空间扩展系统中线性响应的预测因子与预测量
Predictors and Predictands of Linear Response in Spatially Extended Systems
AI总结：
提出量化可观测量的预测能力并排列的方法，以Lorenz '96模型研究空间扩展系统局部扰动下信号传播，发现考虑多强迫与多预测因子可提升预测效率。
摘要：
响应理论在其众多统计力学表述中的每一种中，目标都是根据对未扰动状态和所施加扰动的了解来预测系统的受扰响应。该问题的一个新近角度聚焦于提供一种方法，通过将第二个可观测量的变化作为实际强迫的替代，来预测系统中某一可观测量的变化。这种观点试图解决在仅有不完整信息可用时复杂系统内的因果联系这一非常相关的问题。我们在此提出一种量化和排列可观测量的预测能力的方法，并用它研究一个典型空间扩展系统，即Lorenz '96模型的响应。我们在局部扰动系统，然后研究给定的局部可观测能在多大程度上预测另一独立局部可观测量的行为。我们表明，这种方法能够揭示信号在系统内部传播方式的洞察。我们还表明，如果考虑多个作用强迫，并相应地考虑多个可观测作为感兴趣可观测的预测因子，该过程会变得更加高效。
英文摘要：
The goal of response theory, in each of its many statistical mechanical formulations, is to predict the perturbed response of a system from the knowledge of the unperturbed state and of the applied perturbation. A new recent angle on the problem focuses on providing a method to perform predictions of the change in one observable of the system by using the change in a second observable as a surrogate for the actual forcing. Such a viewpoint tries to address the very relevant problem of causal links within complex system when only incomplete information is available. We present here a method for quantifying and ranking the predictive ability of observables and use it to investigate the response of a paradigmatic spatially extended system, the Lorenz '96 model. We perturb locally the system and we then study to what extent a given local observable can predict the behaviour of a separate local observable. We show that this approach can reveal insights on the way a signal propagates inside the system. We also show that the procedure becomes more efficient if one considers multiple acting forcings and, correspondingly, multiple observables as predictors of the observable of interest.
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