Approximation of Nearly-Periodic Symplectic Maps via Structure-Preserving Neural Networks

Both the paper and the model solution prove universal approximation for nearly-periodic symplectic maps by factoring P_ε into a conjugated circle action and a near-identity symplectic residual, then invoking universal approximation for the symplectic diffeomorphism ψ and the near-identity ε-dependent symplectic map I_ε. The paper states the result (Theorem 3.2) and provides the needed factorization (Lemma 3.3) and architecture definitions, while the model gives a careful compact-set error control argument for stability under composition and inversion. The arguments align closely; the model fills in quantitative details the paper omits.