Research

14 pages, 3753 KiB

Open AccessArticle

Dynamically Meaningful Latent Representations of Dynamical Systems

by Imran Nasim and Michael E. Henderson

Mathematics 2024, 12(3), 476; https://doi.org/10.3390/math12030476 - 02 Feb 2024

Viewed by 851

Dynamical systems are ubiquitous in the physical world and are often well-described by partial differential equations (PDEs). Despite their formally infinite-dimensional solution space, a number of systems have long time dynamics that live on a low-dimensional manifold. However, current methods to probe the [...] Read more.

Dynamical systems are ubiquitous in the physical world and are often well-described by partial differential equations (PDEs). Despite their formally infinite-dimensional solution space, a number of systems have long time dynamics that live on a low-dimensional manifold. However, current methods to probe the long time dynamics require prerequisite knowledge about the underlying dynamics of the system. In this study, we present a data-driven hybrid modeling approach to help tackle this problem by combining numerically derived representations and latent representations obtained from an autoencoder. We validate our latent representations and show they are dynamically interpretable, capturing the dynamical characteristics of qualitatively distinct solution types. Furthermore, we probe the topological preservation of the latent representation with respect to the raw dynamical data using methods from persistent homology. Finally, we show that our framework is generalizable, having been successfully applied to both integrable and non-integrable systems that capture a rich and diverse array of solution types. Our method does not require any prior dynamical knowledge of the system and can be used to discover the intrinsic dynamical behavior in a purely data-driven way. Full article

(This article belongs to the Special Issue Applied Mathematics and Machine Learning)

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21 pages, 666 KiB

Open AccessArticle

The Hybrid Modeling of Spatial Autoregressive Exogenous Using Casetti’s Model Approach for the Prediction of Rainfall

by Annisa Nur Falah, Budi Nurani Ruchjana, Atje Setiawan Abdullah and Juli Rejito

Mathematics 2023, 11(17), 3783; https://doi.org/10.3390/math11173783 - 03 Sep 2023

Cited by 1 | Viewed by 871

Abstract

Spatial Autoregressive (SAR) models are used to model the relationship between variables within a specific region or location, considering the influence of neighboring variables, and have received considerable attention in recent years. However, when the impact of exogenous variables becomes notably pronounced, an [...] Read more.

Spatial Autoregressive (SAR) models are used to model the relationship between variables within a specific region or location, considering the influence of neighboring variables, and have received considerable attention in recent years. However, when the impact of exogenous variables becomes notably pronounced, an alternative approach is warranted. Spatial Expansion, coupled with the Casetti model approach, serves as an extension of the SAR model, accommodating the influence of these exogenous variables. This modeling technique finds application in the realm of rainfall prediction, where exogenous factors, such as air temperature, humidity, solar irradiation, wind speed, and surface pressure, play pivotal roles. Consequently, this research aimed to combine the SAR and Spatial Expansion models through the Casetti model approach, leading to the creation of the Spatial Autoregressive Exogenous (SAR-X) model. The SAR-X was employed to forecast the rainfall patterns in the West Java region, utilizing data obtained from the National Aeronautics and Space Administration Prediction of Worldwide Energy Resources (NASA POWER) dataset. The practical execution of this research capitalized on the computational capabilities of the RStudio software version 2022.12.0. Within the framework of this investigation, a comprehensive and integrated RStudio script, seamlessly incorporated into the RShiny web application, was developed so that it is easy to use. Full article

(This article belongs to the Special Issue Applied Mathematics and Machine Learning)

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10 pages, 1256 KiB

Open AccessArticle

Anomaly Detection in the Molecular Structure of Gallium Arsenide Using Convolutional Neural Networks

by Timothy Roche, Aihua Wood, Philip Cho and Chancellor Johnstone

Mathematics 2023, 11(15), 3428; https://doi.org/10.3390/math11153428 - 07 Aug 2023

Viewed by 748

Abstract

This paper concerns the development of a machine learning tool to detect anomalies in the molecular structure of Gallium Arsenide. We employ a combination of a CNN and a PCA reconstruction to create the model, using real images taken with an electron microscope [...] Read more.

