A property of a parametrized dynamical or statistical model that determines whether its parameters can be uniquely recovered from perfect, noise-free input–output data; structural identifiability is a property of the model equations and parameterization alone.

Principle

Injectivity of the input–output map: a model is (globally) structurally identifiable if the mapping from parameter space to observed behaviour is one-to-one (up to known symmetries), making parameter values theoretically unique given ideal observations.

Demonstration

In a compartmental pharmacokinetic model with two identical compartments and symmetric parameterization, distinct parameter sets may produce identical concentration-time curves, demonstrating non-identifiability arising from model symmetry.

Misapplication

Confusing structural identifiability with practical identifiability: a structurally identifiable parameter may nonetheless be practically unestimable from noisy, sparse data, and assuming otherwise leads to overconfident inference.

Consequence

Establishing structural identifiability guides whether parameter estimation is theoretically possible and informs experimental design (which measurements or inputs are necessary to disambiguate parameters).

Reversal

Non-identifiable (structurally unidentifiable) models permit continuous or discrete parameter transformations that leave all observables unchanged, resulting in infinite or ambiguous parameter solutions even with ideal data.

Boundary

Refers to idealized, noise-free, often continuous observations and assumes the model form is correct; it does not address estimation error, numerical identifiability issues, or model misspecification encountered with real data.

Semantic Tension

Close to concepts of observability and parameter redundancy; observability concerns state reconstruction, while structural identifiability focuses on uniqueness of parameter values given input–output behaviour.

Synthesis

Structural identifiability is the theoretical condition that parameter-to-output mapping is injective under ideal measurements, a prerequisite for unique parameter recovery that shapes model formulation and experimental choices.