Machine Learning for Dynamical Systems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: 31 July 2024 | Viewed by 1007

Special Issue Editors


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Guest Editor
Department of Mathematics and Computer Science, Alabama State University, Montgomery, AL, USA
Interests: dynamical systems; delay; neural network

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Guest Editor
Department of Mathematics and Computer Science, Alabama State University, Montgomery, AL, USA
Interests: matrices; symbolic dynamics

Special Issue Information

Dear Colleagues,

Dynamical systems theory is mainly concerned with describing the long-term qualitative behavior of dynamical systems, or piecewise smooth dynamical systems, which can typically be described as various differential equations such as ordinary differential equations, functional differential equations, stochastic differential equations, difference differential equations, partial differential equations, and so on. However, the qualitative behavior of dynamical systems is understood from models, which are often approximations of the observed reality. It requires a detailed understanding of the processes to be analyzed. On the other hand, the field of machine learning is concerned with algorithms designed to accomplish a certain task, whose performance improves with the input of more data. The machine learning approach is becoming increasingly important in many applications. The aim of this Special Issue is to focus on recent developments in machine learning and analyze dynamic systems on the basis of observed data rather than the models themselves.

Dr. Chunhua Feng
Prof. Dr. Fred Roush
Guest Editors

Manuscript Submission Information

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Keywords

  • dynamical system
  • data
  • machine learning

Published Papers (1 paper)

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Research

14 pages, 8127 KiB  
Article
Sparse Estimation for Hamiltonian Mechanics
by Yuya Note, Masahito Watanabe, Hiroaki Yoshimura, Takaharu Yaguchi and Toshiaki Omori
Mathematics 2024, 12(7), 974; https://doi.org/10.3390/math12070974 - 25 Mar 2024
Viewed by 724
Abstract
Estimating governing equations from observed time-series data is crucial for understanding dynamical systems. From the perspective of system comprehension, the demand for accurate estimation and interpretable results has been particularly emphasized. Herein, we propose a novel data-driven method for estimating the governing equations [...] Read more.
Estimating governing equations from observed time-series data is crucial for understanding dynamical systems. From the perspective of system comprehension, the demand for accurate estimation and interpretable results has been particularly emphasized. Herein, we propose a novel data-driven method for estimating the governing equations of dynamical systems based on machine learning with high accuracy and interpretability. The proposed method enhances the estimation accuracy for dynamical systems using sparse modeling by incorporating physical constraints derived from Hamiltonian mechanics. Unlike conventional approaches used for estimating governing equations for dynamical systems, we employ a sparse representation of Hamiltonian, allowing for the estimation. Using noisy observational data, the proposed method demonstrates a capability to achieve accurate parameter estimation and extraction of essential nonlinear terms. In addition, it is shown that estimations based on energy conservation principles exhibit superior accuracy in long-term predictions. These results collectively indicate that the proposed method accurately estimates dynamical systems while maintaining interpretability. Full article
(This article belongs to the Special Issue Machine Learning for Dynamical Systems)
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