Editor’s Choice Articles

Editor’s Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. Editors select a small number of articles recently published in the journal that they believe will be particularly interesting to readers, or important in the respective research area. The aim is to provide a snapshot of some of the most exciting work published in the various research areas of the journal.

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
17 pages, 929 KiB  
Article
Is NSGA-II Ready for Large-Scale Multi-Objective Optimization?
by Antonio J. Nebro, Jesús Galeano-Brajones, Francisco Luna and Carlos A. Coello Coello
Math. Comput. Appl. 2022, 27(6), 103; https://doi.org/10.3390/mca27060103 - 30 Nov 2022
Cited by 3 | Viewed by 3387
Abstract
NSGA-II is, by far, the most popular metaheuristic that has been adopted for solving multi-objective optimization problems. However, its most common usage, particularly when dealing with continuous problems, is circumscribed to a standard algorithmic configuration similar to the one described in its seminal [...] Read more.
NSGA-II is, by far, the most popular metaheuristic that has been adopted for solving multi-objective optimization problems. However, its most common usage, particularly when dealing with continuous problems, is circumscribed to a standard algorithmic configuration similar to the one described in its seminal paper. In this work, our aim is to show that the performance of NSGA-II, when properly configured, can be significantly improved in the context of large-scale optimization. It leverages a combination of tools for automated algorithmic tuning called irace, and a highly configurable version of NSGA-II available in the jMetal framework. Two scenarios are devised: first, by solving the Zitzler–Deb–Thiele (ZDT) test problems, and second, when dealing with a binary real-world problem of the telecommunications domain. Our experiments reveal that an auto-configured version of NSGA-II can properly address test problems ZDT1 and ZDT2 with up to 217=131,072 decision variables. The same methodology, when applied to the telecommunications problem, shows that significant improvements can be obtained with respect to the original NSGA-II algorithm when solving problems with thousands of bits. Full article
Show Figures

Figure 1

16 pages, 1064 KiB  
Article
Comparison of Two Aspects of a PDE Model for Biological Network Formation
by Clarissa Astuto, Daniele Boffi, Jan Haskovec, Peter Markowich and Giovanni Russo
Math. Comput. Appl. 2022, 27(5), 87; https://doi.org/10.3390/mca27050087 - 17 Oct 2022
Cited by 2 | Viewed by 1520
Abstract
We compare the solutions of two systems of partial differential equations (PDEs), seen as two different interpretations of the same model which describes the formation of complex biological networks. Both approaches take into account the time evolution of the medium flowing through the [...] Read more.
We compare the solutions of two systems of partial differential equations (PDEs), seen as two different interpretations of the same model which describes the formation of complex biological networks. Both approaches take into account the time evolution of the medium flowing through the network, and we compute the solution of an elliptic–parabolic PDE system for the conductivity vector m, the conductivity tensor C and the pressure p. We use finite differences schemes in a uniform Cartesian grid in a spatially two-dimensional setting to solve the two systems, where the parabolic equation is solved using a semi-implicit scheme in time. Since the conductivity vector and tensor also appear in the Poisson equation for the pressure p, the elliptic equation depends implicitly on time. For this reason, we compute the solution of three linear systems in the case of the conductivity vector mR2 and four linear systems in the case of the symmetric conductivity tensor CR2×2 at each time step. To accelerate the simulations, we make use of the Alternating Direction Implicit (ADI) method. The role of the parameters is important for obtaining detailed solutions. We provide numerous tests with various values of the parameters involved to determine the differences in the solutions of the two systems. Full article
(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)
Show Figures

Figure 1

24 pages, 1912 KiB  
Review
A Review of Artificial Intelligence and Machine Learning for Incident Detectors in Road Transport Systems
by Samuel Olugbade, Stephen Ojo, Agbotiname Lucky Imoize, Joseph Isabona and Mathew O. Alaba
Math. Comput. Appl. 2022, 27(5), 77; https://doi.org/10.3390/mca27050077 - 13 Sep 2022
Cited by 15 | Viewed by 7723
Abstract
Road transport is the most prone to accidents, resulting in significant fatalities and injuries. It also faces a plethora of never-ending problems, such as the frequent loss of lives and valuables during an accident. Appropriate actions need to be taken to address these [...] Read more.
Road transport is the most prone to accidents, resulting in significant fatalities and injuries. It also faces a plethora of never-ending problems, such as the frequent loss of lives and valuables during an accident. Appropriate actions need to be taken to address these problems, such as the establishment of an automatic incident detection system using artificial intelligence and machine learning. This article explores the overview of artificial intelligence and machine learning in facilitating automatic incident detector systems to decrease road accidents. The study examines the critical problems and potential remedies for reducing road traffic accidents and the application of artificial intelligence and machine learning in road transportation systems. More, new, and emerging trends that reduce frequent accidents in the transportation sector are discussed extensively. Specifically, the study organized the following sub-topics: an incident detector with machine learning and artificial intelligence and road management with machine learning and artificial intelligence. Additionally, safety is the primary concern of road transport; the internet of vehicles and vehicle ad hoc networks, including the use of wireless communication technologies such as 5G wireless networks and the use of machine learning and artificial intelligence for road transportation systems planning, are elaborated. Key findings from the review indicate that route optimization, cargo volume forecasting, predictive fleet maintenance, real-time vehicle tracking, and traffic management are critical to safeguarding road transportation systems. Finally, the paper summarizes the challenges facing the application of artificial intelligence in road transport systems, highlights the research trends, identifies the unresolved questions, and highlights the essential research takeaways. The work can serve as reference material for road transport system planning and management. Full article
Show Figures

