论文标题
部分可观测时空混沌系统的无模型预测
Non-parametric Reconstruction Of Some Cosmological Parameters
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 present thesis is devoted to the non-parametric reconstruction of some cosmological parameters using diverse observational datasets. The Universe is assumed to be spatially homogeneous and isotropic, thus described by the FLRW metric. The first chapter provides a brief introduction to cosmology and focuses on the reconstruction methods. An assessment of the cosmic distance-duality relation is discussed in chapter 2. In chapter 3, a non-parametric reconstruction of the cosmological jerk parameter is carried out. Chapter 4 explores the possibility of a non-gravitational interaction in the cosmic dark sector. In chapter 5, attempts are made to revisit a non-parametric reconstruction of the cosmic deceleration parameter using various combinations of recently updated background datasets and the growth rate of structure measurements from the redshift-space distortions. Finally, chapter 6 contains the concluding remarks and relevant discussion regarding the overall work presented in the thesis.