This paper concerns the development of a machine learning tool to detect anomalies in the molecular structure of Gallium Arsenide. We employ a combination of a CNN and a PCA reconstruction to create the model, using real images taken with an electron microscope in training and testing. The methodology developed allows for the creation of a defect detection model, without any labeled images of defects being required for training. The model performed well on all tests under the established assumptions, allowing for reliable anomaly detection. To the best of our knowledge, such methods are not currently available in the open literature; thus, this work fills a gap in current capabilities. Full article

(This article belongs to the Special Issue Applied Mathematics and Machine Learning)

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11 pages, 346 KiB

Open AccessArticle

Graph Convolutional-Based Deep Residual Modeling for Rumor Detection on Social Media

by Na Ye, Dingguo Yu, Yijie Zhou, Ke-ke Shang and Suiyu Zhang

Mathematics 2023, 11(15), 3393; https://doi.org/10.3390/math11153393 - 03 Aug 2023

Cited by 1 | Viewed by 820

Abstract

The popularity and development of social media have made it more and more convenient to spread rumors, and it has become especially important to detect rumors in massive amounts of information. Most of the traditional rumor detection methods use the rumor content or [...] Read more.

The popularity and development of social media have made it more and more convenient to spread rumors, and it has become especially important to detect rumors in massive amounts of information. Most of the traditional rumor detection methods use the rumor content or propagation structure to mine rumor characteristics, ignoring the fusion characteristics of the content and structure and their interaction. Therefore, a novel rumor detection method based on heterogeneous convolutional networks is proposed. First, this paper constructs a heterogeneous map that combines both the rumor content and propagation structure to explore their interaction during rumor propagation and obtain a rumor representation. On this basis, this paper uses a deep residual graph convolutional neural network to construct the content and structure interaction information of the current network propagation model. Finally, this paper uses the Twitter15 and Twitter16 datasets to verify the proposed method. Experimental results show that the proposed method has higher detection accuracy compared to the traditional rumor detection method. Full article

(This article belongs to the Special Issue Applied Mathematics and Machine Learning)

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24 pages, 3465 KiB

Open AccessArticle

A Bibliometric Analysis of Digital Twin in the Supply Chain

by Weng Siew Lam, Weng Hoe Lam and Pei Fun Lee

Mathematics 2023, 11(15), 3350; https://doi.org/10.3390/math11153350 - 31 Jul 2023

Cited by 2 | Viewed by 1928

Abstract

Digital twin is the digital representation of an entity, and it drives Industry 4.0. This paper presents a bibliometric analysis of digital twin in the supply chain to help researchers, industry practitioners, and academics to understand the trend, development, and focus of the [...] Read more.

Digital twin is the digital representation of an entity, and it drives Industry 4.0. This paper presents a bibliometric analysis of digital twin in the supply chain to help researchers, industry practitioners, and academics to understand the trend, development, and focus of the areas of digital twin in the supply chain. This paper found several key clusters of research, including the designing of a digital twin model, integration of a digital twin model, application of digital twin in quality control, and digital twin in digitalization. In the embryonic stage of research, digital twin was tested in the production line with limited optimization. In the development stage, the importance of digital twin in Industry 4.0 was observed, as big data, machine learning, Industrial Internet of Things, blockchain, edge computing, and cloud-based systems complemented digital twin models. Digital twin was applied to improve sustainability in manufacturing and production logistics. In the current prosperity stage with high annual publications, the recent trends of this topic focus on the integration of deep learning, data models, and artificial intelligence for digitalization. This bibliometric analysis also found that the COVID-19 pandemic drove the start of the prosperity stage of digital twin research in the supply chain. Researchers in this field are slowly moving towards applying digital twin for human-centric systems and mass personalization to prepare to transit to Industry 5.0. Full article

(This article belongs to the Special Issue Applied Mathematics and Machine Learning)

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14 pages, 1410 KiB

Open AccessArticle

Numerical Simulation of the Korteweg–de Vries Equation with Machine Learning

by Kristina O. F. Williams and Benjamin F. Akers

Mathematics 2023, 11(13), 2791; https://doi.org/10.3390/math11132791 - 21 Jun 2023

Viewed by 1169

Abstract

A machine learning procedure is proposed to create numerical schemes for solutions of nonlinear wave equations on coarse grids. This method trains stencil weights of a discretization of the equation, with the truncation error of the scheme as the objective function for training. [...] Read more.

