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Symmetry
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Optimized Machine Learning Algorithms for Modeling Dynamical Systems
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Optimized Machine Learning Algorithms for Modeling Dynamical Systems

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Computer".

Deadline for manuscript submissions: closed (31 August 2020) | Viewed by 24970

Special Issue Editors

Prof. Dr. Massimiliano Ferrara

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Guest Editor
1. Department of Law, Economics and Human Sciences, University “Mediterranea” of Reggio Calabria, 89124 Reggio Calabria, Italy
2. The Invernizzi Centre for Research in Innovation, Organization, Strategy and Entrepreneurship (ICRIOS), Bocconi University, Via Sarfatti, 25, 20136 Milano, Italy
Interests: mathematical economics; machine learning and data science; epidemics models; fractional calculus
Special Issues, Collections and Topics in MDPI journals
Dr. Mehdi Salimi

E-Mail Website
Guest Editor
1. Department of Law, Economics and Human Sciences & Decisions Lab, University Mediterranea of Reggio Calabria, Italy
2. Center for Dynamics, Department of Mathematics, Technische Universität Dresden, Germany
Interests: game theory; pursuit-evasion games; numerical analysis; machine learning (K-mean)
Special Issues, Collections and Topics in MDPI journals
Dr. Ali Ahmadian

E-Mail Website
Guest Editor
Institute for Mathematical Research (INSPEM), Universiti Putra Malaysia, Serdang, Selangor, Malaysia
Interests: fuzzy sets and systems; fractional calculus; numerical methods; mathematical modelling
Special Issues, Collections and Topics in MDPI journals
Dr. Bruno Antonio Pansera

E-Mail Website
Guest Editor
Department of Law, Economics and Human Sciences, “Mediterranea” University of Reggio Calabria, 89124 Reggio Calabria, Italy
Interests: PDEs; game theory; applied mathematics; topology
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Let us ponder those machine learning algorithms that predict real dynamical systems.

Mathematical objects used to make models of physical phenomena dependent on time are dynamical systems. These models are used in economic forecasting, medical issues, environmental modelings, etc. There is an overlap between machine learning and dynamical systems. To address this relation, let us assume a framework for dynamical system learning, using the idea of instrumental–variable regression to transform dynamical system learning to a sequence of machine learning problems. This transformation allows applying a strong literature on machine learning to incorporate many types of prior knowledge. Hence, a family of fast and practical learning algorithms for a variety of dynamical system models are employed to forecast the real behavior of such dynamical systems precisely. Further, machine learning folks often use dynamical systems’ taxonomy and reformulate it to some fancy term to make the idea sound sort of new.

The aim of this Special Issue is to attract leading researchers in these areas in order to include new high-quality results on these topics involving their dynamical properties as well as their symmetry characteristics, both from a theoretical and an applied point of view. Please note that all submitted papers must be within the general scope of the Symmetry journal.

Prof. Dr. Massimiliano Ferrara
Dr. Mehdi Salimi
Dr. Ali Ahmadian
Dr. Bruno Antonio Pansera
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. Symmetry 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 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • machine learning
  • supervised algorithms
  • unsupervised algorithms
  • optimization
  • dynamical systems
  • symmetry
  • real-world applications

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Published Papers (7 papers)

