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

• URL: http://arxiv.org/abs/2602.14011v1
• Date: Sun, 15 Feb 2026 06:32:23 GMT
• 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,
• Abstract summary: We introduce a generator-based neural Koopman framework that models dynamics through a structured, state-dependent representation of Koopman generators.<n>By exploiting the intrinsic Cartesian decomposition into skew-adjoint and self-adjoint components, KoopGen separates conservative transport from irreversible dissipation.
• Score: 65.11254608352982
• License: http://creativecommons.org/licenses/by/4.0/
• 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. 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.

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