An augmented autoregressive nonlinear mapping multi-fidelity surrogate model construction method

Multi-fidelity (MF) surrogate models are increasingly utilized in engineering design due to their abilities to balance computational costs and data accuracy across different fidelity levels. At this stage, there are many multi-fidelity methods that approximate high-fidelity (HF) models by incrementally modelling multiple low-fidelity (LF) models in a layer-by-layer hierarchical manner or fusing non-hierarchical LF datasets. However, modelling accuracy of multi-fidelity models still has room for further improvement. Therefore, we introduce an augmented autoregressive nonlinear mapping multi-fidelity (AANMMF) surrogate model for adaptive multi-fidelity data fusion. First, LF surrogate models are constructed based on the available LF dataset. Second, the predicted LF data and HF data are incorporated into a trend function, and the corresponding regression terms are designed to characterize the high-fidelity function. Finally, the MF model is refined by tuning its hyperparameters. To assess the performance of AANMMF, it is compared against the commonly used bi-fidelity surrogate model and one standard MF surrogate model. Four numerical test functions and one engineering case study demonstrate that AANMMF achieves accurate and robust predictions with minimal computational cost, highlighting its potential for practical applications.