Adaptive basis construction and improved error estimation for parametric nonlinear dynamical systems
Adaptive basis construction and improved error estimation for parametric nonlinear dynamical systems
复制标题
参数非线性动力系统的自适应基础构造和改进的误差估计
DOI：
10.1002/nme.6462
复制
发表时间：
2019
影响因子：
2.9
通讯作者：
P. Benner
中科院分区：
文献类型：
--
作者：
Sridhar Chellappa;Lihong Feng;P. Benner
提出了一种为参数非线性动力系统生成降阶模型的自适应方案。它的目的是自动化适当的正交分解（POD）-贪心算法与经验插值相结合。在每次迭代时，能够自适应地确定用于基构造的缩减基向量的数量和插值基向量的数量。所提出的技术能够在 RB 和插值基向量之间得出适当的匹配，从而使稳定、紧凑和可靠的 ROM 的生成成为可能。这是通过在贪婪算法的每次迭代中自适应地添加新的基向量或删除不必要的基向量来实现的。有效的输出误差指示器在自适应方案中起着关键作用。我们还根据之前的工作提出了一种改进的输出误差指标。 POD-Greedy 算法收敛后，新的误差指示器比现有的误差指示器更清晰，这意味着可以构建更可靠的 ROM。所提出的方法在几个非线性动力系统上进行了测试，即粘性伯格斯方程和化学工程的其他两个模型。
An adaptive scheme to generate reduced‐order models for parametric nonlinear dynamical systems is proposed. It aims to automatize the proper orthogonal decomposition (POD)‐Greedy algorithm combined with empirical interpolation. At each iteration, it is able to adaptively determine the number of the reduced basis vectors and the number of the interpolation basis vectors for basis construction. The proposed technique is able to derive a suitable match between the RB and the interpolation basis vectors, making the generation of a stable, compact and reliable ROM possible. This is achieved by adaptively adding new basis vectors or removing unnecessary ones, at each iteration of the greedy algorithm. An efficient output error indicator plays a key role in the adaptive scheme. We also propose an improved output error indicator based on previous work. Upon convergence of the POD‐Greedy algorithm, the new error indicator is shown to be sharper than the existing ones, implicating that a more reliable ROM can be constructed. The proposed method is tested on several nonlinear dynamical systems, namely, the viscous Burgers' equation and two other models from chemical engineering.
DOI：
10.1137/17m1123286
发表时间：
2018-02
期刊：
SIAM J. Matrix Anal. Appl.
影响因子：
--
作者：
Ralf Zimmermann;B. Peherstorfer;K. Willcox
通讯作者：
Ralf Zimmermann;B. Peherstorfer;K. Willcox