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Goal-oriented adaptive surrogate construction for stochastic inversion

机译：面向目标的随机反演自适应替代构造

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摘要

For computationally expensive models, surrogate response surfaces are often employed to increase the number of samples used in approximating the solution to a stochastic inverse problem. The result is generally a trade-off in errors where the stochastic error is reduced at the cost of an increase in deterministic/discretization errors in the evaluation of the surrogate. Such stochastic errors pollute predictions based on the stochastic inverse. In this work, we formulate a method for adaptively creating a special class of surrogate response surfaces with these sources of error in mind. Adjoint techniques are used to enhance the local approximation properties of the surrogate allowing the construction of a higher-level enhanced surrogate. Using these two levels of surrogates, appropriately derived local error indicators are computed and used to guide refinement of both levels of the surrogates. Three types of refinement strategies are presented and combined in an iterative adaptive surrogate construction algorithm. Numerical examples, including a complex vibroacoustics application, demonstrate how this adaptive strategy allows for accurate predictions under uncertainty for a much smaller computational cost than uniform refinement. (C) 2018 Elsevier B.V. All rights reserved.
机译：对于计算上昂贵的模型，通常使用代理响应面来增加用于逼近随机反问题的样本数量。结果通常是在错误之间进行权衡，其中减少随机误差以增加代理评估中确定性/离散性误差为代价。这样的随机误差会基于随机逆来污染预测。在这项工作中，我们制定了一种方法，可以在考虑到这些误差源的情况下自适应地创建一类特殊的替代响应面。伴随技术用于增强代理的局部近似特性，从而允许构建更高级别的增强代理。使用这两个代理水平，可以适当地导出局部误差指标，并用于指导两个代理水平的细化。提出了三种类型的优化策略，并将其组合在迭代自适应代理构造算法中。包括复杂的振动声学应用程序在内的数值示例说明了这种自适应策略如何在不确定性下实现准确的预测，并且计算成本要比均匀优化小得多。 （C）2018 Elsevier B.V.保留所有权利。

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