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System representations inspired by the infinite-dimensional Koopman operator(generator) are increasingly considered for predictive modeling. Due to theoperator's linearity, a range of nonlinear systems admit linear predictorrepresentations - allowing for simplified prediction, analysis and control.However, finding meaningful finite-dimensional representations for predictionis difficult as it involves determining features that are bothKoopman-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 forsupervised learning of linear predictors for a class of nonlinear dynamics. Inour model construction a latent diffeomorphically related linear system unfoldsinto a linear predictor through the composition with a monomial basis. Thelifting, its linear dynamics and state reconstruction are learnedsimultaneously, while an unconstrained parameterization of Hurwitz matricesensures asymptotic stability regardless of the operator approximation accuracy.The superior efficacy of Koopmanizing Flows is demonstrated in comparison to astate-of-the-art method on the well-known LASA handwriting benchmark.

Diffeomorphically Learning Stable Koopman Operators