论文标题
部分可观测时空混沌系统的无模型预测
Parastrophes and Cosets of Soft Quasigroups
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。
This paper introduced the concept of soft quasigroup, its parastrophes, soft nuclei, left (right) coset, distributive soft quasigroups and normal soft quasigroups. Necessary and sufficient conditions for a soft set over a quasigroup (loop) to be a soft quasigroup (loop) were established. It was proved that a soft set over a group is a soft group if and only if it is a soft loop or either of two of its parastrophes is a soft groupoid. For a finite quasigroup, it was shown that the orders (arithmetic and geometric means) of the soft quasigroup over it and its parastrophes are equal. It was also proved that if a soft quasigroup is distributive, then all its parastrophes are distributive, idempotent and flexible soft quasigroups. For a distributive soft quasigroup, it was shown that its left and right cosets form families of distributive soft quasigroups that are isomorphic. If in addition, a soft quasigroup is normal, then its left and right cosets forms families of normal soft quasigroups. On another hand, it was found that if a soft quasigroup is a normal and distributive soft quasigroup, then its left (right) quotient is a family of commutative distributive quasigroups which have a 1-1 correspondence with the left (right) coset of the soft quasigroup.
