论文标题
部分可观测时空混沌系统的无模型预测
Infinite-dimensional genetic and evolution algebras generated by Gibbs measures
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。
Genetic and evolution algebras arise naturally from applied probability and stochastic processes. Gibbs measures describe interacting systems commonly studied in thermodynamics and statistical mechanics with applications in several fields. Here, we consider that the algebras are determined by configurations of finite spins on a countable set with their associated Gibbs distributions. The model preserves properties of the finite-dimensional Gibbs algebras found in the literature and extend their results. We introduce infertility in the genetic dynamics when the configurations differ macroscopically. It induces a decomposition of the algebra into a direct sum of fertile ideals with genetic realization. The proposed infinite-dimensional algebras are commutative, non-associative, with uncountable basis and zero divisors. The properties of Gibbs measures allow us to deal with the difficulties arising from the algebraic structure and obtain the results presented in this article.
