5 research outputs found
Surrogate modelling and uncertainty quantification based on multi-fidelity deep neural network
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
Multi-fidelity modeling with different input domain definitions using Deep Gaussian Processes
Multi-fidelity approaches combine different models built on a scarce but
accurate data-set (high-fidelity data-set), and a large but approximate one
(low-fidelity data-set) in order to improve the prediction accuracy. Gaussian
Processes (GPs) are one of the popular approaches to exhibit the correlations
between these different fidelity levels. Deep Gaussian Processes (DGPs) that
are functional compositions of GPs have also been adapted to multi-fidelity
using the Multi-Fidelity Deep Gaussian process model (MF-DGP). This model
increases the expressive power compared to GPs by considering non-linear
correlations between fidelities within a Bayesian framework. However, these
multi-fidelity methods consider only the case where the inputs of the different
fidelity models are defined over the same domain of definition (e.g., same
variables, same dimensions). However, due to simplification in the modeling of
the low-fidelity, some variables may be omitted or a different parametrization
may be used compared to the high-fidelity model. In this paper, Deep Gaussian
Processes for multi-fidelity (MF-DGP) are extended to the case where a
different parametrization is used for each fidelity. The performance of the
proposed multifidelity modeling technique is assessed on analytical test cases
and on structural and aerodynamic real physical problems