论文标题
部分可观测时空混沌系统的无模型预测
Application of Generalized Quaternion in Physics
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 applications of quaternion in physics are discussed with an emphasis on elementary particle symmetry and interaction. Three colours of the quark and the quantum chromodynamics (QCD) can be introduced directly from the invariance of basic equations under the quaternion phase transformation (quaternion gauge invariance). The generalized quaternions obey the SU(3) symmetry. QCD is essentially the quantum quaternion dynamics. The further generalization of SU(3) quaternion to G2 octonion is worked out. We demonstrate that the G2 octonion contains seven tri-generator sets of SU(2) symmetry and three of them form SU(3) subgroup. A model of the elementary particle classification and interaction based on octonion gauge theory is proposed. The model unifies the colour and flavour of all particles. It provides a framework for the unified description of four kinds of elementary particles (quarks, leptons, gauge fields and Higgs bosons) and their interactions.
