论文标题
部分可观测时空混沌系统的无模型预测
Shift symmetries and duality web in gauge theories
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。
Using a generalised Noether prescription we are able to extract all the currents and their conservation laws in space dependent shift symmetric theories. Various identities among the currents in the matter sector are found that form the basis for revealing a dual picture when the full interacting theory is considered by coupling to gauge fields. The coupling is achieved in terms of vector fields by adhering to a modified minimal prescription which is also supported by an iterative Noether scheme. Further, this scheme shows that couplings can also be introduced using higher rank tensor gauge fields that have appeared in recent discussions on fractons. We reveal a connection among these descriptions (using vector or tensor fields) through certain duality maps that relate the various fields (gauge, electric and magnetic) in the two cases. A correspondence is established among the Gauss' law, Faraday's law and Ampere's law. Explicit calculations are provided for linear and quadratic shift symmetric lagrangians.
