  Approximation of high dimensional functions is in the focus of machine
learning and data-based scientific computing. In many applications, empirical
risk minimisation techniques over nonlinear model classes are employed. Neural
networks, kernel methods and tensor decomposition techniques are among the most
popular model classes. We provide a numerical study comparing the performance
of these methods on various high-dimensional functions with focus on optimal
control problems, where the collection of the dataset is based on the
application of the State-Dependent Riccati Equation.
