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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.14011 |
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| _version_ | 1866918339587080192 |
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| author | Su, Liangyu Shu, Jun Liu, Rui Meng, Deyu Xu, Zongben |
| author_facet | Su, Liangyu Shu, Jun Liu, Rui Meng, Deyu Xu, Zongben |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14011 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | KoopGen: Koopman Generator Networks for Representing and Predicting Dynamical Systems with Continuous Spectra Su, Liangyu Shu, Jun Liu, Rui Meng, Deyu Xu, Zongben Machine Learning 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. |
| title | KoopGen: Koopman Generator Networks for Representing and Predicting Dynamical Systems with Continuous Spectra |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2602.14011 |