Figure 1

27 pages, 2770 KiB  
Article
On the Use of High-Order Shape Functions in the SAFE Method and Their Performance in Wave Propagation Problems
by Elyas Mirzaee Kakhki, Jalil Rezaeepazhand, Fabian Duvigneau, Lotfollah Pahlavan, Resam Makvandi, Daniel Juhre, Majid Moavenian and Sascha Eisenträger
Math. Comput. Appl. 2022, 27(4), 63; https://doi.org/10.3390/mca27040063 - 25 Jul 2022
Viewed by 2600
Abstract
In this research, high-order shape functions commonly used in different finite element implementations are investigated with a special focus on their applicability in the semi-analytical finite element (SAFE) method being applied to wave propagation problems. Hierarchical shape functions (p-version of the [...] Read more.
In this research, high-order shape functions commonly used in different finite element implementations are investigated with a special focus on their applicability in the semi-analytical finite element (SAFE) method being applied to wave propagation problems. Hierarchical shape functions (p-version of the finite element method), Lagrange polynomials defined over non-equidistant nodes (spectral element method), and non-uniform rational B-splines (isogeometric analysis) are implemented in an in-house SAFE code, along with different refinement strategies such as h-, p-, and k-refinement. Since the numerical analysis of wave propagation is computationally quite challenging, high-order shape functions and local mesh refinement techniques are required to increase the accuracy of the solution, while at the same time decreasing the computational costs. The obtained results reveal that employing a suitable high-order basis in combination with one of the mentioned mesh refinement techniques has a notable effect on the performance of the SAFE method. This point becomes especially beneficial when dealing with applications in the areas of structural health monitoring or material property identification, where a model problem has to be solved repeatedly. Full article
Show Figures

Figure 1

29 pages, 660 KiB  
Article
A Trust Region Reduced Basis Pascoletti-Serafini Algorithm for Multi-Objective PDE-Constrained Parameter Optimization
by Stefan Banholzer, Luca Mechelli and Stefan Volkwein
Math. Comput. Appl. 2022, 27(3), 39; https://doi.org/10.3390/mca27030039 - 03 May 2022
Cited by 1 | Viewed by 1638
Abstract
In the present paper non-convex multi-objective parameter optimization problems are considered which are governed by elliptic parametrized partial differential equations (PDEs). To solve these problems numerically the Pascoletti-Serafini scalarization is applied and the obtained scalar optimization problems are solved by an augmented Lagrangian [...] Read more.
In the present paper non-convex multi-objective parameter optimization problems are considered which are governed by elliptic parametrized partial differential equations (PDEs). To solve these problems numerically the Pascoletti-Serafini scalarization is applied and the obtained scalar optimization problems are solved by an augmented Lagrangian method. However, due to the PDE constraints, the numerical solution is very expensive so that a model reduction is utilized by using the reduced basis (RB) method. The quality of the RB approximation is ensured by a trust-region strategy which does not require any offline procedure, in which the RB functions are computed in a greedy algorithm. Moreover, convergence of the proposed method is guaranteed and different techniques to prevent the excessive growth of the number of basis functions are explored. Numerical examples illustrate the efficiency of the proposed solution technique. Full article
(This article belongs to the Special Issue Computational Methods for Coupled Problems in Science and Engineering)
Show Figures

Figure 1

23 pages, 3275 KiB  
Article
Can DtN and GenEO Coarse Spaces Be Sufficiently Robust for Heterogeneous Helmholtz Problems?
by Niall Bootland and Victorita Dolean
Math. Comput. Appl. 2022, 27(3), 35; https://doi.org/10.3390/mca27030035 - 21 Apr 2022
Viewed by 2027
Abstract
Numerical solutions of heterogeneous Helmholtz problems present various computational challenges, with descriptive theory remaining out of reach for many popular approaches. Robustness and scalability are key for practical and reliable solvers in large-scale applications, especially for large wave number problems. In this work, [...] Read more.
Numerical solutions of heterogeneous Helmholtz problems present various computational challenges, with descriptive theory remaining out of reach for many popular approaches. Robustness and scalability are key for practical and reliable solvers in large-scale applications, especially for large wave number problems. In this work, we explore the use of a GenEO-type coarse space to build a two-level additive Schwarz method applicable to highly indefinite Helmholtz problems. Through a range of numerical tests on a 2D model problem, discretised by finite elements on pollution-free meshes, we observe robust convergence, iteration counts that do not increase with the wave number, and good scalability of our approach. We further provide results showing a favourable comparison with the DtN coarse space. Our numerical study shows promise that our solver methodology can be effective for challenging heterogeneous applications. Full article
(This article belongs to the Special Issue Domain Decomposition Methods)
Show Figures

