IFF vertex-disjoint paths condition for generic identifiability of analytic DAGs (full measurement)

Establish that, for directed acyclic graphs with node dynamics in the class F of analytic functions, generic identifiability under full measurement holds if and only if there exist vertex-disjoint paths from the set of excited nodes to the set of in-neighbors of every node.

Background

The paper proves that vertex-disjoint paths from excited nodes to each node’s in-neighbors provide a sufficient condition for generic identifiability in directed acyclic graphs (DAGs) when node dynamics are analytic. For the subclass of polynomial node functions, the authors also prove necessity by leveraging tools from algebraic geometry (algebraic varieties).

However, extending the necessity direction from polynomials to the broader analytic function class requires results about analytic varieties that the authors indicate are not presently available. To capture this gap, the authors formulate a conjecture asserting the equivalence (sufficiency and necessity) of the vertex-disjoint paths condition for generic identifiability in the analytic setting.