Gradient and Uncertainty Enhanced Sequential Sampling for Global Fit

Most of these applications require computationally demanding simulation models. Machine learning (ML) models have emerged to mitigate the computational cost and are used as surrogates. For this task, ML models learn the relationship between the response of the expensive simulations from a dataset containing past observations. Various ML methods were proposed as surrogate models (sometimes referred as response surface methods), e.g. as solvers for partial differential equations (PDEs) describing the behavior of high-dimensional vector spaces or fields [1-3], or probabilistic approximators of parametric response functions [4]. Among these types of surrogate models, Gaussian Process Regression (GP) [5] is a popular choice [6, 7] because of its flexibility and ability to predict the model uncertainty. However, drawbacks are the selection of a suitable covariance (kernel) function that is application dependent, and the computational burden for larger data sets. Various extensions to GPs such as the deep GPs[8], sparse GPs based on variational inference [9, 10], and efficient matrix decomposition [11] were developed to overcome some of these limitations. One particularly promising approach is the combination of GPs with Artificial Neural Networks (ANNs) to Deep Gaussian Covariance Networks (DGCNs) [12, 13] to learn the non-stationary hyperparameters of the GP together with combinations of different covariance functions.