论文标题
在ALE框架中，降低对流的模型占主导地位的双曲线问题：离线和在线阶段
Model Reduction for Advection Dominated Hyperbolic Problems in an ALE Framework: Offline and Online Phases
论文作者
论文摘要
降低模型订单（MOR）技术一直在压缩信息以占主导地位的问题。它们的线性性质不允许加速kolmogorov $ n $的缓慢衰减 - 这些问题的宽度。在过去的几年中，新的非线性算法获得了较小的缩小空间。在这些作品中，仅显示了这些算法的离线阶段。在这项工作中，我们研究了MOR算法的不稳定参数对流主导的双曲线问题，提供了完整的离线和在线描述，并显示了在在线阶段节省的时间。我们提出了一种任意的Lagrangian-尤拉利亚的方法，可以修改MOR流程的离线和在线阶段。这允许在相同位置上校准对流特征，并强烈压缩缩小的空间。所使用的基本MOR算法是经典的贪婪，EIM和POD，而校准图是通过多项式回归和人工神经网络学习的。在执行的模拟中，我们展示了新算法如何在具有非线性通量和不同边界条件的许多方程式上击败经典方法。最后，我们比较使用不同的校准图获得的结果。
Model order reduction (MOR) techniques have always struggled in compressing information for advection dominated problems. Their linear nature does not allow to accelerate the slow decay of the Kolmogorov $N$--width of these problems. In the last years, new nonlinear algorithms obtained smaller reduced spaces. In these works only the offline phase of these algorithms was shown. In this work, we study MOR algorithms for unsteady parametric advection dominated hyperbolic problems, giving a complete offline and online description and showing the time saving in the online phase. We propose an arbitrary Lagrangian--Eulerian approach that modifies both the offline and online phases of the MOR process. This allows to calibrate the advected features on the same position and to strongly compress the reduced spaces. The basic MOR algorithms used are the classical Greedy, EIM and POD, while the calibration map is learned through polynomial regression and artificial neural networks. In the performed simulations we show how the new algorithm defeats the classical method on many equations with nonlinear fluxes and with different boundary conditions. Finally, we compare the results obtained with different calibration maps.
