Automatic constraint-count determination and non-separable Dirac structures

Develop a method to automatically determine the number of independent flow constraints n_f in Dirac-interconnected neural elements and extend the framework to non-separable Dirac structures.

Background

Dirac-interconnected neural elements parameterize separable Dirac structures using a prescribed number n_f of independent flow constraints, with the complementary number of effort constraints determined by n_e = n - n_f. Because the interconnection is unknown in applications, the paper currently requires n_f to be swept and selected in practice; a misspecified value excludes the true Dirac structure from the model family. The parameterization also excludes non-separable Dirac structures, including systems involving gyrators. The conclusion explicitly identifies automatic determination of n_f and extension beyond separable structures as unresolved directions for future work.