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Research

17 pages, 3803 KiB  
Article
Deep Neural Network Algorithm Feedback Model with Behavioral Intelligence and Forecast Accuracy
by Taikyeong Jeong
Symmetry 2020, 12(9), 1465; https://doi.org/10.3390/sym12091465 - 7 Sep 2020
Cited by 6 | Viewed by 2393
Abstract
When attempting to apply a large-scale database that holds the behavioral intelligence training data of deep neural networks, the classification accuracy of the artificial intelligence algorithm needs to reflect the behavioral characteristics of the individual. When a change in behavior is recognized, that [...] Read more.
When attempting to apply a large-scale database that holds the behavioral intelligence training data of deep neural networks, the classification accuracy of the artificial intelligence algorithm needs to reflect the behavioral characteristics of the individual. When a change in behavior is recognized, that is, a feedback model based on a data connection model is applied, an analysis of time series data is performed by extracting feature vectors and interpolating data in a deep neural network to overcome the limitations of the existing statistical analysis. Using the results of the first feedback model as inputs to the deep neural network and, furthermore, as the input values of the second feedback model, and interpolating the behavioral intelligence data, that is, context awareness and lifelog data, including physical activities, involves applying the most appropriate conditions. The results of this study show that this method effectively improves the accuracy of the artificial intelligence results. In this paper, through an experiment, after extracting the feature vector of a deep neural network and restoring the missing value, the classification accuracy was verified to improve by about 20% on average. At the same time, by adding behavioral intelligence data to the time series data, a new data connection model, the Deep Neural Network Feedback Model, was proposed, and it was verified that the classification accuracy can be improved by about 8 to 9% on average. Based on the hypothesis, the F (X′) = X model was applied to thoroughly classify the training data set and test data set to present a symmetrical balance between the data connection model and the context-aware data. In addition, behavioral activity data were extrapolated in terms of context-aware and forecasting perspectives to prove the results of the experiment. Full article
(This article belongs to the Special Issue Optimized Machine Learning Algorithms for Modeling Dynamical Systems)
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19 pages, 4851 KiB  
Article
El Niño Index Prediction Using Deep Learning with Ensemble Empirical Mode Decomposition
by Yanan Guo, Xiaoqun Cao, Bainian Liu and Kecheng Peng
Symmetry 2020, 12(6), 893; https://doi.org/10.3390/sym12060893 - 1 Jun 2020
Cited by 36 | Viewed by 5996
Abstract
El Niño is an important quasi-cyclical climate phenomenon that can have a significant impact on ecosystems and societies. Due to the chaotic nature of the atmosphere and ocean systems, traditional methods (such as statistical methods) are difficult to provide accurate El Niño index [...] Read more.
El Niño is an important quasi-cyclical climate phenomenon that can have a significant impact on ecosystems and societies. Due to the chaotic nature of the atmosphere and ocean systems, traditional methods (such as statistical methods) are difficult to provide accurate El Niño index predictions. The latest research shows that Ensemble Empirical Mode Decomposition (EEMD) is suitable for analyzing non-linear and non-stationary signal sequences, Convolutional Neural Network (CNN) is good at local feature extraction, and Recurrent Neural Network (RNN) can capture the overall information of the sequence. As a special RNN, Long Short-Term Memory (LSTM) has significant advantages in processing and predicting long, complex time series. In this paper, to predict the El Niño index more accurately, we propose a new hybrid neural network model, EEMD-CNN-LSTM, which combines EEMD, CNN, and LSTM. In this hybrid model, the original El Niño index sequence is first decomposed into several Intrinsic Mode Functions (IMFs) using the EEMD method. Next, we filter the IMFs by setting a threshold, and we use the filtered IMFs to reconstruct the new El Niño data. The reconstructed time series then serves as input data for CNN and LSTM. The above data preprocessing method, which first decomposes the time series and then reconstructs the time series, uses the idea of symmetry. With this symmetric operation, we extract valid information about the time series and then make predictions based on the reconstructed time series. To evaluate the performance of the EEMD-CNN-LSTM model, the proposed model is compared with four methods including the traditional statistical model, machine learning model, and other deep neural network models. The experimental results show that the prediction results of EEMD-CNN-LSTM are not only more accurate but also more stable and reliable than the general neural network model. Full article
(This article belongs to the Special Issue Optimized Machine Learning Algorithms for Modeling Dynamical Systems)
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17 pages, 853 KiB  
Article
Multi-Classifier Approaches for Supporting Clinical Decision Making
by Maria Carmela Groccia, Rosita Guido and Domenico Conforti
Symmetry 2020, 12(5), 699; https://doi.org/10.3390/sym12050699 - 1 May 2020
Cited by 5 | Viewed by 2245
Abstract
Diagnosis is one of the most important processes in the medical field. Since the knowledge domains of clinical specialties are expanding rapidly in terms of complexity and volume of data, clinicians have, in many cases, difficulties to make an accurate diagnosis. Therefore, intelligent [...] Read more.
Diagnosis is one of the most important processes in the medical field. Since the knowledge domains of clinical specialties are expanding rapidly in terms of complexity and volume of data, clinicians have, in many cases, difficulties to make an accurate diagnosis. Therefore, intelligent and quantitative support for diagnostic tasks can be effectively exploited for improving the effectiveness of the process and reduce misdiagnosis. In this respect, Multi-Classifier Systems represent one of the most promising approaches within Machine Learning methodologies. This paper proposes a Multi-Classifier Systems framework for supporting diagnostic activities with the aim of improving diagnostic accuracy. The framework uses and combines several classification algorithms by dynamically selecting the most competent classifier according to the test sample and its location in the feature space. Here, we extend our previous research. The new experimental results, compared with several multi classifier techniques, based on dynamic classifier selection, on classification datasets, show that the performance of the proposed framework exceeds the state-of-the-art dynamic classifier selection techniques. Full article