Figure 1

28 pages, 11190 KiB  
Article
Reduced Order Modeling Using Advection-Aware Autoencoders
by Sourav Dutta, Peter Rivera-Casillas, Brent Styles and Matthew W. Farthing
Math. Comput. Appl. 2022, 27(3), 34; https://doi.org/10.3390/mca27030034 - 21 Apr 2022
Cited by 9 | Viewed by 2801
Abstract
Physical systems governed by advection-dominated partial differential equations (PDEs) are found in applications ranging from engineering design to weather forecasting. They are known to pose severe challenges to both projection-based and non-intrusive reduced order modeling, especially when linear subspace approximations are used. In [...] Read more.
Physical systems governed by advection-dominated partial differential equations (PDEs) are found in applications ranging from engineering design to weather forecasting. They are known to pose severe challenges to both projection-based and non-intrusive reduced order modeling, especially when linear subspace approximations are used. In this work, we develop an advection-aware (AA) autoencoder network that can address some of these limitations by learning efficient, physics-informed, nonlinear embeddings of the high-fidelity system snapshots. A fully non-intrusive reduced order model is developed by mapping the high-fidelity snapshots to a latent space defined by an AA autoencoder, followed by learning the latent space dynamics using a long-short-term memory (LSTM) network. This framework is also extended to parametric problems by explicitly incorporating parameter information into both the high-fidelity snapshots and the encoded latent space. Numerical results obtained with parametric linear and nonlinear advection problems indicate that the proposed framework can reproduce the dominant flow features even for unseen parameter values. Full article
(This article belongs to the Special Issue Computational Methods for Coupled Problems in Science and Engineering)
Show Figures

Figure 1

18 pages, 1136 KiB  
Article
Evaluation of Machine Learning Algorithms for Early Diagnosis of Deep Venous Thrombosis
by Eduardo Enrique Contreras-Luján, Enrique Efrén García-Guerrero, Oscar Roberto López-Bonilla, Esteban Tlelo-Cuautle, Didier López-Mancilla and Everardo Inzunza-González
Math. Comput. Appl. 2022, 27(2), 24; https://doi.org/10.3390/mca27020024 - 04 Mar 2022
Cited by 4 | Viewed by 4156
Abstract
Deep venous thrombosis (DVT) is a disease that must be diagnosed quickly, as it can trigger the death of patients. Nowadays, one can find different ways to determine it, including clinical scoring, D-dimer, ultrasonography, etc. Recently, scientists have focused efforts on using machine [...] Read more.
Deep venous thrombosis (DVT) is a disease that must be diagnosed quickly, as it can trigger the death of patients. Nowadays, one can find different ways to determine it, including clinical scoring, D-dimer, ultrasonography, etc. Recently, scientists have focused efforts on using machine learning (ML) and neural networks for disease diagnosis, progressively increasing the accuracy and efficacy. Patients with suspected DVT have no apparent symptoms. Using pattern recognition techniques, aiding good timely diagnosis, as well as well-trained ML models help to make good decisions and validation. The aim of this paper is to propose several ML models for a more efficient and reliable DVT diagnosis through its implementation on an edge device for the development of instruments that are smart, portable, reliable, and cost-effective. The dataset was obtained from a state-of-the-art article. It is divided into 85% for training and cross-validation and 15% for testing. The input data in this study are the Wells criteria, the patient’s age, and the patient’s gender. The output data correspond to the patient’s diagnosis. This study includes the evaluation of several classifiers such as Decision Trees (DT), Extra Trees (ET), K-Nearest Neighbor (KNN), Multi-Layer Perceptron Neural Network (MLP-NN), Random Forest (RF), and Support Vector Machine (SVM). Finally, the implementation of these ML models on a high-performance embedded system is proposed to develop an intelligent system for early DVT diagnosis. It is reliable, portable, open source, and low cost. The performance of different ML algorithms was evaluated, where KNN achieved the highest accuracy of 90.4% and specificity of 80.66% implemented on personal computer (PC) and Raspberry Pi 4 (RPi4). The accuracy of all trained models on PC and Raspberry Pi 4 is greater than 85%, while the area under the curve (AUC) values are between 0.81 and 0.86. In conclusion, as compared to traditional methods, the best ML classifiers are effective at predicting DVT in an early and efficient manner. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2021)
Show Figures

