Language：English   Publishing type：Research paper (scientific journal)   Publisher：Institute of Electrical and Electronics Engineers (IEEE)  

DOI： 10.1109/jsen.2024.3388849

Web of Science

Scopus

Language：English   Publishing type：Research paper (scientific journal)   Publisher：MDPI AG  

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.

DOI： 10.3390/math12070974

Web of Science

Scopus

Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP Publishing  

Abstract

This paper investigates the global structures of periodic orbits that appear in Rayleigh–Bénard convection, which is modelled by a two-dimensional perturbed Hamiltonian model, by focusing upon resonance, symmetry and bifurcation of the periodic orbits. First, we show the global structures of periodic orbits in the extended phase space by numerically detecting the associated periodic points on the Poincaré section. Then, we illustrate how resonant periodic orbits appear and specifically clarify that there exist some symmetric properties of such resonant periodic orbits which are projected on the phase space; namely, the period m and the winding number n become odd when an m-periodic orbit is symmetric with respect to the horizontal and vertical centre lines of a cell. Furthermore, the global structures of bifurcations of periodic orbits are depicted when the amplitude ɛ of the perturbation is varied, since in experiments the amplitude of the oscillation of the convection gradually increases when the Rayleigh number is raised.

DOI： 10.1088/1361-6544/aca73b

Other Link： https://iopscience.iop.org/article/10.1088/1361-6544/aca73b/pdf

Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

Authorship：Lead author   Language：English   Publishing type：Research paper (international conference proceedings)