论文标题
（1,2） - 曲面中的简单振动
Simple fibrations in (1,2)-surfaces
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 introduce the notion of a simple fibration in $(1,2)$-surfaces. That is, a hypersurface inside a certain weighted projective space bundle over a curve such that the general fibre is a minimal surface of general type with $p_g=2$ and $K^2=1$. We prove that almost all Gorenstein simple fibrations over the projective line with at worst canonical singularities are canonical threefolds "on the Noether line" with $K^3=\frac43 p_g-\frac{10}3$, and we classify them. Among them, we find all the canonical threefolds on the Noether line that have previously appeared in the literature. The Gorenstein simple fibrations over $\mathbb{P}^1$ are Cartier divisors in a toric $4$-fold. This allows to us to show among other things, that the previously known canonical threefolds on the Noether line form an open subset of the moduli space of canonical threefolds, that the general element of this component is a Mori Dream Space, and that there is a second component when the geometric genus is congruent to $6$ modulo $8$; the threefolds in this component are new.