Figure 1

20 pages, 28880 KiB  
Article
Attention Measurement of an Autism Spectrum Disorder User Using EEG Signals: A Case Study
by José Jaime Esqueda-Elizondo, Reyes Juárez-Ramírez, Oscar Roberto López-Bonilla, Enrique Efrén García-Guerrero, Gilberto Manuel Galindo-Aldana, Laura Jiménez-Beristáin, Alejandra Serrano-Trujillo, Esteban Tlelo-Cuautle and Everardo Inzunza-González
Math. Comput. Appl. 2022, 27(2), 21; https://doi.org/10.3390/mca27020021 - 02 Mar 2022
Cited by 12 | Viewed by 5412
Abstract
Autism Spectrum Disorder (ASD) is a neurodevelopmental life condition characterized by problems with social interaction, low verbal and non-verbal communication skills, and repetitive and restricted behavior. People with ASD usually have variable attention levels because they have hypersensitivity and large amounts of environmental [...] Read more.
Autism Spectrum Disorder (ASD) is a neurodevelopmental life condition characterized by problems with social interaction, low verbal and non-verbal communication skills, and repetitive and restricted behavior. People with ASD usually have variable attention levels because they have hypersensitivity and large amounts of environmental information are a problem for them. Attention is a process that occurs at the cognitive level and allows us to orient ourselves towards relevant stimuli, ignoring those that are not, and act accordingly. This paper presents a methodology based on electroencephalographic (EEG) signals for attention measurement in a 13-year-old boy diagnosed with ASD. The EEG signals are acquired with an Epoc+ Brain–Computer Interface (BCI) via the Emotiv Pro platform while developing several learning activities and using Matlab 2019a for signal processing. For this article, we propose to use electrodes F3, F4, P7, and P8. Then, we calculate the band power spectrum density to detect the Theta Relative Power (TRP), Alpha Relative Power (ARP), Beta Relative Power (BRP), Theta–Beta Ratio (TBR), Theta–Alpha Ratio (TAR), and Theta/(Alpha+Beta), which are features related to attention detection and neurofeedback. We train and evaluate several machine learning (ML) models with these features. In this study, the multi-layer perceptron neural network model (MLP-NN) has the best performance, with an AUC of 0.9299, Cohen’s Kappa coefficient of 0.8597, Matthews correlation coefficient of 0.8602, and Hamming loss of 0.0701. These findings make it possible to develop better learning scenarios according to the person’s needs with ASD. Moreover, it makes it possible to obtain quantifiable information on their progress to reinforce the perception of the teacher or therapist. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2021)
Show Figures

Figure 1

20 pages, 24807 KiB  
Article
Multi-Physics Inverse Homogenization for the Design of Innovative Cellular Materials: Application to Thermo-Elastic Problems
by Matteo Gavazzoni, Nicola Ferro, Simona Perotto and Stefano Foletti
Math. Comput. Appl. 2022, 27(1), 15; https://doi.org/10.3390/mca27010015 - 15 Feb 2022
Cited by 3 | Viewed by 2508
Abstract
We present a new algorithm to design lightweight cellular materials with required properties in a multi-physics context. In particular, we focus on a thermo-elastic setting by promoting the design of unit cells characterized both by an isotropic and an anisotropic behavior with respect [...] Read more.
We present a new algorithm to design lightweight cellular materials with required properties in a multi-physics context. In particular, we focus on a thermo-elastic setting by promoting the design of unit cells characterized both by an isotropic and an anisotropic behavior with respect to mechanical and thermal requirements. The proposed procedure generalizes the microSIMPATY algorithm to a thermo-elastic framework by preserving all the good properties of the reference design methodology. The resulting layouts exhibit non-standard topologies and are characterized by very sharp contours, thus limiting the post-processing before manufacturing. The new cellular materials are compared with the state-of-art in engineering practice in terms of thermo-elastic properties, thus highlighting the good performance of the new layouts which, in some cases, outperform the consolidated choices. Full article
(This article belongs to the Special Issue Computational Methods for Coupled Problems in Science and Engineering)
Show Figures

Figure 1

25 pages, 4188 KiB  
Article
AutoML for Feature Selection and Model Tuning Applied to Fault Severity Diagnosis in Spur Gearboxes
by Mariela Cerrada, Leonardo Trujillo, Daniel E. Hernández, Horacio A. Correa Zevallos, Jean Carlo Macancela, Diego Cabrera and René Vinicio Sánchez
Math. Comput. Appl. 2022, 27(1), 6; https://doi.org/10.3390/mca27010006 - 13 Jan 2022
Cited by 13 | Viewed by 3770
Abstract
Gearboxes are widely used in industrial processes as mechanical power transmission systems. Then, gearbox failures can affect other parts of the system and produce economic loss. The early detection of the possible failure modes and their severity assessment in such devices is an [...] Read more.
Gearboxes are widely used in industrial processes as mechanical power transmission systems. Then, gearbox failures can affect other parts of the system and produce economic loss. The early detection of the possible failure modes and their severity assessment in such devices is an important field of research. Data-driven approaches usually require an exhaustive development of pipelines including models’ parameter optimization and feature selection. This paper takes advantage of the recent Auto Machine Learning (AutoML) tools to propose proper feature and model selection for three failure modes under different severity levels: broken tooth, pitting and crack. The performance of 64 statistical condition indicators (SCI) extracted from vibration signals under the three failure modes were analyzed by two AutoML systems, namely the H2O Driverless AI platform and TPOT, both of which include feature engineering and feature selection mechanisms. In both cases, the systems converged to different types of decision tree methods, with ensembles of XGBoost models preferred by H2O while TPOT generated different types of stacked models. The models produced by both systems achieved very high, and practically equivalent, performances on all problems. Both AutoML systems converged to pipelines that focus on very similar subsets of features across all problems, indicating that several problems in this domain can be solved by a rather small set of 10 common features, with accuracy up to 90%. This latter result is important in the research of useful feature selection for gearbox fault diagnosis. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2021)
Show Figures

