论文标题
部分可观测时空混沌系统的无模型预测
The role of symmetrical inhomogeneity in problems of electromagnetic wave propagation
论文作者
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。
Media with symmetric inhomogeneity have been of great interest due to numerous effects which occur when electromagnetic waves propagate through such media. In general, the inhomogeneity of a certain medium means that the refraction index of the medium is not constant and has some sort of spatial dependency. These types of media are called gradient index (GRIN) media. Different optical effects related to GRIN media are described by GRIN optics. GRIN optics examines different phenomena related to the gradient of the refractive index of the medium and/or the material. Electromagnetic waves propagating in such materials result in many effects that are being exploited to produce lenses, optical fibers, and other devices. By symmetric inhomogeneity, we refer to the case when the inhomogeneity of the medium or material is not an arbitrary function of position but has some sort of symmetry. In this dissertation, our primary focus is on two types of inhomogeneous media. Firstly, we examine photonic crystals which are optical structures where the refractive index changes periodically. The other type of inhomogeneity, that is examined, is the case when the refractive index of a medium is a continuous function of position. Moreover, the central focus is given to profiles possessing different symmetries. Specifically, we investigate the effects occurring in Maxwell Fish eye profile which has spherical symmetry as well as an extended symmetry which will be thoroughly studied in Chapters 3 and 4.
