论文标题
部分可观测时空混沌系统的无模型预测
B-mode constraints from Planck low multipole polarisation data
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 present constraints on primordial B modes from large angular scale cosmic microwave background polarisation anisotropies measured with the Planck satellite. To remove Galactic polarised foregrounds, we use a Bayesian parametric component separation method, modelling synchrotron radiation as a power law and thermal dust emission as a modified blackbody. This method propagates uncertainties from the foreground cleaning into the noise covariance matrices of the maps. We construct two likelihoods: (i) a semi-analytical cross-spectrum-based likelihood-approximation scheme (momento) and (ii) an exact polarisation-only pixel-based likelihood (pixlike). Since momento is based on cross-spectra it is statistically less powerful than pixlike, but is less sensitive to systematic errors correlated across frequencies. Both likelihoods give a tensor-to-scalar ratio, r, that is consistent with zero from low multipole (2 <= ell < 30) Planck polarisation data. From full-mission maps we obtain r_0.05<0.274, at 95 per cent confidence, at a pivot scale of k = 0.05 Mpc^-1, using pixlike. momento gives a qualitatively similar but weaker 95 per cent confidence limit of r_0.05<0.408.
