A multi-fidelity neural network surrogate sampling method for uncertainty quantification

TL;DR

This paper introduces a multi-fidelity neural network approach that efficiently combines low- and high-fidelity data to improve uncertainty quantification in complex systems, significantly reducing computational costs.

Contribution

The paper presents a novel multi-fidelity neural network surrogate method that accelerates high-fidelity uncertainty quantification using low-fidelity data within a Monte Carlo framework.

Findings

Significant computational savings achieved.

High accuracy in surrogate predictions demonstrated.

Effective in complex physical/biological systems.

Abstract

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.