Matrix-Free Moment-Matching Method for Reduced-Order Modeling of Quadratic-Bilinear Descriptor Systems with Multiple Inputs
Abstract
This paper develops a new moment-matching order reduction method for multi-input quadratic-bilinear descriptor systems. The proposed approach accommodates multiple inputs acting on both the differential and algebraic equations and constructs separate projection spaces associated with different input channels and input combinations. The method uses a matrix-free algorithm, allowing the reduced-order matrices and tensors to be computed without explicitly assembling or storing the full-order system matrices and tensors. This feature makes the proposed method particularly suitable for large-scale computational fluid dynamics problems. Numerical experiments carried out for two-dimensional flow problems demonstrate that the resulting reduced-order models accurately reproduce the transient responses of the full-order models under multiple time-varying inputs.
Related
- Truncated ℋ2 Optimal Model Order Reduction for Bilinear Quadratic Output Systems
- Fluctuations of the quadratic matching cost on the flat torus: dimensions five and higher
- Fluctuations of the quadratic matching cost on the flat torus: dimensions two, three and four
- Near-Quadratic Error-Free Graph Matching above Otter's Threshold via Approximate Local Tree Correlation Testing
- Global existence of classical solutions to a system modeling propagation of urban crime with quadratic logistic damping
BibTeX
@misc{gao2026matrixfree,
title = {{Matrix-Free Moment-Matching Method for Reduced-Order Modeling of Quadratic-Bilinear Descriptor Systems with Multiple Inputs}},
author = {Zeyuan Gao and Cheol W. Lee and Oleg Zikanov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00830},
eprint = {2610.00830},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00830},
}
RIS
TY - UNPB
TI - Matrix-Free Moment-Matching Method for Reduced-Order Modeling of Quadratic-Bilinear Descriptor Systems with Multiple Inputs
AU - Zeyuan Gao
AU - Cheol W. Lee
AU - Oleg Zikanov
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00830
UR - https://arxiv.org/abs/2610.00830
AB - This paper develops a new moment-matching order reduction method for multi-input quadratic-bilinear descriptor systems. The proposed approach accommodates multiple inputs acting on both the differential and algebraic equations and constructs separate projection spaces associated with different input channels and input combinations. The method uses a matrix-free algorithm, allowing the reduced-order matrices and tensors to be computed without explicitly assembling or storing the full-order system matrices and tensors. This feature makes the proposed method particularly suitable for large-scale computational fluid dynamics problems. Numerical experiments carried out for two-dimensional flow problems demonstrate that the resulting reduced-order models accurately reproduce the transient responses of the full-order models under multiple time-varying inputs.
ER -