论文标题
部分可观测时空混沌系统的无模型预测
Biot model with generalized eigenvalue problems for scalability and robustness to parameters
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 consider Biot model with block preconditioners and generalized eigenvalue problems for scalability and robustness to parameters. A discontinuous Galerkin discretization is employed with the displacement and Darcy flow flux discretized as piecewise continuous in $P_1$ elements, and the pore pressure as piecewise constant in the $P_0$ element with a stabilizing term. Parallel algorithms are designed to solve the resulting linear system. Specifically, the GMRES method is employed as the outer iteration algorithm and block-triangular preconditioners are designed to accelerate the convergence. In the preconditioners, the elliptic operators are further approximated by using incomplete Cholesky factorization or two-level additive overlapping Schwartz method where coarse grids are constructed by generalized eigenvalue problems in the overlaps (GenEO). Extensive numerical experiments show a scalability and parametric robustness of the resulting parallel algorithms.
