Abstract
We discuss discrete-time dynamical systems depending on a parameter𝜇.Assuming that the system matrix𝐴(𝜇)is given, but the parameter𝜇is unknown,we infer the most-likely parameter𝜇𝑚ALMOST EQUAL TO𝜇from an observed trajectory𝑥ofthe dynamical system. We use parametric eigenpairs(𝑣𝑖(𝜇),𝜆𝑖(𝜇))of the systemmatrix𝐴(𝜇)computed with Newton's method based on a Chebyshev expansion.We then represent𝑥in the eigenvector basis defined by the𝑣𝑖(𝜇)and comparethe decay of the components with predictions based on the𝜆𝑖(𝜇).
The resultingestimates for𝜇are combined using a kernel density estimator to find the mostlikely value for𝜇𝑚and a corresponding uncertainty quantification.