![[2602.14011] KoopGen: Koopman Generator Networks for Representing and Predicting Dynamical Systems with Continuous Spectra](https://arxiv.org/static/browse/0.3.4/images/arxiv-logo-fb.png){kind=logo}
[2602.14011] KoopGen: Koopman Generator Networks for Representing and Predicting Dynamical Systems with Continuous Spectra
Summary
The paper introduces KoopGen, a neural framework for modeling and predicting high-dimensional dynamical systems with continuous spectra, addressing limitations of existing methods.
Why It Matters
KoopGen enhances the stability and interpretability of predictions in complex dynamical systems, which is crucial for applications in various fields such as physics, engineering, and climate modeling. By overcoming the limitations of traditional methods, it opens new avenues for research and practical implementations in machine learning.
Key Takeaways
- KoopGen improves prediction accuracy for chaotic dynamical systems.
- The framework separates conservative transport from irreversible dissipation.
- It enforces operator-theoretic constraints during the learning process.
- KoopGen provides interpretable representations of continuous-spectrum dynamics.
- The approach is applicable to a wide range of high-dimensional systems.
Computer Science > Machine Learning arXiv:2602.14011 (cs) [Submitted on 15 Feb 2026] Title:KoopGen: Koopman Generator Networks for Representing and Predicting Dynamical Systems with Continuous Spectra Authors:Liangyu Su, Jun Shu, Rui Liu, Deyu Meng, Zongben Xu View a PDF of the paper titled KoopGen: Koopman Generator Networks for Representing and Predicting Dynamical Systems with Continuous Spectra, by Liangyu Su and 3 other authors View PDF HTML (experimental) Abstract: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. ...
