Learning Stable Deep Dynamics Models for Partially Observed or Delayed Dynamical Systems

Andreas Schlaginhaufen, Philippe Wenk, Andreas Krause, Florian Dörfler

incompletemedium confidence

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

Audit review

The candidate reproduces the Razumikhin-based decay in part (i) with the correct rate γ = 0.5·min{α, (log q)/r} and overshoot M = c2/c1, exactly as in Theorem 1 of the paper, and extends it via the covering/continuous-dependence argument in part (ii). Crucially, the candidate identifies two missing hypotheses in the paper’s Theorem 2: (a) to select a nearby training history at all intermediate times t one needs S to contain the forward reachable tube (or the training set to δ-cover γ+_{[0,tf)}(S)), and (b) to absorb the additive ε-term into a multiplicative bound one needs ||x_t||_r ≥ ε along the horizon (or else weaken the bound). The paper states the result “on S\Bε(0)” but does not ensure these forward-time properties, so the uniform (γ, M̄)-decay claim is not fully justified as written .

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The stability analysis via Lyapunov–Razumikhin is solid and part (i) matches classical results. The extension (ii) via covering and continuous dependence is standard but presently omits two forward-time conditions needed to turn an additive ε-term into a uniform multiplicative bound. Adding (1) a forward-invariance or forward-tube covering requirement, and (2) either a forward lower bound ||x\_t||\_r ≥ ε (until the bound is used) or a max-form conclusion, would close the gap and align the statement with the proof. The technical contribution remains useful and the fixes are modest. The issues above align with what is implicitly used in the argument but should be made explicit for correctness and clarity.