# DLKoopman: A deep learning software package for Koopman theory

arXiv: https://arxiv.org/abs/2211.08992 · HTML: https://mlsanity.com/paper/2211.08992/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 25 references that are in the map.
- First posted on arXiv 15 Nov 2022.

## Builds on (most cited first, 11 of 11)

- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition](https://mlsanity.com/paper/1710.04340/) (2017)
- [Linearly-Recurrent Autoencoder Networks for Learning Dynamics](https://mlsanity.com/paper/1712.01378/) (2017)
- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1708.06850/) (2017)
- [Forecasting Sequential Data using Consistent Koopman Autoencoders](https://mlsanity.com/paper/2003.02236/) (2020)
- [Transformers for Modeling Physical Systems](https://mlsanity.com/paper/2010.03957/) (2020)
- [Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics](https://mlsanity.com/paper/1710.11239/) (2017)
- [Deep Learning Enhanced Dynamic Mode Decomposition](https://mlsanity.com/paper/2108.04433/) (2021)
- [Dynamic Mode Decomposition and Koopman Theory](https://mlsanity.com/paper/2211.07561/) (2022)
- [Deep-n-Cheap: An Automated Search Framework for Low Complexity Deep Learning](https://mlsanity.com/paper/2004.00974/) (2020)

## Built on by (most cited first, 4 of 4)

- [Koopcon: A new approach towards smarter and less complex learning](https://mlsanity.com/paper/2405.13866/) (2024)
- [Generative Expansion of Small Datasets: An Expansive Graph Approach](https://mlsanity.com/paper/2406.17238/) (2024)
- [Certified Neural Approximations of Nonlinear Dynamics](https://mlsanity.com/paper/2505.15497/) (2025)
- [kooplearn: A Scikit-Learn Compatible Library of Algorithms for Evolution Operator Learning](https://mlsanity.com/paper/2512.21409/) (2025)

## Abstract (arXiv)

We present DLKoopman -- a software package for Koopman theory that uses deep learning to learn an encoding of a nonlinear dynamical system into a linear space, while simultaneously learning the linear dynamics. While several previous efforts have either restricted the ability to learn encodings, or been bespoke efforts designed for specific systems, DLKoopman is a generalized tool that can be applied to data-driven learning and optimization of any dynamical system. It can either be trained on data from individual states (snapshots) of a system and used to predict its unknown states, or trained on data from trajectories of a system and used to predict unknown trajectories for new initial states. DLKoopman is available on the Python Package Index (PyPI) as 'dlkoopman', and includes extensive documentation and tutorials. Additional contributions of the package include a novel metric called Average Normalized Absolute Error for evaluating performance, and a ready-to-use hyperparameter search module for improving performance.