Application of operator inference to reduced-order modeling of constrained mechanical systems

Peter Benner, Yevgeniya Filanova, Igor Pontes Duff, Jens Saak

incompletehigh confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper correctly outlines how to eliminate algebraic constraints via POD subspaces and sets up two data-driven least-squares identification problems for the reduced operators, but it omits crucial identifiability/normalization conditions. As written, the state-fit problem (16) admits the trivial zero solution when the input matrix is treated as unknown, and the paper’s appeal to “SPD constraints” is only semidefinite in practice, which is insufficient to guarantee strict energy positivity and stability without further assumptions. The candidate model solution recognizes convexity and gives a Moore–Penrose solution for (P2), but it also accepts the trivial minimizer for (P1) and then proceeds to a stability claim that presumes strict positive definiteness not established by the identification step. Hence both are incomplete: the paper for formulation gaps and missing assumptions, and the model for not addressing identifiability, nontriviality, and SPD enforcement.

Referee report (LaTeX)

\textbf{Recommendation:} major revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The submission presents a clear and practically relevant pipeline for data-driven reduced modeling of constrained mechanical systems using operator inference on POD subspaces that respect the constraints. Numerical demonstrations are convincing. However, the current optimization formulation is ill-posed when the input matrix is treated as unknown, as a trivial zero solution exists, and the stability discussion conflates enforceable semidefinite constraints with the strict positive definiteness required by the energy argument. These issues can be remedied by explicit identifiability/normalization constraints and a carefully stated stability result under the actual enforced constraints.