EFFICIENT LOCALIZATION OF DISCONTINUITIES IN COMPLEX COMPUTATIONAL SIMULATIONS

被引:22
|
作者
Gorodetsky, Alex [1 ]
Marzouk, Youssef [1 ]
机构
[1] MIT, Dept Aeronaut & Astronaut, Cambridge, MA 02139 USA
来源
SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2014年 / 36卷 / 06期
关键词
discontinuity detection; polynomial annihilation; function approximation; support vector machines; active learning; uncertainty quantification; STOCHASTIC COLLOCATION; UNCERTAINTY QUANTIFICATION; DESIGN;
D O I
10.1137/140953137
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Surrogate models for computational simulations are input-output approximations that allow computationally intensive analyses, such as uncertainty propagation and inference, to be performed efficiently. When a simulation output does not depend smoothly on its inputs, the error and convergence rate of many approximation methods deteriorate substantially. This paper details a method for efficiently localizing discontinuities in the input parameter domain, so that the model output can be approximated as a piecewise smooth function. The approach comprises an initialization phase, which uses polynomial annihilation to assign function values to different regions and thus seed an automated labeling procedure, followed by a refinement phase that adaptively updates a kernel support vector machine representation of the separating surface via active learning. The overall approach avoids structured grids and exploits any available simplicity in the geometry of the separating surface, thus reducing the number of model evaluations required to localize the discontinuity. The method is illustrated on examples of up to eleven dimensions, including algebraic models and ODE/PDE systems, and demonstrates improved scaling and efficiency over other discontinuity localization approaches.
引用
收藏
页码:A2584 / A2610
页数:27
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