论文标题

部分可观测时空混沌系统的无模型预测

Markovian Features of the Solar Wind at Sub-Proton Scales

论文作者

Benella, Simone, Stumpo, Mirko, Consolini, Giuseppe, Alberti, Tommaso, Carbone, Vincenzo, Laurenza, Monica

论文摘要

储层计算是预测湍流的有力工具,其简单的架构具有处理大型系统的计算效率。然而,其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间,然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用,该系统模拟了湍流的若干特征。我们表明,使用径向基函数作为非线性投影器,即使只有部分观测并且不知道控制方程,也能稳健地捕捉复杂的系统非线性。最后,我们表明,当测量稀疏、不完整且带有噪声,甚至控制方程变得不准确时,我们的网络仍然可以产生相当准确的预测,从而为实际湍流系统的无模型预测铺平了道路。

The interplanetary magnetic field carried out from the Sun by the solar wind displays fluctuations on a wide range of scales. While at large scales, say at frequencies lower than 0.1-1 Hz, fluctuations display clear universal characteristics of fully developed turbulence with a well defined Kolmogorov's like inertial range, the physical and dynamical properties of the small-scale regime as well as their connection with the large-scale ones are still a debated topic. In this work we investigate the near-Sun magnetic field fluctuations at sub-proton scales by analyzing the Markov property of fluctuations and recovering basic information about the nature of the energy transfer across different scales. By evaluating the Kramers-Moyal coefficients we find that fluctuations in the sub-proton range are well described as a Markovian process with Probability Density Functions (PDFs) modeled via a Fokker-Planck (FP) equation. Furthermore, we show that the shape of the PDFs is globally scale-invariant and similar to the one recovered for the stationary solution of the FP equation at different scales. The relevance of our results on the Markovian character of sub-proton scale fluctuations is also discussed in connection with the occurrence of turbulence in this domain.

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