Robust additive Gaussian process models using reference priors and cut-off-designs

When powerful numerical tools like the finite element method encounter their limits for the evaluation of physical systems it is very common to use surrogate models as an approximation. There are many possible choices concerning the model approach, among which Gaussian process models are the most popular ones due to their clear statistical basis. A very desirable attribute of such surrogates is a high flexibility for making them applicable to a great class of underlying problems while obtaining interpretable results. To achieve this Gaussian processes are used as basis functions of an additive model in this work. Another important property of a surrogate is stability, which can be especially challenging when it comes to the estimation of the correlation parameters. To solve this we use a Bayesian approach where a reference prior is assigned to each component of the additive model assuring robust correlation matrices. Due to the additive structure of the model a simplified parameter estimation process is proposed that reduces the usually high-dimensional optimization problem to a few sub-routines of low dimension. Finally, we demonstrate this concept by modeling the magnetic field of a magnetic linear position detection system.