# A Convex Optimization Approach to Learning Koopman Operators

arXiv: https://arxiv.org/abs/2102.03934 · HTML: https://mlsanity.com/paper/2102.03934/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2021.

## Built on by (most cited first, 3 of 3)

- [Online Estimation of the Koopman Operator Using Fourier Features](https://mlsanity.com/paper/2212.01503/) (2022)
- [System Norm Regularization Methods for Koopman Operator Approximation](https://mlsanity.com/paper/2110.09658/) (2021)
- [Autoregressive models for biomedical signal processing](https://mlsanity.com/paper/2304.11070/) (2023)

## Abstract (arXiv)

Koopman operators provide tractable means of learning linear approximations of non-linear dynamics. Many approaches have been proposed to find these operators, typically based upon approximations using an a-priori fixed class of models. However, choosing appropriate models and bounding the approximation error is far from trivial. Motivated by these difficulties, in this paper we propose an optimization based approach to learning Koopman operators from data. Our results show that the Koopman operator, the associated Hilbert space of observables and a suitable dictionary can be obtained by solving two rank-constrained semi-definite programs (SDP). While in principle these problems are NP-hard, the use of standard relaxations of rank leads to convex SDPs. Further, these SDPs exhibit chordal sparsity leading to algorithms that scale linearly with the number of data points.