论文标题

部分可观测时空混沌系统的无模型预测

Analysis and design of transition radiation in layered uniaxial crystals using Tandem neural networks

论文作者

Gao, Xiaoke, Zhao, Xiaoyu, Huang, Ruoyu, Ma, Siyuan, Ma, Xikui, Dong, Tianyu

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。

With the flourishing development of nanophotonics, Cherenkov radiation pattern can be designed to achieve superior performance in particle detection by fine-tuning the properties of metamaterials such as photonic crystals (PCs) surrounding the swift particle. However, the radiation pattern can be sensitive to the geometry and material properties of PCs, such as periodicity, unit thickness, and dielectric fraction, making direct analysis and inverse design difficult. In this article, we propose a systematic method to analyze and design PC-based transition radiation, which is assisted by deep learning neural networks. By matching boundary conditions at the interfaces, Cherenkov-like radiation of multilayered structures can be resolved analytically using the cascading scattering matrix method, despite the optical axes not being aligned with the swift electron trajectory. Once well trained, forward deep learning neural networks can be utilized to predict the radiation pattern without further direct electromagnetic simulations; moreover, Tandem neural networks have been proposed to inversely design the geometry and/or material properties for desired Cherenkov radiation pattern. Our proposal demonstrates a promising strategy for dealing with layered-medium-based Cherenkov radiation detectors, and it can be extended for other emerging metamaterials, such as photonic time crystals.

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