Figure 1

21 pages, 1318 KiB  
Review
Predictive Maintenance in the Automotive Sector: A Literature Review
by Fabio Arena, Mario Collotta, Liliana Luca, Marianna Ruggieri and Francesco Gaetano Termine
Math. Comput. Appl. 2022, 27(1), 2; https://doi.org/10.3390/mca27010002 - 31 Dec 2021
Cited by 22 | Viewed by 13247
Abstract
With the rapid advancement of sensor and network technology, there has been a notable increase in the availability of condition-monitoring data such as vibration, temperature, pressure, voltage, and other electrical and mechanical parameters. With the introduction of big data, it is possible to [...] Read more.
With the rapid advancement of sensor and network technology, there has been a notable increase in the availability of condition-monitoring data such as vibration, temperature, pressure, voltage, and other electrical and mechanical parameters. With the introduction of big data, it is possible to prevent potential failures and estimate the remaining useful life of the equipment by developing advanced mathematical models and artificial intelligence (AI) techniques. These approaches allow taking maintenance actions quickly and appropriately. In this scenario, this paper presents a systematic literature review of statistical inference approaches, stochastic methods, and AI techniques for predictive maintenance in the automotive sector. It provides a summary on these approaches, their main results, challenges, and opportunities, and it supports new research works for vehicle predictive maintenance. Full article
Show Figures

Figure 1

29 pages, 761 KiB  
Article
Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics
by Dmytro Sytnyk and Roderick Melnik
Math. Comput. Appl. 2021, 26(4), 73; https://doi.org/10.3390/mca26040073 - 23 Oct 2021
Cited by 5 | Viewed by 3770
Abstract
Nonlocal models are ubiquitous in all branches of science and engineering, with a rapidly expanding range of mathematical and computational applications due to the ability of such models to capture effects and phenomena that traditional models cannot. While spatial nonlocalities have received considerable [...] Read more.
Nonlocal models are ubiquitous in all branches of science and engineering, with a rapidly expanding range of mathematical and computational applications due to the ability of such models to capture effects and phenomena that traditional models cannot. While spatial nonlocalities have received considerable attention in the research community, the same cannot be said about nonlocality in time, in particular when nonlocal initial conditions are present. This paper aims at filling this gap, providing an overview of the current status of nonlocal models and focusing on the mathematical treatment of such models when nonlocal initial conditions are at the heart of the problem. Specifically, our representative example is given for a nonlocal-in-time problem for the abstract Schrödinger equation. By exploiting the linear nature of nonlocal conditions, we derive an exact representation of the solution operator under assumptions that the spectrum of Hamiltonian is contained in the horizontal strip of the complex plane. The derived representation permits us to establish the necessary and sufficient conditions for the problem’s well-posedness and the existence of its solution under different regularities. Furthermore, we present new sufficient conditions for the existence of the solution that extend the existing results in this field to the case when some nonlocal parameters are unbounded. Two further examples demonstrate the developed methodology and highlight the importance of its computer algebra component in the reduction procedures and parameter estimations for nonlocal models. Finally, a connection of the considered models and developed analysis is discussed in the context of other reduction techniques, concentrating on the most promising from the viewpoint of data-driven modelling environments, and providing directions for further generalizations. Full article
Show Figures

Figure 1

17 pages, 1023 KiB  
Article
Modelling Forest Fires Using Complex Networks
by Sara Perestrelo, Maria C. Grácio, Nuno A. Ribeiro and Luís M. Lopes
Math. Comput. Appl. 2021, 26(4), 68; https://doi.org/10.3390/mca26040068 - 28 Sep 2021
Cited by 3 | Viewed by 2614
Abstract
Forest fires have been a major threat to the environment throughout history. In order to mitigate its consequences, we present, in a first of a series of works, a mathematical model with the purpose of predicting fire spreading in a given land portion [...] Read more.
Forest fires have been a major threat to the environment throughout history. In order to mitigate its consequences, we present, in a first of a series of works, a mathematical model with the purpose of predicting fire spreading in a given land portion divided into patches, considering the area and the rate of spread of each patch as inputs. The rate of spread can be estimated from previous knowledge on fuel availability, weather and terrain conditions. We compute the time duration of the spreading process in a land patch in order to construct and parametrize a landscape network, using cellular automata simulations. We use the multilayer network model to propose a network of networks at the landscape scale, where the nodes are the local patches, each with their own spreading dynamics. We compute some respective network measures and aim, in further work, for the establishment of a fire-break structure according to increasing accuracy simulation results. Full article
Show Figures

Figure 1

37 pages, 16808 KiB  
Review
Review of Multi-Physics Modeling on the Active Magnetic Regenerative Refrigeration
by Julien Eustache, Antony Plait, Frédéric Dubas and Raynal Glises
Math. Comput. Appl. 2021, 26(2), 47; https://doi.org/10.3390/mca26020047 - 15 Jun 2021
Cited by 6 | Viewed by 3064
Abstract
Compared to conventional vapor-compression refrigeration systems, magnetic refrigeration is a promising and potential alternative technology. The magnetocaloric effect (MCE) is used to produce heat and cold sources through a magnetocaloric material (MCM). The material is submitted to a magnetic field with active magnetic [...] Read more.
Compared to conventional vapor-compression refrigeration systems, magnetic refrigeration is a promising and potential alternative technology. The magnetocaloric effect (MCE) is used to produce heat and cold sources through a magnetocaloric material (MCM). The material is submitted to a magnetic field with active magnetic regenerative refrigeration (AMRR) cycles. Initially, this effect was widely used for cryogenic applications to achieve very low temperatures. However, this technology must be improved to replace vapor-compression devices operating around room temperature. Therefore, over the last 30 years, a lot of studies have been done to obtain more efficient devices. Thus, the modeling is a crucial step to perform a preliminary study and optimization. In this paper, after a large introduction on MCE research, a state-of-the-art of multi-physics modeling on the AMRR cycle modeling is made. To end this paper, a suggestion of innovative and advanced modeling solutions to study magnetocaloric regenerator is described. Full article
Show Figures

