| Autor: |
Romor, Francesco, Tezzele, Marco, Mrosek, Markus, Othmer, Carsten, Rozza, Gianluigi |
| Rok vydání: |
2021 |
| Předmět: |
|
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1002/nme.7349 |
| Popis: |
Multi-fidelity models are of great importance due to their capability of fusing information coming from different numerical simulations, surrogates, and sensors. We focus on the approximation of high-dimensional scalar functions with low intrinsic dimensionality. By introducing a low dimensional bias we can fight the curse of dimensionality affecting these quantities of interest, especially for many-query applications. We seek a gradient-based reduction of the parameter space through linear active subspaces or a nonlinear transformation of the input space. Then we build a low-fidelity response surface based on such reduction, thus enabling nonlinear autoregressive multi-fidelity Gaussian process regression without the need of running new simulations with simplified physical models. This has a great potential in the data scarcity regime affecting many engineering applications. In this work we present a new multi-fidelity approach that involves active subspaces and the nonlinear level-set learning method, starting from the preliminary analysis previously conducted in Romor et al. 2020. The proposed framework is tested on two high-dimensional benchmark functions, and on a more complex car aerodynamics problem. We show how a low intrinsic dimensionality bias can increase the accuracy of Gaussian process response surfaces. |
| Databáze: |
arXiv |
| Externí odkaz: |
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