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 an expensive high-fidelity model are available. The method employs proper orthogonal decomposition method to generate the high-fidelity reduced basis and a shallow multilayer perceptron to learn the high-fidelity reduced coefficients. In contrast to previously proposed methods, besides the model parameters, we also augmented the features extracted from the data generated by an efficient bi-fidelity surrogate developed in Narayan et al. (SIAM J Sci Comput 36(2):A495-A521, 2014) and Zhu et al. (SIAM/ASA J Uncertain Quantif 2(1):444-463, 2014) as the input feature of the proposed neural network. By incorporating relevant bi-fidelity features, we demonstrate that such an approach can improve the predictive capability and robustness of the neural network via several benchmark examples. Due to its nonintrusive nature, it is also applicable to general parameterized problems.