Dynamical Systems
Functional Dimensionality of Koopman Eigenfunction Space
I Cohen, E Appleboim, G Wolansky
Results in Applied Mathematics
This work presents the general form solution of Koopman Partial Differential Equation for an autonomous system of N ordinary differential equations. We identify a domain in R N for which any number in the complex plane is an eigenvalue of the Koopman operator, and all eigensolutions are obtained from N− 1 functionally independent invariants of the system. Thus, we demonstrate that one may, in principle, diagonalize the system with only N functionally independent Koopman eigenfunctions.
Koopman Regularization
I Cohen
arXiv preprint arXiv:2403.11302
Koopman Regularization is a constrained optimization-based method to learn the governing equations from sparse and corrupted samples of the vector field. Koopman Regularization extracts a functionally independent set of Koopman eigenfunctions from the samples. This set implements the principle of parsimony, since, even though its cardinality is finite, it restores the dynamics precisely.
presentation | arXiv | code
