论文标题
部分可观测时空混沌系统的无模型预测
Supersymmetric non-Hermitian topological interface laser
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。
We investigate laser emission at the interface of a topological and trivial phases with loss and gain. The system is described by a Su-Schrieffer-Heeger model with site-dependent hopping parameters. We study numerically and analytically the interface states. The ground state is described by the Jackiw-Rebbi mode with a pure imaginary energy, reflecting the non-Hermiticity of the system. It is strictly localized only at the A sites. We also find a series of analytic solutions of excited states based on SUSY quantum mechanics, where the A and B sites of the bipartite lattice form SUSY partners. We then study the system containing loss and gain with saturation. The Jackiw-Rebbi mode is extended to a nonlinear theory, where B sites are also excited. The relative phases between A and B sites are fixed, and hence it will serve as a large area coherent laser.
