How many experiments?

An ODE model with parameters is said to be structurally identifiable if the values of parameter can be uniquely determined from continuous noise-free data. This property is a natural prerequisite for practical identifiability. It may happen that, although the model is not identifiable, it becomes identifiable if several independent experiments (with the same parameter values but different initial conditions) are conducted. A natural question is: how many experiments are sufficient to get "the maximal possible identifiability"?

We give an algorithm for computing a bound for the number of experiments "providing the maximal possible identifiability" which is off at most by one. The algorithm is fast in practice (and has polynomial arithmetic complexity). The algorithm is based on our theoretical results about expressing the field of definition of a (differential-algebraic) variety in terms of several its generic points. Interestingly, the process of discovery and establishing of these properties originated from model theory.

This is joint work with Alexey Ovchinnikov, Anand Pillay, and Thomas Scanlon.