# KoopGen: Koopman Generator Networks for Representing and Predicting Dynamical Systems with Continuous Spectra

arXiv: https://arxiv.org/abs/2602.14011 · HTML: https://mlsanity.com/paper/2602.14011/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 34 references that are in the map.
- First posted on arXiv 15 Feb 2026.

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

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [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)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [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)
- [Deep Learning Enhanced Dynamic Mode Decomposition](https://mlsanity.com/paper/2108.04433/) (2021)
- [Temporally Consistent Koopman Autoencoders for Forecasting Dynamical Systems](https://mlsanity.com/paper/2403.12335/) (2024)

## Built on by (most cited first, 1 of 1)

- [Understanding Latent-Dimension Scaling in Dynamical-System Learning through Spectral Reliability](https://mlsanity.com/paper/2610.11866/) (2026)

## Abstract (arXiv)

Representing and predicting high-dimensional and spatiotemporally chaotic dynamical systems remains a fundamental challenge in dynamical systems and machine learning. Although data-driven models can achieve accurate short-term forecasts, they often lack stability, interpretability, and scalability in regimes dominated by broadband or continuous spectra. Koopman-based approaches provide a principled linear perspective on nonlinear dynamics, but existing methods rely on restrictive finite-dimensional assumptions or explicit spectral parameterizations that degrade in high-dimensional settings. Against these issues, we introduce KoopGen, a generator-based neural Koopman framework that models dynamics through a structured, state-dependent representation of Koopman generators. By exploiting the intrinsic Cartesian decomposition into skew-adjoint and self-adjoint components, KoopGen separates conservative transport from irreversible dissipation while enforcing exact operator-theoretic constraints during learning. Across systems ranging from nonlinear oscillators to high-dimensional chaotic and spatiotemporal dynamics, KoopGen improves prediction accuracy and stability, while clarifying which components of continuous-spectrum dynamics admit interpretable and learnable representations.