Data-driven system identification using quadratic embeddings of nonlinear dynamics

Stefan Klus, Joel-Pascal Ntwali N’konzi

correctmedium confidence

Category: Not specified
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper’s infinite-data argument for QENDy/SINDy proceeds by scaling the finite-sample normal equations, invoking Monte Carlo/LLN convergence of empirical Gram and cross terms to μ–inner products, and interpreting the limit as a Hilbert-space best approximation; Appendix B clarifies rank-deficiency/pseudoinverse issues. The candidate solution follows the same route—same block normal equations, same LLN step, same projection theorem interpretation, same comments on singular Gram matrices—arriving at equivalent conclusions.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The work cleanly formulates QENDy, derives its normal equations, and establishes an infinite-data best-approximation interpretation that aligns with SINDy and generator-based approaches. The mathematics are correct and the narrative is clear; minor clarifications about sampling assumptions (LLN/ergodicity) and coefficient non-uniqueness in rank-deficient limits would further improve readability and rigor.