Combining multiple surrogate models to accelerate failure probability estimation with expensive high-fidelity models
Combining multiple surrogate models to accelerate failure probability estimation with expensive high-fidelity models
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DOI：
10.1016/j.jcp.2017.04.012
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发表时间：
2017-07
期刊：
影响因子：
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通讯作者：
B. Peherstorfer;B. Kramer;K. Willcox
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文献类型：
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作者：
B. Peherstorfer;B. Kramer;K. Willcox
在失效概率估计中，重要性抽样构造了一个以失效事件为目标的偏置分布，使得少量的模型评估足以以可接受的精度实现失效概率的蒙特卡罗估计;然而，偏置分布的构造通常需要大量的模型评估，这可能会变得计算昂贵。我们提出了一种混合多保真度重要性抽样（MMFIS）的方法，利用计算便宜，但错误的代理模型的建设的偏置分布，并使用原来的高保真模型，以保证无偏估计的故障概率。我们的MMFIS估计的关键属性是，它可以利用多个代理模型的偏置分布的建设，而不是一个单一的代理模型。我们表明，我们的MMFIS估计有一个均方误差，这是一个常数低于相应的估计，使用任何给定的代理模型单独的均方误差，即使在设置中没有信息的近似质量的代理模型是可用的。特别是，我们的MMFIS方法避免了选择代理模型的问题，导致估计具有最低的均方误差，这是具有挑战性的，如果近似质量的代理模型是未知的。我们证明了我们的MMFIS方法的数值例子，在那里我们实现了数量级的加速比只使用高保真模型。
In failure probability estimation, importance sampling constructs a biasing distribution that targets the failure event such that a small number of model evaluations is sufficient to achieve a Monte Carlo estimate of the failure probability with an acceptable accuracy; however, the construction of the biasing distribution often requires a large number of model evaluations, which can become computationally expensive. We present a mixed multifidelity importance sampling (MMFIS) approach that leverages computationally cheap but erroneous surrogate models for the construction of the biasing distribution and that uses the original high-fidelity model to guarantee unbiased estimates of the failure probability. The key property of our MMFIS estimator is that it can leverage multiple surrogate models for the construction of the biasing distribution, instead of a single surrogate model alone. We show that our MMFIS estimator has a mean-squared error that is up to a constant lower than the mean-squared errors of the corresponding estimators that uses any of the given surrogate models alone—even in settings where no information about the approximation qualities of the surrogate models is available. In particular, our MMFIS approach avoids the problem of selecting the surrogate model that leads to the estimator with the lowest mean-squared error, which is challenging if the approximation quality of the surrogate models is unknown. We demonstrate our MMFIS approach on numerical examples, where we achieve orders of magnitude speedups compared to using the high-fidelity model only.