(This article belongs to the Special Issue Optimized Machine Learning Algorithms for Modeling Dynamical Systems)
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21 pages, 7509 KiB  
Article
Learning the Kinematics of a Manipulator Based on VQTAM
by Luo Lan, Hou Li, Wu Yang, Wei Yongqiao and Zhang Qi
Symmetry 2020, 12(4), 519; https://doi.org/10.3390/sym12040519 - 2 Apr 2020
Viewed by 3134
Abstract
The kinematics of a robotic manipulator is critical to the real-time performance and robustness of the robot control system. This paper proposes a surrogate model of inverse kinematics for the serial six-degree of freedom (6-DOF) robotic manipulator, based on its kinematics symmetry. Herein, [...] Read more.
The kinematics of a robotic manipulator is critical to the real-time performance and robustness of the robot control system. This paper proposes a surrogate model of inverse kinematics for the serial six-degree of freedom (6-DOF) robotic manipulator, based on its kinematics symmetry. Herein, the inverse kinematics model is derived via the training of the Vector-Quantified Temporal Associative Memory (VQTAM) network, which originates from Self-Organized Mapping (SOM). During the processes of training, testing, and estimating of this neural network, a priority K-means tree search algorithm is utilized, thus improving the training efficacy. Furthermore, Local Linear Regression (LLR), Local Weighted Linear Regression (LWR), and Local Linear Embedding (LLE) algorithms are, respectively, combined with VQTAM to obtain three improvement algorithms, all of which aim to further optimize the prediction accuracy of the networks for subsequent comparison and selection. To speed up the solving of the least squared equation, which is common among the three algorithms, Singular Value Decomposition (SVD) is introduced. Finally, data from forward kinematics, in the form of the exponential product of a motion screw, are obtained, and are used for the construction and validation of the VQTAM neural network. Our results show that the prediction effect of the LLE algorithm is better than others, and that the LLE algorithm is a potential surrogate model to estimate the output of inverse kinematics. Full article
(This article belongs to the Special Issue Optimized Machine Learning Algorithms for Modeling Dynamical Systems)
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11 pages, 281 KiB  
Article
Bifurcation Analysis of a Duopoly Game with R&D Spillover, Price Competition and Time Delays
by B. A. Pansera, L. Guerrini, M. Ferrara and T. Ciano
Symmetry 2020, 12(2), 257; https://doi.org/10.3390/sym12020257 - 7 Feb 2020
Cited by 4 | Viewed by 2253
Abstract
The aim of this study is to analyse a discrete-time two-stage game with R&D competition by considering a continuous-time set-up with fixed delays. The model is represented in the form of delay differential equations. The stability of all the equilibrium points is studied. [...] Read more.
The aim of this study is to analyse a discrete-time two-stage game with R&D competition by considering a continuous-time set-up with fixed delays. The model is represented in the form of delay differential equations. The stability of all the equilibrium points is studied. It is found that the model exhibits very complex dynamical behaviours, and its Nash equilibrium is destabilised via Hopf bifurcations. Full article
(This article belongs to the Special Issue Optimized Machine Learning Algorithms for Modeling Dynamical Systems)
21 pages, 41741 KiB  
Article
A Novel Hybrid Data-Driven Modeling Method for Missiles
by Yongxiang He, Hongwu Guo and Yang Han
Symmetry 2020, 12(1), 30; https://doi.org/10.3390/sym12010030 - 22 Dec 2019
Cited by 3 | Viewed by 3612
Abstract
This paper proposes a novel hybrid data-driven modeling method for missiles. Based on actual flight test data, the missile hybrid model is established by combining neural networks and the mechanism modeling method, considering the uncertainties and nonlinear factors in missiles. This method can [...] Read more.
This paper proposes a novel hybrid data-driven modeling method for missiles. Based on actual flight test data, the missile hybrid model is established by combining neural networks and the mechanism modeling method, considering the uncertainties and nonlinear factors in missiles. This method can avoid the problems in missile mechanism modeling and traditional data-driven modeling, and can also provide a solution for nonlinear dynamic system modeling problems in offline usage scenarios. Finally, the feasibility of the proposed method and the credibility of the established model are verified by simulation experiments and statistical analysis. Full article
(This article belongs to the Special Issue Optimized Machine Learning Algorithms for Modeling Dynamical Systems)
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18 pages, 1482 KiB  
Article
A Satellite Task Planning Algorithm Based on a Symmetric Recurrent Neural Network
by Sikai Liu and Jun Yang
Symmetry 2019, 11(11), 1373; https://doi.org/10.3390/sym11111373 - 6 Nov 2019
Cited by 10 | Viewed by 3769
Abstract
The intelligent satellite, iSAT, is a concept based on software-defined satellites. Earth observation is one of the important applications of intelligent satellites. With the increasing demand for rapid satellite response and observation tasks, intelligent satellite in-orbit task planning has become an inevitable trend. [...] Read more.
The intelligent satellite, iSAT, is a concept based on software-defined satellites. Earth observation is one of the important applications of intelligent satellites. With the increasing demand for rapid satellite response and observation tasks, intelligent satellite in-orbit task planning has become an inevitable trend. In this paper, a mixed integer programming model for observation tasks is established, and a heuristic search algorithm based on a symmetric recurrent neural network is proposed. The configurable probability of the observation task is obtained by constructing a structural symmetric recurrent neural network, and finally, the optimal task planning scheme is obtained. The experimental results are compared with several typical heuristic search algorithms, which have certain advantages, and the validity of the paper is verified. Finally, future application prospects of the method are discussed. Full article
(This article belongs to the Special Issue Optimized Machine Learning Algorithms for Modeling Dynamical Systems)
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