On Few Shot Learning of Dynamical Systems: A Koopman Operator Theoretic Approach

The paper’s Theorem 6 claims an equivalence between a robust EDMD min–max and a Frobenius-regularized least-squares, but key parts of the proof are underspecified or internally inconsistent: the uncertainty set U is only stated to be compact, the symbols Δ̄ and Π_KΔ̄ are never defined, λ is not tied to any explicit norm radius, and steps such as “≤ λ ||K−1||2” and the appearance of √(||K||^2_F + K) mix the decision variable K with the dimension K and lack a clear norm-geometry justification (eqs. (15)–(22) in the paper) . By contrast, the model’s solution gives a precise, standard robust least-squares reduction under explicit norm-bounded uncertainty (||δG||_2 ≤ ρ_G, ||δA||_F ≤ ρ_A), yielding an exact inner maximization equal to ||GK−A||_F + ρ_G||K||_F + ρ_A, which rigorously implies the stated ridge-type regularization (up to an additive constant).