The complexity of reconstructing a function in high dimensions is too complex for modern computers with regular grids. This curse of dimensionality can be tackled with the sparse grid combination technique. By reducing the number of grid points, the complexity is reduced while still having accurate results.
In this thesis, regression with the spatially adaptive combination technique is implemented for different execution options. We introduce and analyze two approaches for regularization, which tackle the problem of overfitting. Additionally, we implemented three different versions for Opticom which update the coefficients of the component grids according to different criteria as additional optimizations. The various execution options which are implemented in the sparseSpACE framework are compared with each other regarding accuracy and complexity. Moreover, we compare the implementation to other common regression approaches. The results show that we can outperform neural networks and polynomial models in certain cases.