# Learning Parametric Koopman Decompositions for Prediction and Control

arXiv: https://arxiv.org/abs/2310.01124 · HTML: https://mlsanity.com/paper/2310.01124/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2023.

## Built on by (most cited first, 6 of 6)

- [Nonparametric Control Koopman Operators](https://mlsanity.com/paper/2405.07312/) (2024)
- [The Seismic Wavefield Common Task Framework](https://mlsanity.com/paper/2512.19927/) (2025)
- [Sparse identification of nonlinear dynamics with library optimization mechanism: Recursive long-term prediction perspective](https://mlsanity.com/paper/2507.18220/) (2025)
- [From Product Hilbert Spaces to the Generalized Koopman Operator and the Nonlinear Fundamental Lemma](https://mlsanity.com/paper/2508.07494/) (2025)
- [Beyond Static Models: Hypernetworks for Adaptive and Generalizable Forecasting in Complex Parametric Dynamical Systems](https://mlsanity.com/paper/2506.19609/) (2025)
- [Parametric Interpolation of Dynamic Mode Decomposition for Predicting Nonlinear Systems](https://mlsanity.com/paper/2604.12103/) (2026)

## Abstract (arXiv)

We present an approach to construct approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously constructs an invariant subspace and a parametric family of projected Koopman operators acting on this subspace. We parametrize both the projected Koopman operator family and the dictionary that spans the invariant subspace by neural networks and jointly train them with trajectory data. We show theoretically the validity of our approach, and demonstrate via numerical experiments that it exhibits significant improvements over existing methods in solving prediction problems, especially those with large state or parameter dimensions, and those possessing strongly non-linear dynamics. Moreover, our method enables data-driven solution of optimal control problems involving non-linear dynamics, with interesting implications on controllability.