2509.12393
Data-driven balanced truncation for linear systems with quadratic outputs
Reetish Padhi, Ion Victor Gosea, Igor Pontes Duff, Serkan Gugercin
correctmedium confidence
- Category
- Not specified
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:57 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The candidate solution reproduces, step by step, the paper’s derivations for Theorems 1–3 and the non-intrusive (quadrature-based) balanced truncation construction. The entrywise expansions of H̃ = L̃^⊤Ũ and M̃ = L̃^⊤AŨ match equations (19a)–(19b) and (21a)–(21b) in the paper, respectively, including the ζ2-partial derivative for h2, and the formulas for h̃, g̃, and K̃ align with (22) . The final reduced matrices (Ar, Br, Cr, Mr) obtained via the SVD of H̃ coincide with Algorithm 1’s data-driven BT formulas, which replace the intrusive cross terms in the standard square-root BT expressions (10) with their data-based surrogates (17) . No logical gaps were found in either argument; both rely on the same algebraic identities and block-structured indexing.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
This work delivers a clean, well-motivated extension of quadrature-based data-driven balanced truncation to LQO systems, retaining BT-level accuracy without intrusive access to state-space matrices. The algebraic development is correct and tractable, and the numerical demonstration supports the claims. Minor improvements in clarity around derivative data acquisition and indexing would further enhance accessibility and reproducibility.