In this work, we consider the general problem of constructing a neural network surrogate model using multi-fidelity information. Given an inexpensive low-fidelity and an expensive high-fidelity computational model, we present a residual multi-fidelity computational framework that formulates the correlation between models as a residual function, a possibly non-linear mapping between 1) the shared input space of the models together with the low-fidelity model output and 2) the discrepancy between the two model outputs. To accomplish this, we train two neural networks to work in concert. The first network learns the residual function on a small set of high-fidelity and low-fidelity data. Once trained, this network is used to generate additional synthetic high-fidelity data, which is used in the training of a second network. This second network, once trained, acts as our surrogate for the high-fidelity quantity of interest. We present three numerical examples to demonstrate the power of the proposed framework. In particular, we show that dramatic savings in computational cost may be achieved when the output predictions are desired to be accurate within small tolerances.

翻译：本文研究了利用多保真信息构建神经网络代理模型的一般性问题。给定一个低成本的低保真计算模型和一个昂贵的高保真计算模型，我们提出了一种残差多保真计算框架，将模型之间的相关性表述为残差函数——该函数可能是1）模型共享输入空间与低保真模型输出之间的映射，以及2）两种模型输出差异之间的非线性映射。为此，我们训练两个神经网络协同工作：第一个网络利用少量高保真与低保真数据学习残差函数，训练完成后用于生成额外的合成高保真数据，供第二个网络训练使用；第二个网络经训练后作为高保真感兴趣量的代理模型。我们通过三个数值算例展示了所提框架的强大能力，特别证明了在输出预测需达到小容差精度时，该方法可显著降低计算成本。