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.

翻译：多保真模型因能够融合来自不同数值模拟、代理模型及传感器的信息而具有重要价值。本文聚焦于具有低本征维数的高维标量函数逼近问题。通过引入低维偏差，我们可有效缓解影响这些关注量的维数灾难问题，尤其在多查询应用中。我们通过线性活性子空间或输入空间的非线性变换来实现基于梯度的参数空间约简，并在此基础上构建低保真响应曲面，从而无需运行简化物理模型的新模拟即可实现非线性自回归多保真高斯过程回归。该方法在数据稀疏场景中具有巨大潜力，而这类场景广泛存在于工程应用中。本文基于Romor等人2020年的前期分析，提出一种融合活性子空间与非线性水平集学习方法的全新多保真框架。该框架在两个高维基准函数及一个更复杂的汽车空气动力学问题上进行了测试，结果表明低本征维数偏差能有效提升高斯过程响应曲面的精度。