Petrov-Galerkin operator inference with application to stability-encouraging identification
Abstract
Data-driven model order reduction methods such as operator inference enable the efficient construction of reduced-order models directly from high-dimensional time-domain data. Standard operator inference typically seeks a Galerkin-type reduced model in a prescribed low-dimensional subspace by identifying its reduced operators from projected snapshot data. The resulting inference problem is formulated as a least-squares problem admitting an efficient closed-form solution. However, it is well known from intrusive model order reduction for linear time-invariant systems that Petrov-Galerkin projections can additionally preserve important system properties such as stability and passivity. To overcome the limitations of standard operator inference, we extend the framework for linear time-invariant systems to incorporate Petrov-Galerkin projections and provide explicit error expressions and bounds between the intrusive and nonintrusive reduced operators, thus generalizing results from the literature. We demonstrate the proposed approach in the context of dissipative and port-Hamiltonian systems. Furthermore, we introduce a novel convex optimization formulation that explicitly enforces the port-Hamiltonian structure on the inferred operators. The effectiveness of the proposed methods is demonstrated on several well-established benchmark problems, including the CD player, an atmospheric model, a mass-spring-damper system, and a poroelasticity system.
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BibTeX
@misc{rettberg2026petrovgalerkin,
title = {{Petrov-Galerkin operator inference with application to stability-encouraging identification}},
author = {Johannes Rettberg and Jonas Nicodemus and Harsh Sharma and Boris Kramer and Jörg Fehr and Benjamin Unger},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01295},
eprint = {2610.01295},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01295},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Petrov-Galerkin operator inference with application to stability-encouraging identification
AU - Johannes Rettberg
AU - Jonas Nicodemus
AU - Harsh Sharma
AU - Boris Kramer
AU - Jörg Fehr
AU - Benjamin Unger
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01295
UR - https://arxiv.org/abs/2610.01295
AB - Data-driven model order reduction methods such as operator inference enable the efficient construction of reduced-order models directly from high-dimensional time-domain data. Standard operator inference typically seeks a Galerkin-type reduced model in a prescribed low-dimensional subspace by identifying its reduced operators from projected snapshot data. The resulting inference problem is formulated as a least-squares problem admitting an efficient closed-form solution. However, it is well known from intrusive model order reduction for linear time-invariant systems that Petrov-Galerkin projections can additionally preserve important system properties such as stability and passivity. To overcome the limitations of standard operator inference, we extend the framework for linear time-invariant systems to incorporate Petrov-Galerkin projections and provide explicit error expressions and bounds between the intrusive and nonintrusive reduced operators, thus generalizing results from the literature. We demonstrate the proposed approach in the context of dissipative and port-Hamiltonian systems. Furthermore, we introduce a novel convex optimization formulation that explicitly enforces the port-Hamiltonian structure on the inferred operators. The effectiveness of the proposed methods is demonstrated on several well-established benchmark problems, including the CD player, an atmospheric model, a mass-spring-damper system, and a poroelasticity system.
ER -