642 RWTH Publication No: 981225        2024       
TITLE A comparison study of supervised learning techniques for the approximation of high dimensional functions and feedback control
AUTHORS Mathias Oster, Luca Saluzzi, Tizian Wenzel
ABSTRACT 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.
KEYWORDS Optimal Control, High-Dimensionality, Neural Networks, Kernel Methods, Tensor Trains