Fixed‐precision randomized low‐rank approximation methods for nonlinear model order reduction of large systems
Fixed‐precision randomized low‐rank approximation methods for nonlinear model order reduction of large systems
复制标题
大型系统非线性模型降阶的固定精度随机低阶近似方法
DOI：
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复制
发表时间：
2019
影响因子：
2.9
通讯作者：
L. Song
中科院分区：
文献类型：
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作者：
C. Bach;F. Duddeck;L. Song
许多模型降阶（莫尔）方法采用降阶基V∈Rm×k来逼近状态变量。对于非线性模型，V通常使用快照方法计算。快照矩阵A∈Rm×n的相关低秩近似随着m，n变大而变得非常昂贵。广泛使用的传统奇异值分解方法具有O（min（mn2，m2n））的渐近时间复杂度，这通常使得它们对于具有许多快照的大型模型的约简不切实际。已经提出了不同的方法来缓解这个问题，包括迭代和增量方法。最近，提出了使用快速和准确的随机化方法。然而，到目前为止，大多数工作都集中在固定秩近似上，其中秩k被假设为先验已知。在非线性莫尔的情况下，说明精度的界限通常更合适。我们扩展了现有的随机固定精度算法的研究，并提出了一个新的启发式算法，通过预测秩来加速缩减基计算。理论分析和数值结果表明，新算法具有良好的性能，可用于计算大型快拍矩阵的约简基，其精度可达给定的ε。
Many model order reduction (MOR) methods employ a reduced basis V∈Rm×k to approximate the state variables. For nonlinear models, V is often computed using the snapshot method. The associated low‐rank approximation of the snapshot matrix A∈Rm×n can become very costly as m,n grow larger. Widely used conventional singular value decomposition methods have an asymptotic time complexity of O(min(mn2,m2n)) , which often makes them impractical for the reduction of large models with many snapshots. Different methods have been suggested to mitigate this problem, including iterative and incremental approaches. More recently, the use of fast and accurate randomized methods was proposed. However, most work so far has focused on fixed‐rank approximations, where rank k is assumed to be known a priori. In case of nonlinear MOR, stating a bound on the precision is usually more appropriate. We extend existing research on randomized fixed‐precision algorithms and propose a new heuristic for accelerating reduced basis computation by predicting the rank. Theoretical analysis and numerical results show a good performance of the new algorithms, which can be used for computing a reduced basis from large snapshot matrices, up to a given precision ε.
DOI：
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发表时间：
2014-12
期刊：
ArXiv
影响因子：
--
作者：
Arthur Szlam;Y. Kluger;M. Tygert
通讯作者：
Arthur Szlam;Y. Kluger;M. Tygert