Figure 1

37 pages, 1551 KiB  
Article
Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models
by Manuel Berkemeier and Sebastian Peitz
Math. Comput. Appl. 2021, 26(2), 31; https://doi.org/10.3390/mca26020031 - 15 Apr 2021
Cited by 4 | Viewed by 2913
Abstract
We present a local trust region descent algorithm for unconstrained and convexly constrained multiobjective optimization problems. It is targeted at heterogeneous and expensive problems, i.e., problems that have at least one objective function that is computationally expensive. Convergence to a Pareto critical point [...] Read more.
We present a local trust region descent algorithm for unconstrained and convexly constrained multiobjective optimization problems. It is targeted at heterogeneous and expensive problems, i.e., problems that have at least one objective function that is computationally expensive. Convergence to a Pareto critical point is proven. The method is derivative-free in the sense that derivative information need not be available for the expensive objectives. Instead, a multiobjective trust region approach is used that works similarly to its well-known scalar counterparts and complements multiobjective line-search algorithms. Local surrogate models constructed from evaluation data of the true objective functions are employed to compute possible descent directions. In contrast to existing multiobjective trust region algorithms, these surrogates are not polynomial but carefully constructed radial basis function networks. This has the important advantage that the number of data points needed per iteration scales linearly with the decision space dimension. The local models qualify as fully linear and the corresponding general scalar framework is adapted for problems with multiple objectives. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2020)
Show Figures

Figure 1

23 pages, 746 KiB  
Article
ROM-Based Inexact Subdivision Methods for PDE-Constrained Multiobjective Optimization
by Stefan Banholzer, Bennet Gebken, Lena Reichle and Stefan Volkwein
Math. Comput. Appl. 2021, 26(2), 32; https://doi.org/10.3390/mca26020032 - 15 Apr 2021
Cited by 1 | Viewed by 1964
Abstract
The goal in multiobjective optimization is to determine the so-called Pareto set. Our optimization problem is governed by a parameter-dependent semi-linear elliptic partial differential equation (PDE). To solve it, we use a gradient-based set-oriented numerical method. The numerical solution of the PDE by [...] Read more.
The goal in multiobjective optimization is to determine the so-called Pareto set. Our optimization problem is governed by a parameter-dependent semi-linear elliptic partial differential equation (PDE). To solve it, we use a gradient-based set-oriented numerical method. The numerical solution of the PDE by standard discretization methods usually leads to high computational effort. To overcome this difficulty, reduced-order modeling (ROM) is developed utilizing the reduced basis method. These model simplifications cause inexactness in the gradients. For that reason, an additional descent condition is proposed. Applying a modified subdivision algorithm, numerical experiments illustrate the efficiency of our solution approach. Full article
(This article belongs to the Special Issue Set Oriented Numerics 2022)
Show Figures

Figure 1

25 pages, 2805 KiB  
Article
Data Augmentation and Feature Selection for Automatic Model Recommendation in Computational Physics
by Thomas Daniel, Fabien Casenave, Nissrine Akkari and David Ryckelynck
Math. Comput. Appl. 2021, 26(1), 17; https://doi.org/10.3390/mca26010017 - 16 Feb 2021
Cited by 3 | Viewed by 2388
Abstract
Classification algorithms have recently found applications in computational physics for the selection of numerical methods or models adapted to the environment and the state of the physical system. For such classification tasks, labeled training data come from numerical simulations and generally correspond to [...] Read more.
Classification algorithms have recently found applications in computational physics for the selection of numerical methods or models adapted to the environment and the state of the physical system. For such classification tasks, labeled training data come from numerical simulations and generally correspond to physical fields discretized on a mesh. Three challenging difficulties arise: the lack of training data, their high dimensionality, and the non-applicability of common data augmentation techniques to physics data. This article introduces two algorithms to address these issues: one for dimensionality reduction via feature selection, and one for data augmentation. These algorithms are combined with a wide variety of classifiers for their evaluation. When combined with a stacking ensemble made of six multilayer perceptrons and a ridge logistic regression, they enable reaching an accuracy of 90% on our classification problem for nonlinear structural mechanics. Full article
Show Figures

