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

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 nonin-trusive nature, it is applicable to general parameterized problems. We also provide several numerical examples to illustrate the effectiveness and performance of the proposed method.