Breaking the Kolmogorov Barrier with Nonlinear Model Reduction
Breaking the Kolmogorov Barrier with Nonlinear Model Reduction
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DOI：
10.1090/noti2475
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发表时间：
2022-05
影响因子：
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通讯作者：
B. Peherstorfer
中科院分区：
文献类型：
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作者：
B. Peherstorfer
导论.模型降阶是计算科学与工程中普遍存在的问题。它在制作计算上易于处理的外环应用程序中起着关键作用，这些应用程序需要模拟具有不同参数和输入的许多场景的系统。典型的外环应用是控制、不确定性量化、逆问题和优化设计[RHP 08，BGW 15]。通过简化模型，在依赖于问题的低维简化空间中数值地求解描述感兴趣的物理系统的微分方程，这与在通用的高维全空间中制定的传统的全模型相反，有限元/体积法约化空间构造在一个
Introduction. Model reduction is ubiquitous in computational science and engineering. It plays a key role in making computationally tractable outer-loop applications that require simulating systems for many scenarios with different parameters and inputs. Typical outer-loop applications are control, uncertainty quantification, inverse problems, and optimal design [RHP08,BGW15]. With reduced models, one numerically solves the differential equations, which describe the physical system of interest, in problemdependent, low-dimensional reduced spaces, in contrast to traditional, full models that are formulated in generic, high-dimensional full spaces with, e.g., finite-element/ -volume methods. Reduced spaces are constructed in a