Section: New Results
Low–rank dynamic mode decomposition: optimal solution in polynomial time
Participant : Patrick Héas.
This is a collaboration with Cédric Herzet (EPI FLUMINANCE, Inria Rennes–Bretagne Atlantique)
The works [15] and [41]
study the linear approximation of high–dimensional dynamical systems
using low-rank dynamic mode decomposition (DMD). Searching this
approximation in a data–driven approach can be formalised as
attempting to solve a low-rank constrained optimisation problem.
This problem is non–convex and state–of–the–art algorithms are all
sub–optimal. We show that there exists a closed-form solution, which
can be computed in polynomial time, and characterises the