  System representations inspired by the infinite-dimensional Koopman operator
(generator) are increasingly considered for predictive modeling. Due to the
operator's linearity, a range of nonlinear systems admit linear predictor
representations - allowing for simplified prediction, analysis and control.
However, finding meaningful finite-dimensional representations for prediction
is difficult as it involves determining features that are both
Koopman-invariant (evolve linearly under the dynamics) as well as relevant
(spanning the original state) - a generally unsupervised problem. In this work,
we present Koopmanizing Flows - a novel continuous-time framework for
supervised learning of linear predictors for a class of nonlinear dynamics. In
our model construction a latent diffeomorphically related linear system unfolds
into a linear predictor through the composition with a monomial basis. The
lifting, its linear dynamics and state reconstruction are learned
simultaneously, while an unconstrained parameterization of Hurwitz matrices
ensures asymptotic stability regardless of the operator approximation accuracy.
The superior efficacy of Koopmanizing Flows is demonstrated in comparison to a
state-of-the-art method on the well-known LASA handwriting benchmark.
