Structure-preserving interpolation reduced-order modelling for efficient simulation of parametric port-Hamiltonian systems

Authors

Yu-Han Hu, Zhen Li, Kang-Li Xu

Abstract

In this paper, we propose a structure-preserving model order reduction (MOR) method for parametric port-Hamiltonian (PH) systems. First, Laguerre polynomials are applied to generate the local reduced-order bases at selected parameter sample points. By expanding the system state variables in the time domain through Laguerre polynomials, we obtain the expansion coefficients for each parameter sample point. These coefficients are subsequently processed to derive the local transformation matrix necessary for the reduction procedure. We then introduce the Riemannian geometry of the Grassmann manifold and employ its tangent space for interpolation. The precomputed local reduced-order bases are organised into several groups, where the reference points are independently chosen form each group to ensure that the remaining points in each group are sufficiently proximate to their corresponding reference points. By utilising logarithmic mapping, the local reduced-order bases are transferred to the tangent spaces of the Grassmann manifold at the reference points. For a new parameter, the local reduced-order bases are interpolated within the tangent spaces of the Grassmann manifold, which facilitates the structure-preserving MOR of parametric PH systems. Finally, numerical experiments are given to validate the effectiveness of the proposed method.

Citation

• Journal: International Journal of Systems Science
• Year: 2026
• Volume: 57
• Issue: 7
• Pages: 1894–1907
• Publisher: Informa UK Limited
• DOI: 10.1080/00207721.2025.2546345

BibTeX

@article{Hu_2025,
  title={{Structure-preserving interpolation reduced-order modelling for efficient simulation of parametric port-Hamiltonian systems}},
  volume={57},
  ISSN={1464-5319},
  DOI={10.1080/00207721.2025.2546345},
  number={7},
  journal={International Journal of Systems Science},
  publisher={Informa UK Limited},
  author={Hu, Yu-Han and Li, Zhen and Xu, Kang-Li},
  year={2025},
  pages={1894--1907}
}

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