论文标题
从量子场理论中的框架$ \ mathbb e_n $ -algebras
Framed $\mathbb E_n$-Algebras from Quantum Field Theory
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 addresses the following question: given a topological quantum field theory on $\mathbb R^n$ built from an action functional, when is it possible to globalize the theory so that it makes sense on an arbitrary smooth oriented $n$-manifold? We study a broad class of topological field theories -- those of AKSZ type -- and obtain an explicit condition for the vanishing of the framing anomaly, i.e., the obstruction to performing this globalization procedure. We also interpret our results in terms of identifying the observables as an algebra over the framed little $n$-disks operad. Our analysis uses the BV formalism for perturbative field theory and the notion of factorization homology.
