We propose a multi-fidelity neural network surrogate sampling method for the uncertainty quantification of physical/biological systems described by ordinary or partial differential equations. We first generate a set of low/high-fidelity data by low/high-fidelity computational models, e.g. using coarser/finer discretizations of the governing differential equations. We then construct a two-level neural network, where a large set of low-fidelity data are utilized in order to accelerate the construction of a high-fidelity surrogate model with a small set of high-fidelity data. We then embed the constructed high-fidelity surrogate model in the framework of Monte Carlo sampling. The proposed algorithm combines the approximation power of neural networks with the advantages of Monte Carlo sampling within a multi-fidelity framework. We present two numerical examples to demonstrate the accuracy and efficiency of the proposed method. We show that dramatic savings in computational cost may be achieved when the output predictions are desired to be accurate within small tolerances.

中文翻译：

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一种用于不确定性量化的多保真神经网络代理抽样方法

我们提出了一种多保真神经网络代理采样方法，用于对由常微分方程或偏微分方程描述的物理/生物系统的不确定性量化。我们首先通过低/高保真计算模型生成一组低/高保真数据，例如使用控制微分方程的更粗/更细的离散化。然后，我们构建了一个两级神经网络，其中利用了大量低保真数据，以加速构建具有少量高保真数据的高保真代理模型。然后我们将构建的高保真代理模型嵌入到蒙特卡罗采样的框架中。所提出的算法在多保真框架内结合了神经网络的逼近能力和蒙特卡罗采样的优点。我们提供了两个数值例子来证明所提出方法的准确性和效率。我们表明，当希望输出预测在小容差内准确时，可以显着节省计算成本。