A machine learning procedure is proposed to create numerical schemes for solutions of nonlinear wave equations on coarse grids. This method trains stencil weights of a discretization of the equation, with the truncation error of the scheme as the objective function for training. The method uses centered finite differences to initialize the optimization routine and a second-order implicit-explicit time solver as a framework. Symmetry conditions are enforced on the learned operator to ensure a stable method. The procedure is applied to the Korteweg–de Vries equation. It is observed to be more accurate than finite difference or spectral methods on coarse grids when the initial data is near enough to the training set. Full article

(This article belongs to the Special Issue Applied Mathematics and Machine Learning)

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15 pages, 624 KiB

Open AccessArticle

Performance Evaluation of the Efficiency of Logistics Companies with Data Envelopment Analysis Model

by Pei Fun Lee, Weng Siew Lam and Weng Hoe Lam

Mathematics 2023, 11(3), 718; https://doi.org/10.3390/math11030718 - 31 Jan 2023

Cited by 8 | Viewed by 2239

Abstract

Malaysia has great geo-economic advantages, especially in becoming a major logistics and investment hub. However, as operational risk events create uncertainties, logistics companies suffer from supply and demand issues which affect their bottom lines, customer satisfaction and reputations. This is a pioneer paper [...] Read more.

Malaysia has great geo-economic advantages, especially in becoming a major logistics and investment hub. However, as operational risk events create uncertainties, logistics companies suffer from supply and demand issues which affect their bottom lines, customer satisfaction and reputations. This is a pioneer paper to propose the optimization of the efficiency of listed logistics companies in Malaysia with operational risk factor using a data envelopment analysis (DEA) model. The basic indicator approach (BIA) is used as an output indicator for the operational risk capital requirement factor in the proposed model. This paper has practical and managerial implications with the identification of potential improvements for the inefficient listed logistics companies based on the optimal solution of the DEA model. This proposed model can be applied in emerging fields such as finance and project-based construction companies, where operational risk is a high concern. Full article

(This article belongs to the Special Issue Applied Mathematics and Machine Learning)

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18 pages, 629 KiB

Open AccessArticle

Decision Analysis on the Financial Performance of Companies Using Integrated Entropy-Fuzzy TOPSIS Model

by Weng Hoe Lam, Weng Siew Lam, Kah Fai Liew and Pei Fun Lee

Mathematics 2023, 11(2), 397; https://doi.org/10.3390/math11020397 - 12 Jan 2023

Cited by 7 | Viewed by 2500

Abstract

Sustainable economic development plans have been shattered by the devastating COVID-19 crisis, which brought about an economic recession. The companies are suffering from financial losses, leading to financial distress and disengagement from sustainable economic goals. Many companies fail to achieve considerable financial performances, [...] Read more.

Sustainable economic development plans have been shattered by the devastating COVID-19 crisis, which brought about an economic recession. The companies are suffering from financial losses, leading to financial distress and disengagement from sustainable economic goals. Many companies fail to achieve considerable financial performances, which may lead to unachieved organizational goal and a loss of direction in decision-making and investment. According to the past studies, there has been no comprehensive study done on the financial performance of the companies based on liquidity, solvency, efficiency, and profitability ratios by integrating the entropy method and fuzzy technique for order reference based on similarity to the ideal solution (TOPSIS) model in portfolio investment. Therefore, this paper aims to propose a multi-criteria decision-making (MCDM) model, namely the entropy-fuzzy TOPSIS model, to evaluate the financial performances of companies based on these important financial ratios for portfolio investment. The fuzzy concept helps reduce vagueness and strengthen the meaningful information extracted from the financial ratios. The proposed model is illustrated using the financial ratios of companies in the Dow Jones Industrial Average (DJIA). The results show that return on equity and debt-to-equity ratios are the most influential financial ratios for the performance evaluation of the companies. The companies with good financial performance, such as the best HD company, have been determined based on the proposed model for portfolio selection. A mean-variance (MV) model is used to validate the proposed model in the portfolio investment. At a minimum level of risk, the proposed model is able to generate a higher mean return than the benchmark DJIA index. This paper is significant as it helps to evaluate the financial performance of the companies and select the well-performing companies with the proposed model for portfolio investment. Full article

