Injectivity analysis using interval analysis: Application to structural identifiability

This paper presents a new numerical algorithm based on interval analysis able to prove that a differentiable function f : A ⊂ R n → R n is injective. This algorithm also performs a partition of the domain A in subsets A i where, for all x ∈ A i , the cardinality of f − 1 ( f ( x ) ) is constant. In the context of parameter estimation, we show how this algorithm provides an efficient and numerical method to study the structural identifiability of parametric models.