Koopman representation: Linear representation of nonlinear dynamics

Ordinary differential equations (ODEs) are among the most widely used tools
for describing deterministic dynamical systems. However, the nonlinear nature of many
ODEs often complicates the analysis of these systems. In this talk, we introduce
Koopman theory, which offers a powerful approach by providing a (potentially infinite-
dimensional) linear representation of nonlinear dynamics. This framework allows for the
application of linear system analysis tools to nonlinear problems. We demonstrate that
the PageRank algorithm, famously used in Google Search, can be effectively employed
to approximate these Koopman linear representations. Finally, we present results on -
error bounds for this approximation, which are crucial for quantifying the accuracy of
Koopman approximations and assessing their reliability in practical applications.

Bio
https://people.math.wisc.edu/~hhong78/