研究人员开发了一个名为RC-Koopman的新框架，该框架利用储层计算来创建非线性动力学系统的线性表示。该方法旨在克服Koopman算子理论中固有的字典选择和时间记忆编码的挑战。RC-Koopman框架将储层解释为有状态字典，记忆深度由谱半径控制，与扩展动态模式分解（EDMD）等方法相比，具有更好的数值条件和稳定性。此外，另一项研究提出了一种通过整合子系统控制方程信息来学习耦合系统Koopman算子的方法，解决了EDMD等纯数据驱动方法在数据稀缺时的局限性。 AI
影响 引入了对复杂非线性系统进行建模的新技术，有可能提高科学和工程应用中的预测精度。
排序理由 两篇arXiv论文介绍了学习Koopman算子的新方法，这是动力学系统的一个核心研究课题。
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arXiv:2605.04917v1 Announce Type: new Abstract: Learning tractable linear representations of nonlinear dynamical systems via Koopman operator theory is often hindered by dictionary selection, temporal memory encoding, and numerical ill-conditioning. Inspired by Reservoir Computin…
Learning tractable linear representations of nonlinear dynamical systems via Koopman operator theory is often hindered by dictionary selection, temporal memory encoding, and numerical ill-conditioning. Inspired by Reservoir Computing (RC) paradigm, this paper introduces the RC-Ko…
Learning tractable linear representations of nonlinear dynamical systems via Koopman operator theory is often hindered by dictionary selection, temporal memory encoding, and numerical ill-conditioning. Inspired by Reservoir Computing (RC) paradigm, this paper introduces the RC-Ko…
arXiv:2605.01835v1 Announce Type: new Abstract: Nonlinear coupled systems are ubiquitous in science and engineering. The analysis and modeling of such systems is challenging due to their high dimensionality and complex interactions among subsystems. In recent years, operator-theo…