Examining the impact of forcing function inputs on structural identifiability

The paper’s central claim is that introducing a known, time-varying forcing input by scaling (or replacing) a parameter cannot worsen structural identifiability. This is formalized as Theorem 1 and proved via an analysis of Ritt’s pseudo-division with a ranking that places inputs (including the new forcing) below outputs and states, leading to the conclusion that the parameter-solution set for the forced model is contained in that of the original; hence identifiability does not degrade , with the key technical steps laid out in the proposition showing order-of-operations invariance and the Enforce Monic step under the ranking , . The candidate model solution proves the same “no-worsening” result by a different route: it works at the level of input–output ideals and the coefficient field generated by a characteristic set, arguing that adjoining the forcing amounts to a purely transcendental base-field extension and that the coefficient fields satisfy L_{tilde M} = K⟨ũ⟩ L_M, preserving rational/algebraic dependence (and thus (global/local) identifiability). This yields the same conclusion as Theorem 1. The model also does not contradict the paper’s improvement results (e.g., the additive-combination case, Theorem 2 ), though it does not attempt to prove them. The only caveat is that the model solution asserts an equality of coefficient fields that, while plausible, is stronger than the inclusion needed for the main claim and would benefit from a more explicit justification about functoriality of characteristic sets under base-field scaling. Overall, both are correct, with different proof strategies.