论文标题
部分可观测时空混沌系统的无模型预测
Correspondences between scalar field and fluid fluctuations in curved spacetime
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。
A correspondence between scalar field fluctuations and generalized fluctuations in a hydrodynamic approximation of fields is obtained. The results presented here are of interest to field-fluid correspondences and form part of theoretical foundations in this area. The intention for such developments is to explore sub-hydro range mesoscopic physics for the relativistic fluids in curved spacetime. The fluid correspondences fall in the classical domain and can replace the quantum fields and fluctuations for scales around the hydrodynamic limits.The present article extends our earlier results with a more elaborate physical insight towards the quantum fluids and retention of partial quantum nature in a stochastic description in bulk of the fluids. This also accounts for non-thermal effects along with thermal and quantum fluctuations for the fields in the hydro limit. Hence the expressions presented here are very general in nature for various applications. The further scope of research that such developments give is discussed in the concluding section.
