论文标题
部分可观测时空混沌系统的无模型预测
Space-time wave packets propagating a kilometer in air
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 report on the diffraction-free propagation of space-time wave packets (STWPs) -- a class of propagation-invariant pulsed beams -- for $\sim\!1$ km in an open-air laser range in a low-turbulence scenario. Making use of $\approx\!100$-fs pulses (bandwidth $\sim\!25$ nm) at a wavelength of $\approx\!1$ $μ$m, we construct an STWP with a transverse width of $\approx\!2$ mm that expands to $\approx\!3$ mm after $\sim\!500$ m, and another that expands from $\approx\!8$ mm to $\approx\!10$ mm after 1 km. The propagation of the STWPs is compared to Gaussian wave packets of the same transverse spatial width and bandwidth. We establish a theoretical model that accounts for the significant factors limiting the STWP propagation distance and suggests the path to further extending this distance.