Figure 1

14 pages, 3165 KiB  
Article
Mathematical Model and Numerical Simulation for Electric Field Induced Cancer Cell Migration
by Antonino Amoddeo
Math. Comput. Appl. 2021, 26(1), 4; https://doi.org/10.3390/mca26010004 - 31 Dec 2020
Viewed by 2299
Abstract
A mathematical model describing the interaction of cancer cells with the urokinase plasminogen activation system is represented by a system of partial differential equations, in which cancer cell dynamics accounts for diffusion, chemotaxis, and haptotaxis contributions. The mutual relations between nerve fibers and [...] Read more.
A mathematical model describing the interaction of cancer cells with the urokinase plasminogen activation system is represented by a system of partial differential equations, in which cancer cell dynamics accounts for diffusion, chemotaxis, and haptotaxis contributions. The mutual relations between nerve fibers and tumors have been recently investigated, in particular, the role of nerves in the development of tumors, as well neurogenesis induced by cancer cells. Such mechanisms are mediated by neurotransmitters released by neurons as a consequence of electrical stimuli flowing along the nerves, and therefore electric fields can be present inside biological tissues, in particular, inside tumors. Considering cancer cells as negatively charged particles immersed in the correct biological environment and subjected to an external electric field, the effect of the latter on cancer cell dynamics is still unknown. Here, we implement a mathematical model that accounts for the interaction of cancer cells with the urokinase plasminogen activation system subjected to a uniform applied electric field, simulating the first stage of cancer cell dynamics in a three-dimensional axial symmetric domain. The obtained numerical results predict that cancer cells can be moved along a preferred direction by an applied electric field, suggesting new and interesting strategies in cancer therapy. Full article
(This article belongs to the Section Natural Sciences)
Show Figures

Figure 1

27 pages, 1564 KiB  
Review
Surrogate Modeling Approaches for Multiobjective Optimization: Methods, Taxonomy, and Results
by Kalyanmoy Deb, Proteek Chandan Roy and Rayan Hussein
Math. Comput. Appl. 2021, 26(1), 5; https://doi.org/10.3390/mca26010005 - 31 Dec 2020
Cited by 21 | Viewed by 3843
Abstract
Most practical optimization problems are comprised of multiple conflicting objectives and constraints which involve time-consuming simulations. Construction of metamodels of objectives and constraints from a few high-fidelity solutions and a subsequent optimization of metamodels to find in-fill solutions in an iterative manner remain [...] Read more.
Most practical optimization problems are comprised of multiple conflicting objectives and constraints which involve time-consuming simulations. Construction of metamodels of objectives and constraints from a few high-fidelity solutions and a subsequent optimization of metamodels to find in-fill solutions in an iterative manner remain a common metamodeling based optimization strategy. The authors have previously proposed a taxonomy of 10 different metamodeling frameworks for multiobjective optimization problems, each of which constructs metamodels of objectives and constraints independently or in an aggregated manner. Of the 10 frameworks, five follow a generative approach in which a single Pareto-optimal solution is found at a time and other five frameworks were proposed to find multiple Pareto-optimal solutions simultaneously. Of the 10 frameworks, two frameworks (M3-2 and M4-2) are detailed here for the first time involving multimodal optimization methods. In this paper, we also propose an adaptive switching based metamodeling (ASM) approach by switching among all 10 frameworks in successive epochs using a statistical comparison of metamodeling accuracy of all 10 frameworks. On 18 problems from three to five objectives, the ASM approach performs better than the individual frameworks alone. Finally, the ASM approach is compared with three other recently proposed multiobjective metamodeling methods and superior performance of the ASM approach is observed. With growing interest in metamodeling approaches for multiobjective optimization, this paper evaluates existing strategies and proposes a viable adaptive strategy by portraying importance of using an ensemble of metamodeling frameworks for a more reliable multiobjective optimization for a limited budget of solution evaluations. Full article
(This article belongs to the Collection Numerical Optimization Reviews)
Show Figures

Figure 1

21 pages, 10058 KiB  
Article
A Localized Collocation Solver Based on T-Complete Functions for Anti-Plane Transverse Elastic Wave Propagation Analysis in 2D Phononic Crystals
by Zhuo-Jia Fu, Lu-Feng Li, De-Shun Yin and Li-Li Yuan
Math. Comput. Appl. 2021, 26(1), 2; https://doi.org/10.3390/mca26010002 - 30 Dec 2020
Cited by 3 | Viewed by 1980
Abstract
In this paper, we introduce a novel localized collocation solver for two-dimensional (2D) phononic crystal analysis. In the proposed collocation solver, the displacement at each node is expressed as a linear combination of T-complete functions in each stencil support and the sparse linear [...] Read more.
In this paper, we introduce a novel localized collocation solver for two-dimensional (2D) phononic crystal analysis. In the proposed collocation solver, the displacement at each node is expressed as a linear combination of T-complete functions in each stencil support and the sparse linear system is obtained by satisfying the considered governing equation at interior nodes and boundary conditions at boundary nodes. As compared with finite element method (FEM) results and the analytical solutions, the efficiency and accuracy of the proposed localized collocation solver are verified under a benchmark example. Then, the proposed method is applied to 2D phononic crystals with various lattice forms and scatterer shapes, where the related band structures, transmission spectra, and displacement amplitude distributions are calculated as compared with the FEM. Full article
(This article belongs to the Section Engineering)
Show Figures

