Adaptive data-driven reduced-order models for reciprocal MIMO port-Hamiltonian dynamical systems
Abstract
Port-Hamiltonian (pH) systems provide a general framework for modeling a broad class of physical dynamical systems, including systems with dissipation. Constructing accurate and robust data-driven reduced-order models for general pH systems is challenging. In this work, we focus on an important subclass of pH systems satisfying reciprocity, a property arising naturally in a variety of models. Rather than seeking to preserve the full pH structure, we exploit the additional symmetry provided by reciprocity to develop an efficient data-driven reduced-order modeling approach. We show that every minimal realization of a reciprocal system is self-adjoint with respect to a generally indefinite inner product and can, up to a similarity transformation preserving the pH structure, be represented in a Krein space with a signature inner product. This observation motivates a Galerkin projection onto a tangential rational Krylov subspace with respect to the corresponding indefinite inner product. Although the resulting projection involves full-order state solutions and the unknown inner product, we show that its reduced mass and stiffness matrices can be constructed directly from transfer-function data through a Loewner formulation. We then propose a greedy data-driven procedure that adaptively selects both interpolation frequencies and tangential directions. At every iteration, the frequency is chosen according to the largest transfer-function approximation error, while the tangential direction is selected from a dominant singular direction of the corresponding matrix-valued residual. Numerical experiments for wave propagation in lossy media demonstrate improved approximation efficiency compared with block adaptive interpolation. We further apply the method to spectral mass gauging of a three-dimensional propellant tank to provide an accurate estimate of the tank volume through Weyl's law.
Related
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- Spatio-temporal Latent Denoising Diffusion Probabilistic Models for Reduced-order Modeling of Parametrized Dynamical Systems
- A simple derivation of the zero-temperature BCS functional from the reduced BCS Hamiltonian
- Hamiltonian Interface Dynamics for Reduced-Order Optimization of Incompressible Mixing
- Stable Dynamical Mass Transportation via port-Hamiltonian Structure
BibTeX
@misc{abilgazy2026adaptive,
title = {{Adaptive data-driven reduced-order models for reciprocal MIMO port-Hamiltonian dynamical systems}},
author = {Anarzhan Abilgazy and Mikhail Zaslavsky},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04065},
eprint = {2611.04065},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04065},
}
RIS
TY - UNPB
TI - Adaptive data-driven reduced-order models for reciprocal MIMO port-Hamiltonian dynamical systems
AU - Anarzhan Abilgazy
AU - Mikhail Zaslavsky
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.04065
UR - https://arxiv.org/abs/2611.04065
AB - Port-Hamiltonian (pH) systems provide a general framework for modeling a broad class of physical dynamical systems, including systems with dissipation. Constructing accurate and robust data-driven reduced-order models for general pH systems is challenging. In this work, we focus on an important subclass of pH systems satisfying reciprocity, a property arising naturally in a variety of models. Rather than seeking to preserve the full pH structure, we exploit the additional symmetry provided by reciprocity to develop an efficient data-driven reduced-order modeling approach. We show that every minimal realization of a reciprocal system is self-adjoint with respect to a generally indefinite inner product and can, up to a similarity transformation preserving the pH structure, be represented in a Krein space with a signature inner product. This observation motivates a Galerkin projection onto a tangential rational Krylov subspace with respect to the corresponding indefinite inner product. Although the resulting projection involves full-order state solutions and the unknown inner product, we show that its reduced mass and stiffness matrices can be constructed directly from transfer-function data through a Loewner formulation. We then propose a greedy data-driven procedure that adaptively selects both interpolation frequencies and tangential directions. At every iteration, the frequency is chosen according to the largest transfer-function approximation error, while the tangential direction is selected from a dominant singular direction of the corresponding matrix-valued residual. Numerical experiments for wave propagation in lossy media demonstrate improved approximation efficiency compared with block adaptive interpolation. We further apply the method to spectral mass gauging of a three-dimensional propellant tank to provide an accurate estimate of the tank volume through Weyl's law.
ER -