Multi-fidelity modeling using Gaussian Processes for the Helmholtz Equation

In engineering practice, accurate physical experiments as well as large-scale numerical simulations are often accompanied with high resource and time expenses. Therefore, the data generation process can only be performed for a limited number of sample size which leads to insufficient model results. The idea of multi-fidelity modeling is to holistically evaluate data from different sources with varying complexity and costs. For instance, high-fidelity models expose highly accurate results at high costs, whereas low-fidelity models are rather inaccurate but fast to evaluate. In general, physical experiments and large-scale numerical simulations belong to the group of high-fidelity models, while analytical solutions as well as numerical simulations at small scale can be considered as low-fidelity models. For an ideally positive correlation between the low-fidelity and the high-fidelity models, multi-fidelity models allow to obtain additional data at lower costs. The aim of this contribution is to present a multi-fidelity model applied on a sound propagation problem in interior acoustics. Regarding the high-fidelity model, a boundary element model with a finer mesh is considered, whereas a model with a coarser mesh is adopted as the low-fidelity model. The multi-fidelity model is realized as a vector-valued Gaussian process.