A survey on multi-fidelity surrogates for simulators with functional outputs: unified framework and benchmark
<|reference_start|>A survey on multi-fidelity surrogates for simulators with functional outputs: unified framework and benchmark: Multi-fidelity surrogate models combining dimensionality reduction and an intermediate surrogate in the reduced space allow a cost-effective emulation of simulators with functional outputs. The surrogate is an input-output mapping learned from a limited number of simulator evaluations. This computational efficiency makes surrogates commonly used for many-query tasks. Diverse methods for building them have been proposed in the literature, but they have only been partially compared.   This paper introduces a unified framework encompassing the different surrogate families, followed by a methodological comparison and the exposition of practical considerations. More than a dozen of existing multi-fidelity surrogates have been implemented under the unified framework and evaluated on a set of benchmark problems. Based on the results, guidelines and recommendations are proposed regarding multi-fidelity surrogates with functional outputs.   Our study shows that most multi-fidelity surrogates outperform their tested single-fidelity counterparts under the considered settings. But no particular surrogate is performing better on every test case. Therefore, the selection of a surrogate should consider the specific properties of the emulated functions, in particular the correlation between the low- and high-fidelity simulators, the size of the training set, the local nonlinear variations in the residual fields, and the size of the training datasets.<|reference_end|>
@article{brunel2024a,
    title={A survey on multi-fidelity surrogates for simulators with functional
  outputs: unified framework and benchmark},
    author={Lucas Brunel, Mathieu Balesdent, Lo"ic Brevault, Rodolphe Le Riche
  and Bruno Sudret},
    journal={arXiv preprint arXiv:2408.17075},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.17075},
    primaryClass={cs.CE}
}