Online multi-fidelity data aggregation via hierarchical neural network

In many industrial applications requiring computational modeling, the acquisition of highfidelity data is often constrained by cost and technical limitations, while low-fidelity data, though cheaper and easier to obtain, lacks the same level of accuracy. Multi-fidelity data aggregation addresses this challenge by combining both types of data to construct surrogate models, balancing modeling accuracy with data cost. Optimizing the placement and distribution of high-fidelity samples is also essential to improving model performance. In this work, we propose online multi-fidelity data aggregation via hierarchical neural network (OMA-HNN). This method comprises two key components: multi-fidelity data aggregation via hierarchical neural network (MA-HNN) and an online progressive sampling framework. MA-HNN integrates data of varying fidelities within a hierarchical network structure, employing nonlinear components to capture the differences across multi-fidelity levels. The online progressive sampling framework manages high-fidelity data acquisition through two stages: initial sampling and incremental sampling. For these stages, we develop the low-fidelity-surrogate assisted sampling (LAS) strategy for the initial phase and the model divergence-based active learning (MDAL) strategy for incremental sampling. OMA-HNN was rigorously tested on 15 numerical examples across diverse multi-fidelity scenarios and further validated through three real-world applications. The results demonstrate its effectiveness and practicality, underscoring OMA-HNN's potential to enhance the reliability and efficiency of multi-fidelity data aggregation in industrial contexts.