Karl Meerbergen (KU Leuven): Rational approximation for dynamical systems

Intrusive methods for model order reduction of dynamical systems is well understood. Recently nonintrusive (data driven) methods were introduced relying on rational approximation of the system’s output. In this talk, I will present variations of the AAA method and how they can be used for model order reduction of nonlinear and parametric systems.

In the first part of the talk, I discuss variations of AAA to build rational approximations of a set of functions that use the same support points and weights. This has some advantages in the solution of nonlinear eigenvalue problems and dynamical systems with multiple input and outputs. The discussed methods are Set Valued AAA, Weighted AAA, QR-AAA.

In the second part, I discuss the use of these methods for data driven model order reduction. First, I show Time Domain AAA as an alternative to Time Domain Vector Fitting. Second, I show the use of AAA for model order reduction of nonlinear systems with parameters. To this end, a combination of p-AAA and SV-AAA is made to deal with the difference in degree of dependency on parameters.

This is joint work with Giovanni Conni and Simon Dirckx.