A nonlinearity integrated bi-fidelity surrogate model based on nonlinear mapping

Abstract

The variable-fidelity surrogate (VFS) modeling technique is a data fusion method used to enhance the prediction accuracy of less intensively sampled primary quantities of interest (i.e., high-fidelity samples) by incorporating a large number of auxiliary samples (i.e., low-fidelity samples). However, the VFS model constructed based on the work of Kennedy and O'Hagan overemphasizes the linear correlations between high-fidelity and low-fidelity models, thereby limiting the generalizability and application scenarios of VFS models. To address this issue, this study proposes a nonlinear integrated bi-fidelity (NI-BFS) model, which maps predictions of the low-fidelity model to the high-fidelity level in a nonlinear manner. This approach strengthens the model's ability to learn the nonlinear correlation relationship between high-fidelity and low-fidelity models and alleviates the difficulty of fitting the discrepancy function. The performance of the NI-BFS model has been validated through a series of comparative experiments, where four advanced VFS models were used as benchmark models. Additionally, the NI-BFS model's robustness and practical applicability have been investigated. The results demonstrate that the NI-BFS model outperforms the other benchmark models in all cases.