Sparse identification of nonlinear dynamics with library optimization mechanism: Recursive long-term prediction perspective

The paper precisely defines the bilevel SINDy-LOM objective Jms, the inner sparse-regression map Ξ, the RLT prediction recursion, and the final model (its Eqs. (6)–(11)), but gives no existence/continuity guarantees and explicitly treats the outer problem as nonconvex, to be handled by heuristics such as GA/PSO, with R(v)=γ||v||0 in practice . The candidate solution supplies a correct existence/continuity and sparsity argument under explicit additional assumptions (compact Φ-domain, continuity of θi, nonzero normalizers, deterministic tie-breaking, and optionally a small ℓ2 ridge). These hypotheses are not stated (nor used) in the paper, but under them the candidate’s reasoning is sound by standard arguments (finite-support decomposition and Weierstrass) and aligns with the paper’s definitions of Jms and the model recursion .