论文标题

部分可观测时空混沌系统的无模型预测

Lattice dielectric properties of rutile $\mathrm{TiO}_2$: First-principles anharmonic self-consistent phonon study

论文作者

Amano, Tomohito, Yamazaki, Tamio, Akashi, Ryosuke, Tadano, Terumasa, Tsuneyuki, Shinji

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 calculate the lattice dielectric function of strongly anharmonic rutile $\mathrm{TiO}_2$ from ab initio anharmonic lattice dynamics methods. Since an accurate calculation of the $Γ$ point phonons is essential for determining optical properties, we employ the modified self-consistent approach, including third-order anharmonicity as well as fourth-order anharmonicity. The resulting optical phonon frequencies and linewidths at the $Γ$ point much better agree with experimental measurements than those from a perturbative approach. We show that the four-phonon scattering process contributes as much as the third-order anharmonic term to phonon linewidths. Furthermore, incorporating the frequency dependence of phonon linewidth reveals that experimentally known but unidentified peaks of the dielectric function are due to two-phonon process. This work emphasizes the importance of a self-consistent approach in predicting the optical properties of highly anharmonic materials.

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