Universal set of Observables for the Koopman Operator through Causal Embedding
Universal set of Observables for the Koopman Operator through Causal Embedding
复制标题
通过因果嵌入为 Koopman 算子提供通用可观察集
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
A. D. Clercq
中科院分区：
文献类型：
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作者：
G. Manjunath;A. D. Clercq
从物理和自然系统中获得重复测量值以建立此类系统的信息量更大的动力学模型已铭刻在现代科学中。通过延迟坐标映射、基于Koopman算子的数据驱动方法和水库计算方法重建等价混沌动力系统的结果表明，在一个新的相空间上找到与产生数据的动力系统相关的模型方程是可能的。最近，严格的结果表明，减少功能的复杂性的地图，描述了在新的阶段的动态Koopman算子为基础的方法非常有吸引力的数据驱动的建模。然而，选择一组可以用于不同数据集的非线性可观测函数是一个公开的挑战。我们使用驱动的动力系统与水库计算的因果嵌入属性，以获得正确的一组可观的动态在新的空间是等价的或拓扑共轭的原始系统。深度学习方法用于学习作为拓扑共轭的结果而出现的地图。除了稳定性，硬件实现的顺从性，基于因果嵌入的模型提供了长期的一致性，即使是在以前报告的数据驱动或机器学习方法下失败的地图。
Obtaining repeated measurements from physical and natural systems for building a more informative dynamical model of such systems is engraved in modern science. Results in reconstructing equivalent chaotic dynamical systems through delay coordinate mappings, Koopman operator based data-driven approach and reservoir computing methods have shown the possibility of finding model equations on a new phase space that is relatable to the dynamical system generating the data. Recently, rigorous results that point to reducing the functional complexity of the map that describes the dynamics in the new phase have made the Koopman operator based approach very attractive for data-driven modeling. However, choosing a set of nonlinear observable functions that can work for different data sets is an open challenge. We use driven dynamical systems comparable to that in reservoir computing with the causal embedding property to obtain the right set of observables through which the dynamics in the new space is made equivalent or topologically conjugate to the original system. Deep learning methods are used to learn a map that emerges as a consequence of the topological conjugacy. Besides stability, amenability for hardware implementations, causal embedding based models provide long-term consistency even for maps that have failed under previously reported data-driven or machine learning methods.
影响因子：
7.8
作者：
Grigoryeva, Lyudmila;Ortega, Juan-Pablo
通讯作者：
Ortega, Juan-Pablo