ZERO-SHOT IMPUTATION WITH FOUNDATION INFERENCE MODELS FOR DYNAMICAL SYSTEMS

Patrick Seifner, Kostadin Cvejoski, Antonia Körner, Ramsés J. Sánchez

incompletemedium confidence

Category: math.DS
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper explicitly defines the reconstruction x̂(τ) = x̂0 + ∫_0^τ f̂(s) ds and uses it for zero-shot phase-portrait reconstruction with f̂ as a learned time-derivative, but it does not state or prove the uniform error bounds or convergence claims at issue here. The candidate solution’s bound follows directly from that integral representation under the stated uniform errors on the initial condition and the derivative, via the triangle inequality, so the solution is correct given those assumptions. The paper provides the construction and empirical validation but not the theoretical bound or its proof (see the model outputs/formula for x̂ and the phase-portrait section).

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

FIM-ℓ compellingly demonstrates zero-shot interpolation and phase-portrait reconstruction across varied systems and datasets. The empirical evidence and architecture are solid, but the paper overlooks a simple, general error bound that follows immediately from its own reconstruction equation. Including a short lemma with a uniform max-norm bound (and the phase-portrait bound) would improve theoretical clarity without changing claims or experiments.