Bifidelity data-assisted neural networks in nonintrusive reduced-order modeling

TL;DR

This paper introduces a nonintrusive reduced-order modeling approach that combines low- and high-fidelity data using POD and neural networks, improving prediction accuracy and decoupling simulations.

Contribution

It proposes a novel bifidelity method integrating low-fidelity features into neural networks for enhanced nonintrusive reduced-order modeling.

Findings

Improved predictive accuracy over traditional methods

Decouples high-fidelity simulation from online computations

Effective across various parameterized problems

Abstract

In this paper, we present a new nonintrusive reduced basis method when a cheap low-fidelity model and expensive high-fidelity model are available. The method relies on proper orthogonal decomposition (POD) to generate the high-fidelity reduced basis and a shallow multilayer perceptron to learn the high-fidelity reduced coefficients. In contrast to other methods, one distinct feature of the proposed method is to incorporate the features extracted from the low-fidelity data as the input feature, this approach not only improves the predictive capability of the neural network but also enables the decoupling the high-fidelity simulation from the online stage. Due to its nonintrusive nature, it is applicable to general parameterized problems. We also provide several numerical examples to illustrate the effectiveness and performance of the proposed method.