Figure 1

14 pages, 608 KiB  
Article
A Transformational Modified Markov Process for Chord-Based Algorithmic Composition
by Meirav Amram, Etan Fisher, Shai Gul and Uzi Vishne
Math. Comput. Appl. 2020, 25(3), 43; https://doi.org/10.3390/mca25030043 - 10 Jul 2020
Cited by 2 | Viewed by 2405
Abstract
The goal of this research is to maximize chord-based composition possibilities given a relatively small amount of information. A transformational approach, based in group theory, was chosen, focusing on chord intervals as the components of a modified Markov process. The Markov process was [...] Read more.
The goal of this research is to maximize chord-based composition possibilities given a relatively small amount of information. A transformational approach, based in group theory, was chosen, focusing on chord intervals as the components of a modified Markov process. The Markov process was modified to balance between average harmony, representing familiarity, and entropy, representing novelty. Uniform triadic transformations are suggested as a further extension of the transformational approach, improving the quality of tonality. The composition algorithms are demonstrated given a short chord progression and also given a larger database of albums by the Beatles. Results demonstrate capabilities and limitations of the algorithms. Full article
(This article belongs to the Section Natural Sciences)
Show Figures

Figure 1

21 pages, 989 KiB  
Article
Parallel Matrix-Free Higher-Order Finite Element Solvers for Phase-Field Fracture Problems
by Daniel Jodlbauer, Ulrich Langer and Thomas Wick
Math. Comput. Appl. 2020, 25(3), 40; https://doi.org/10.3390/mca25030040 - 07 Jul 2020
Cited by 15 | Viewed by 2811
Abstract
Phase-field fracture models lead to variational problems that can be written as a coupled variational equality and inequality system. Numerically, such problems can be treated with Galerkin finite elements and primal-dual active set methods. Specifically, low-order and high-order finite elements may be employed, [...] Read more.
Phase-field fracture models lead to variational problems that can be written as a coupled variational equality and inequality system. Numerically, such problems can be treated with Galerkin finite elements and primal-dual active set methods. Specifically, low-order and high-order finite elements may be employed, where, for the latter, only few studies exist to date. The most time-consuming part in the discrete version of the primal-dual active set (semi-smooth Newton) algorithm consists in the solutions of changing linear systems arising at each semi-smooth Newton step. We propose a new parallel matrix-free monolithic multigrid preconditioner for these systems. We provide two numerical tests, and discuss the performance of the parallel solver proposed in the paper. Furthermore, we compare our new preconditioner with a block-AMG preconditioner available in the literature. Full article
(This article belongs to the Special Issue High-Performance Computing 2020)
Show Figures

Figure 1

21 pages, 3219 KiB  
Article
Numerical Approach to a Nonlocal Advection-Reaction-Diffusion Model of Cartilage Pattern Formation
by Tilmann Glimm and Jianying Zhang
Math. Comput. Appl. 2020, 25(2), 36; https://doi.org/10.3390/mca25020036 - 19 Jun 2020
Cited by 3 | Viewed by 2619
Abstract
We propose a numerical approach that combines a radial basis function (RBF) meshless approximation with a finite difference discretization to solve a nonlinear system of integro-differential equations. The equations are of advection-reaction-diffusion type modeling the formation of pre-cartilage condensations in embryonic chicken limbs. [...] Read more.
We propose a numerical approach that combines a radial basis function (RBF) meshless approximation with a finite difference discretization to solve a nonlinear system of integro-differential equations. The equations are of advection-reaction-diffusion type modeling the formation of pre-cartilage condensations in embryonic chicken limbs. The computational domain is four dimensional in the sense that the cell density depends continuously on two spatial variables as well as two structure variables, namely membrane-bound counterreceptor densities. The biologically proper Dirichlet boundary conditions imposed in the semi-infinite structure variable region is in favor of a meshless method with Gaussian basis functions. Coupled with WENO5 finite difference spatial discretization and the method of integrating factors, the time integration via method of lines achieves optimal complexity. In addition, the proposed scheme can be extended to similar models with more general boundary conditions. Numerical results are provided to showcase the validity of the scheme. Full article
(This article belongs to the Section Natural Sciences)
Show Figures

Figure 1

14 pages, 17146 KiB  
Article
Mechanism of Coup and Contrecoup Injuries Induced by a Knock-Out Punch
by Milan Toma, Rosalyn Chan-Akeley, Christopher Lipari and Sheng-Han Kuo
Math. Comput. Appl. 2020, 25(2), 22; https://doi.org/10.3390/mca25020022 - 15 Apr 2020
Cited by 16 | Viewed by 9108
Abstract
Primary Objective: The interaction of cerebrospinal fluid with the brain parenchyma in an impact scenario is studied. Research Design: A computational fluid-structure interaction model is used to simulate the interaction of cerebrospinal fluid with a comprehensive brain model. Methods and Procedures: The method [...] Read more.
Primary Objective: The interaction of cerebrospinal fluid with the brain parenchyma in an impact scenario is studied. Research Design: A computational fluid-structure interaction model is used to simulate the interaction of cerebrospinal fluid with a comprehensive brain model. Methods and Procedures: The method of smoothed particle hydrodynamics is used to simulate the fluid flow, induced by the impact, simultaneously with finite element analysis to solve the large deformations in the brain model. Main Outcomes and Results: Mechanism of injury resulting in concussion is demonstrated. The locations with the highest stress values on the brain parenchyma are shown. Conclusions: Our simulations found that the damage to the brain resulting from the contrecoup injury is more severe than that resulting from the coup injury. Additionally, we show that the contrecoup injury does not always appear on the side opposite from where impact occurs. Full article
(This article belongs to the Special Issue Numerical Modelling and Simulation Applied to Head Trauma)
Show Figures

Figure 1

Back to TopTop