论文标题
随机凯勒 - 塞格模型在一个维度中的独特性
Uniqueness of the stochastic Keller-Segel model in one dimension
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。
In a recent paper (J. Differential Equations, 310: 506-554, 2022), the authors proved the existence of martingale solutions to a stochastic version of the classical Patlak-Keller-Segel system in 1 dimension (1D), driven by time-homogeneous spatial Wiener processes. The current paper is a continuation and consists of two results about the stochastic Patlak-Keller-Segel system in 1D. First, we establish some additional regularity results of the solutions. The additional regularity is, e.g. important for its numerical modeling. Then, as a second result, we obtain the pathwise uniqueness of the solutions to the stochastic Patlak-Keller-Segel system in 1D. Finally, we conclude the paper with the existence of the strong solution to this system in 1D.