(This article belongs to the Special Issue Applied Mathematics and Machine Learning)

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14 pages, 14601 KiB

Open AccessArticle

Dbar-Dressing Method and N-Soliton Solutions of the Derivative NLS Equation with Non-Zero Boundary Conditions

by Hui Zhou, Yehui Huang and Yuqin Yao

Mathematics 2022, 10(23), 4424; https://doi.org/10.3390/math10234424 - 24 Nov 2022

Cited by 5 | Viewed by 1110

Abstract

The Dbar-dressing method is extended to investigate the derivative non-linear Schrödinger equation with non-zero boundary conditions (DNLSENBC). Based on a meromorphic complex function outside an annulus with center 0, a local Dbar-problem inside the annulus is constructed. By use of the asymptotic expansion [...] Read more.

The Dbar-dressing method is extended to investigate the derivative non-linear Schrödinger equation with non-zero boundary conditions (DNLSENBC). Based on a meromorphic complex function outside an annulus with center 0, a local Dbar-problem inside the annulus is constructed. By use of the asymptotic expansion at infinity and zero, the spatial and temporal spectral problems of DNLSENBC are worked out. Thus, the relation between the potential of DNLSENBC with the solution of the Dbar-problem is established. Further, symmetry conditions and a special spectral distribution matrix are presented to construct the explicit solutions of DNLSENBC. In addition, the explicit expressions of the soliton solution, the breather solution and the solution of the interaction between solitons and breathers are given. Full article

(This article belongs to the Special Issue Applied Mathematics and Machine Learning)

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20 pages, 3971 KiB

Open AccessArticle

Machine Learning-Based Estimation of the Compressive Strength of Self-Compacting Concrete: A Multi-Dataset Study

by Nhat-Duc Hoang

Mathematics 2022, 10(20), 3771; https://doi.org/10.3390/math10203771 - 13 Oct 2022

Cited by 11 | Viewed by 1733

Abstract

This paper aims at performing a comparative study to investigate the predictive capability of machine learning (ML) models used for estimating the compressive strength of self-compacting concrete (SCC). Seven prominent ML models, including deep neural network regression (DNNR), extreme gradient boosting machine (XGBoost), [...] Read more.

This paper aims at performing a comparative study to investigate the predictive capability of machine learning (ML) models used for estimating the compressive strength of self-compacting concrete (SCC). Seven prominent ML models, including deep neural network regression (DNNR), extreme gradient boosting machine (XGBoost), gradient boosting machine (GBM), adaptive boosting machine (AdaBoost), support vector regression (SVR), Levenberg–Marquardt artificial neural network (LM-ANN), and genetic programming (GP), are employed. Four experimental datasets, compiled in previous studies, are used to construct the ML-based methods. The models’ generalization capabilities are reliably evaluated by 20 independent runs. Experimental results point out the superiority of the DNNR, which has excelled other models in three out of four datasets. The XGBoost is the second-best model, which has gained the first rank in one dataset. The outcomes point out the great potential of the utilized ML approaches in modeling the compressive strength of SCC. In more details, the coefficient of determination (R²) surpasses 0.8 and the mean absolute percentage error (MAPE) is always below 15% for all datasets. The best results of R² and MAPE are 0.93 and 7.2%, respectively. Full article

(This article belongs to the Special Issue Applied Mathematics and Machine Learning)

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