论文标题
上下文感知的替代建模，用于平衡多保真重要性抽样和贝叶斯反问题的近似和采样成本
Context-aware surrogate modeling for balancing approximation and sampling costs in multi-fidelity importance sampling and Bayesian inverse problems
论文作者
论文摘要
多保真方法利用低成本替代模型来加快计算的速度，并偶尔求助于昂贵的高保真模型以建立准确性保证。由于替代和高保真模型被一起使用，因此可以通过频繁地求助于高保真模型来补偿替代模型的不良预测。因此，投资计算资源以提高替代模型的准确性与仅仅使昂贵的高保真模型更频繁地求助之间存在权衡；但是，传统的建模方法忽略了这种权衡，这些方法构建了旨在替代高保真模型而不是与高保真模型一起使用的替代模型。这项工作考虑了多余的重要性采样，理论上和计算在造成了替代，从而增加了替代模型的忠诚度，以构建更准确的偏见密度以及高效率模型所需的样本数量，以补偿较差的偏见密度。数值示例表明，这种上下文感知的替代模型的多效率重要性采样比通常将其视为传统模型降低中的公差，从而导致示例中最高一个数量级的运行时速度。
Multi-fidelity methods leverage low-cost surrogate models to speed up computations and make occasional recourse to expensive high-fidelity models to establish accuracy guarantees. Because surrogate and high-fidelity models are used together, poor predictions by surrogate models can be compensated with frequent recourse to high-fidelity models. Thus, there is a trade-off between investing computational resources to improve the accuracy of surrogate models versus simply making more frequent recourse to expensive high-fidelity models; however, this trade-off is ignored by traditional modeling methods that construct surrogate models that are meant to replace high-fidelity models rather than being used together with high-fidelity models. This work considers multi-fidelity importance sampling and theoretically and computationally trades off increasing the fidelity of surrogate models for constructing more accurate biasing densities and the numbers of samples that are required from the high-fidelity models to compensate poor biasing densities. Numerical examples demonstrate that such context-aware surrogate models for multi-fidelity importance sampling have lower fidelity than what typically is set as tolerance in traditional model reduction, leading to runtime speedups of up to one order of magnitude in the presented examples.
