A door to model reduction in high-dimensional parameter space
A door to model reduction in high-dimensional parameter space
复制标题
高维参数空间模型简化的一扇门
DOI：
10.1016/j.crme.2018.04.009
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
P. Ladevèze
中科院分区：
文献类型：
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作者：
C. Paillet;D. Néron;P. Ladevèze
适当广义分解 (PGD) 等模型简化技术是即将彻底改变许多领域的决策工具。不幸的是，它们的计算对于涉及许多参数的问题仍然存在问题，为此必须面对“维数诅咒”。固体力学中所谓的“参数多尺度 PGD”给出了对这一挑战的答案，它基于圣维南原理。在这篇文章中，提出了一个由多达一千个参数组成的模型问题，表明该方法能够克服“维数灾难”。
Model reduction techniques such as Proper Generalized Decomposition (PGD) are decision-making tools that are about to revolutionize many domains. Unfortunately, their computation is still problematic for problems involving many parameters, for which one has to face the “curse of dimensionality”. An answer to this challenge is given in solid mechanics by the so-called “parameter-multiscale PGD”, which is based on Saint-Venant's principle. In this article, a model problem composed of up to a thousand parameters is presented, showing that the method is able to overcome the “curse of dimensionality”.