr. Sílvio Gama
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. Computation is an international peer-reviewed open access monthly 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 1800 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

  • computational mathematics
  • numerical methods
  • data analysis
  • computational simulation
  • high-performance computing
  • engineering and science applications

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (4 papers)

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Research

17 pages, 5047 KiB  
Article
Data Augmentation for Regression Machine Learning Problems in High Dimensions
by Clara Guilhaumon, Nicolas Hascoët, Francisco Chinesta, Marc Lavarde and Fatima Daim
Computation 2024, 12(2), 24; https://doi.org/10.3390/computation12020024 - 1 Feb 2024
Cited by 3 | Viewed by 2353
Abstract
Machine learning approaches are currently used to understand or model complex physical systems. In general, a substantial number of samples must be collected to create a model with reliable results. However, collecting numerous data is often relatively time-consuming or expensive. Moreover, the problems [...] Read more.
Machine learning approaches are currently used to understand or model complex physical systems. In general, a substantial number of samples must be collected to create a model with reliable results. However, collecting numerous data is often relatively time-consuming or expensive. Moreover, the problems of industrial interest tend to be more and more complex, and depend on a high number of parameters. High-dimensional problems intrinsically involve the need for large amounts of data through the curse of dimensionality. That is why new approaches based on smart sampling techniques have been investigated to minimize the number of samples to be given to train the model, such as active learning methods. Here, we propose a technique based on a combination of the Fisher information matrix and sparse proper generalized decomposition that enables the definition of a new active learning informativeness criterion in high dimensions. We provide examples proving the performances of this technique on a theoretical 5D polynomial function and on an industrial crash simulation application. The results prove that the proposed strategy outperforms the usual ones. Full article
(This article belongs to the Special Issue Applications of Computational Mathematics to Simulation and Data Analysis II)
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14 pages, 639 KiB  
Article
An Improved Approach for Implementing Dynamic Mode Decomposition with Control
by Gyurhan Nedzhibov
Computation 2023, 11(10), 201; https://doi.org/10.3390/computation11100201 - 8 Oct 2023
Cited by 1 | Viewed by 2707
Abstract
Dynamic Mode Decomposition with Control is a powerful technique for analyzing and modeling complex dynamical systems under the influence of external control inputs. In this paper, we propose a novel approach to implement this technique that offers computational advantages over the existing method. [...] Read more.
Dynamic Mode Decomposition with Control is a powerful technique for analyzing and modeling complex dynamical systems under the influence of external control inputs. In this paper, we propose a novel approach to implement this technique that offers computational advantages over the existing method. The proposed scheme uses singular value decomposition of a lower order matrix and requires fewer matrix multiplications when determining corresponding approximation matrices. Moreover, the matrix of dynamic modes also has a simpler structure than the corresponding matrix in the standard approach. To demonstrate the efficacy of the proposed implementation, we applied it to a diverse set of numerical examples. The algorithm’s flexibility is demonstrated in tests: accurate modeling of ecological systems like Lotka-Volterra, successful control of chaotic behavior in the Lorenz system and efficient handling of large-scale stable linear systems. This showcased its versatility and efficacy across different dynamical systems. Full article
(This article belongs to the Special Issue Applications of Computational Mathematics to Simulation and Data Analysis II)
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17 pages, 5574 KiB  
Communication
On the Time Frequency Compactness of the Slepian Basis of Order Zero for Engineering Applications
by Zuwen Sun and Natalie Baddour
Computation 2023, 11(6), 116; https://doi.org/10.3390/computation11060116 - 13 Jun 2023
Cited by 2 | Viewed by 1205
Abstract
Time and frequency concentrations of waveforms are often of interest in engineering applications. The Slepian basis of order zero is an index-limited (finite) vector that is known to be optimally concentrated in the frequency domain. This paper proposes a method of mapping the [...] Read more.
Time and frequency concentrations of waveforms are often of interest in engineering applications. The Slepian basis of order zero is an index-limited (finite) vector that is known to be optimally concentrated in the frequency domain. This paper proposes a method of mapping the index-limited Slepian basis to a discrete-time vector, hence obtaining a time-limited, discrete-time Slepian basis that is optimally concentrated in frequency. The main result of this note is to demonstrate that the (discrete-time) Slepian basis achieves minimum time-bandwidth compactness under certain conditions. We distinguish between the characteristic (effective) time/bandwidth of the Slepians and their defining time/bandwidth (the time and bandwidth parameters used to generate the Slepian basis). Using two different definitions of effective time and bandwidth of a signal, we show that when the defining time-bandwidth product of the Slepian basis increases, its effective time-bandwidth product tends to a minimum value. This implies that not only are the zeroth order Slepian bases known to be optimally time-limited and band-concentrated basis vectors, but also as their defining time-bandwidth products increase, their effective time-bandwidth properties approach the known minimum compactness allowed by the uncertainty principle. Conclusions are also drawn about the smallest defining time-bandwidth parameters to reach the minimum possible compactness. These conclusions give guidance for applications where the time-bandwidth product is free to be selected and hence may be selected to achieve minimum compactness. Full article
(This article belongs to the Special Issue Applications of Computational Mathematics to Simulation and Data Analysis II)
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23 pages, 7260 KiB  
Article
Reconstruction of Meteorological Records by Methods Based on Dimension Reduction of the Predictor Dataset
by Carlos Balsa, Murilo M. Breve, Carlos V. Rodrigues and José Rufino
Computation 2023, 11(5), 98; https://doi.org/10.3390/computation11050098 - 12 May 2023
Viewed by 1641
Abstract
The reconstruction or prediction of meteorological records through the Analog Ensemble (AnEn) method is very efficient when the number of predictor time series is small. Thus, in order to take advantage of the richness and diversity of information contained in a large number [...] Read more.
The reconstruction or prediction of meteorological records through the Analog Ensemble (AnEn) method is very efficient when the number of predictor time series is small. Thus, in order to take advantage of the richness and diversity of information contained in a large number of predictors, it is necessary to reduce their dimensions. This study presents methods to accomplish such reduction, allowing the use of a high number of predictor variables. In particular, the techniques of Principal Component Analysis (PCA) and Partial Least Squares (PLS) are used to reduce the dimension of the predictor dataset without loss of essential information. The combination of the AnEn and PLS techniques results in a very efficient hybrid method (PLSAnEn) for reconstructing or forecasting unstable meteorological variables, such as wind speed. This hybrid method is computationally demanding but its performance can be improved via parallelization or the introduction of variants in which all possible analogs are previously clustered. The multivariate linear regression methods used on the new variables resulting from the PCA or PLS techniques also proved to be efficient, especially for the prediction of meteorological variables without local oscillations, such as the pressure. Full article
(This article belongs to the Special Issue Applications of Computational Mathematics to Simulation and Data Analysis II)
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