论文标题
部分可观测时空混沌系统的无模型预测
dS${}_4$ universe emergent from Kerr-AdS${}_5$ spacetime: bubble nucleation catalyzed by a black hole
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。
The emergence of a four-dimensional de Sitter (dS${}_4$) universe on an expanding bubble in the five-dimensional anti-de Sitter (AdS${}_5$) background has been suggested as a possible cosmological scenario. It is motivated by the difficulties in the realization of a stable de Sitter vacua in string theory. The bubble can be nucleated in a meta-stable pure AdS${}_5$ spacetime, but it is known that a pure AdS spacetime is non-perturbatively unstable. It means that the pure AdS${}_5$ background is an idealized situation, and in realistic situations, non-linear perturbations in AdS may lead to the formation of black holes due to the gravitational turbulent instability. To investigate how the proposed scenario works in a more realistic situation, we here study the nucleation process of a vacuum bubble in the Kerr-AdS${}_5$ spacetime. Especially we investigate conditions sufficient to ensure the nucleation of a vacuum bubble with a rotating black hole and how the black hole affects the transition rate. We find that even in the Kerr-AdS${}_5$ spacetime, a quasi-dS${}_4$ expansion can be realized on the nucleated vacuum bubble without contradicting the de Sitter swampland conjectures.
