Surrogate modelling and uncertainty quantification based on multi-fidelity deep neural network

TL;DR

This paper introduces a novel multi-fidelity deep neural network architecture that efficiently learns from both high- and low-fidelity data, demonstrating superior approximation and uncertainty quantification capabilities in complex engineering problems.

Contribution

A new MF-DNN architecture that autonomously learns correlations between fidelities, improving surrogate modeling and uncertainty quantification without manual weight tuning.

Findings

MF-DNN accurately approximates high-dimensional benchmark functions.

It effectively predicts probability distributions and statistical moments in UQ tasks.

Successfully models physical flow with limited experimental data.

Abstract

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.