Multifidelity models integrate data from multiple sources to produce a single approximator for the underlying process. Dense low-fidelity samples are used to reduce interpolation error, while sparse high-fidelity samples are used to compensate for bias or noise in the low-fidelity samples. Deep Gaussian processes (GPs) are attractive for multifidelity modelling as they are non-parametric, robust to overfitting, perform well for small datasets, and, critically, can capture nonlinear and input-dependent relationships between data of different fidelities. Many datasets naturally contain gradient data, especially when they are generated by computational models that are compatible with automatic differentiation or have adjoint solutions. Principally, this work extends deep GPs to incorporate gradient data. We demonstrate this method on an analytical test problem and a realistic partial differential equation problem, where we predict the aerodynamic coefficients of a hypersonic flight vehicle over a range of flight conditions and geometries. In both examples, the gradient-enhanced deep GP outperforms a gradient-enhanced linear GP model and their non-gradient-enhanced counterparts.

翻译：多保真度模型整合来自多个来源的数据，为底层过程生成单一近似器。密集的低保真度样本用于减少插值误差，而稀疏的高保真度样本则用于补偿低保真度样本中的偏差或噪声。深度高斯过程（GPs）因具有非参数性、对过拟合鲁棒、在小数据集上表现良好，且关键能够捕捉不同保真度数据之间的非线性与输入依赖关系，在多保真度建模中颇具吸引力。许多数据集天然包含梯度数据，尤其是当它们由兼容自动微分或具有伴随解的数值计算模型生成时。本研究主要将深度高斯过程扩展至融合梯度数据。我们在一个解析测试问题与一个实际偏微分方程问题（预测高超声速飞行器在多种飞行条件与几何构型下的气动系数）上验证了该方法。在两个示例中，梯度增强深度高斯过程均优于梯度增强线性GP模型及其非梯度增强对应模型。