  To reduce training costs, several Deep neural networks (DNNs) that can learn
from a small set of HF data and a sufficient number of low-fidelity (LF) data
have been proposed. In these established neural networks, a parallel structure
is commonly proposed to separately approximate the non-linear and linear
correlation between the HF- and LF data. In this paper, a new architecture of
multi-fidelity deep neural network (MF-DNN) was proposed where one subnetwork
was built to approximate both the non-linear and linear correlation
simultaneously. Rather than manually allocating the output weights for the
paralleled linear and nonlinear correction networks, the proposed MF-DNN can
autonomously learn arbitrary correlation. The prediction accuracy of the
proposed MF-DNN was firstly demonstrated by approximating the 1-, 32- and
100-dimensional benchmark functions with either the linear or non-linear
correlation. The surrogating modelling results revealed that MF-DNN exhibited
excellent approximation capabilities for the test functions. Subsequently, the
MF DNN was deployed to simulate the 1-, 32- and 100-dimensional aleatory
uncertainty propagation progress with the influence of either the uniform or
Gaussian distributions of input uncertainties. The uncertainty quantification
(UQ) results validated that the MF-DNN efficiently predicted the probability
density distributions of quantities of interest (QoI) as well as the
statistical moments without significant compromise of accuracy. MF-DNN was also
deployed to model the physical flow of turbine vane LS89. The distributions of
isentropic Mach number were well-predicted by MF-DNN based on the 2D Euler flow
field and few experimental measurement data points. The proposed MF-DNN should
be promising in solving UQ and robust optimization problems in practical
engineering applications with multi-fidelity data sources.
