Gradient-enhanced deep Gaussian processes for multifidelity modelling
This work addresses multifidelity modeling for applications like computational fluid dynamics, where gradient data is available, but it is incremental as it builds on existing deep GP methods.
The paper tackled the problem of multifidelity modeling by extending deep Gaussian processes to incorporate gradient data, resulting in improved performance over gradient-enhanced linear GP models and non-gradient-enhanced counterparts in analytical and realistic aerodynamic test cases.
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.