Self-Adaptive Reliable Numerical Treatment of Polymorphic Uncertainty by Hierarchical Tensors

层次张量多态不确定性的自适应可靠数值处理

基本信息

批准号：
312863472
负责人：
Professor Dr. Lars Grasedyck
金额：
--
依托单位：
Institut für Geometrie und Praktische Mathematik (IGPM)
依托单位国家：
德国
项目类别：
Priority Programmes
财政年份：
2016
资助国家：
德国
起止时间：
2015-12-31 至 2020-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/312863472?language=en
关键词：
Self Adaptive Reliable Numerical Treatment

Self Adaptive Reliable Numerical Treatment

项目摘要

The aim of this project is to develop a fast and reliable self-adaptive simulation tool that can be used for polymorphic uncertainty quantification. The idea is to use model reduction techniques intertwined with tensor compression in order to produce a parametric representation of the high resolution model under consideration. The self-adaptivity is necessary since the compressed model should be used as a black box by researchers that are not specialized in tensors. The model reduction part is responsible for the reduction of the high resolution from the discretisation of the PDE model. The tensor compression part can cope with the many parameters or equivalently high dimensionality from the uncertainty in the model. Both parts combined provide a tool that produces the compressed representation in a complexity that is linear in the number of parameters and linear in the size of the number of unknowns for the PDE discretisation. We consider several practical model problems involving a mixture of uncertainties that arise from parameters in the model, external forces and initial data. We transform this problem into a multiparametric and high-dimensional one where parameters may come from different sources of uncertainty. The reduction of the parametric model gives rise to a compressed hierarchical low rank tensor representation which can be evaluated instantly for any given choice of parameters.

该项目的目的是开发一种可以用于多态性不确定性定量的快速可靠的自适应仿真工具。这个想法是使用与张量压缩交织在一起的模型还原技术，以产生所考虑的高分辨率模型的参数表示。自适应性是必要的，因为压缩模型应由不专门用于张量的研究人员用作黑匣子。模型还原部分负责从PDE模型的离散化中减少高分辨率。张量压缩零件可以应对许多参数，也可以与模型中的不确定性相等的高维度。这两个部分组合都提供了一种工具，该工具以复杂性产生压缩表示，该复杂性在参数数量中是线性的，并且以PDE离散化的未知数数量的大小为线性。我们考虑了几个实用的模型问题，这些问题涉及由模型，外部力和初始数据中的参数引起的不确定性的混合。我们将此问题转换为多参数和高维的问题，其中参数可能来自不同的不确定性来源。参数模型的降低产生了压缩的层次低等级张量表示，可以立即评估任何给定参数的选择。