Before revision:  We illustrate these concepts on a repressilator circuit , a classical biological system from the field of synthetic biology, to motivate the proper selection of initial conditions. We show that when the rank properties of the flow's spectra are degenerate, the trained Koopman operator does not produce robust predictions on test data .
After revision:  We illustrate these identifiability conditions with a simulated synthetic gene circuit model, the repressilator. We illustrate how rank degeneracy in datasets results in overfitted nonlinear models of the repressilator, resulting in poor predictive accuracy. Our findings provide novel experimental design criteria for discovery of globally predictive nonlinear models of biological phenomena .