KoopmanizingFlows: Diffeomorphically Learning Stable Koopman Operators

by   Petar Bevanda, et al.

We propose a novel framework for constructing linear time-invariant (LTI) models for data-driven representations of the Koopman operator for a class of stable nonlinear dynamics. The Koopman operator (generator) lifts a finite-dimensional nonlinear system to a possibly infinite-dimensional linear feature space. To utilize it for modeling, one needs to discover finite-dimensional representations of the Koopman operator. Learning suitable features is challenging, as one needs to learn LTI features that are both Koopman-invariant (evolve linearly under the dynamics) as well as relevant (spanning the original state) - a generally unsupervised learning task. For a theoretically well-founded solution to this problem, we propose learning Koopman-invariant coordinates by composing a diffeomorphic learner with a lifted aggregate system of a latent linear model. Using an unconstrained parameterization of stable matrices along with the aforementioned feature construction, we learn the Koopman operator features without assuming a predefined library of functions or knowing the spectrum, while ensuring stability regardless of the operator approximation accuracy. We demonstrate the superior efficacy of the proposed method in comparison to a state-of-the-art method on the well-known LASA handwriting dataset.


page 9

page 18

page 19


Towards Data-driven LQR with KoopmanizingFlows

We propose a novel framework for learning linear time-invariant (LTI) mo...

Learning Stable Koopman Embeddings

In this paper, we present a new data-driven method for learning stable m...

Learning the Koopman Eigendecomposition: A Diffeomorphic Approach

We present a novel data-driven approach for learning linear representati...

Learning Data-Driven Stable Koopman Operators

In this paper, we consider the problem of improving the long-term accura...

NOMAD: Nonlinear Manifold Decoders for Operator Learning

Supervised learning in function spaces is an emerging area of machine le...

Physics-informed invertible neural network for the Koopman operator learning

In Koopman operator theory, a finite-dimensional nonlinear system is tra...

Learning High Dimensional Demonstrations Using Laplacian Eigenmaps

This article proposes a novel methodology to learn a stable robot contro...

Please sign up or login with your details

Forgot password? Click here to reset