LEARNING DYNAMICAL SYSTEMS FROM DATA: A SIMPLE CROSS-VALIDATION PERSPECTIVE, PART III: IRREGULARLY-SAMPLED TIME SERIES

The paper defines the regular and time-aware formulations (models (1) and (7)), recalls the Kernel Flows criterion ρ and the pointwise RKHS error bound σ, and presents convincing experiments, but it does not supply formal proofs connecting (7) versus (1) in terms of hypothesis-class inclusion, best-achievable in-sample error, pointwise error bounds, or minimized ρ. Those four items are precisely what the model’s solution establishes under clear kernel-family assumptions (not stated in the paper): (i) that Θ7 contains a Δ-nulling embedding of Θ1; and (ii) optional sufficient conditions for σ7≤σ1. The paper’s statements of (1), (6), (7), the KF objective (5)/(16)–(17), and the local bound (18) are correct as recalled, but the paper does not prove the comparison claims that the model addresses. Hence the paper is incomplete on these theoretical fronts, while the model’s solution is correct under its stated hypotheses (and does not contradict the paper’s empirical findings) .