Data Denoising and Derivative Estimation for Data-Driven Modeling of Nonlinear Dynamical Systems

Jiaqi Yao, Lewis Mitchell, John Maclean, Hemanth Saratchandran

incompletemedium confidence

Category: math.DS
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:57 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper correctly defines L2 and L3 and gives a clear discrete-to-continuum identity for L3 (eqs. (4.5)–(4.6) with an appendix derivation), which the model’s Step 1 essentially rederives with a slightly stronger argument; these are consistent . However, for L2 the paper offers only an intuitive consistency explanation without rates , while the model’s Step 2 asserts an o(h^4) local Simpson error under only C^3 regularity, which is not justified (Simpson’s error typically requires f ∈ C^4 for O(h^5) local error). The conclusion L2→0 as h→0 is reasonable, but the rate claim and regularity assumptions are flawed. Step 3 (eΞ=0 under idealized exact-identification) is tautologically true only under strong identifiability assumptions not stated in the paper (the paper just defines eΞ) .

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The paper introduces a practical and effective two-step INR-based denoising and derivative estimation framework with RK4 residuals and second-derivative TV regularization, and demonstrates strong empirical performance. The L3 discrete-to-continuum argument is sound. The RK4-based consistency rationale is clear but informal; adding precise assumptions and, optionally, rates would improve rigor. Minor terminology and appendix-detail fixes would enhance clarity.