We consider isogeometric function spaces that are generated from tensor-product spline spaces by composing the basis functions with the inverse of the domain parameterization. Depending on the geometry of the domain and on the data of the considered PDE, the exact solution might have a low order of Sobolev regularity, leading to a reduced convergence rate even for high degree discretization spaces. In this case it is necessary to reduce the local mesh size close to the singularities. Classical approaches perform adaptive h-refinement, which either leads to an unnecessarily large number of degrees of freedom or to a spline space that does not possess a tensor-product structure. In this talk we discuss a novel approach, presented in [Rios, Scholz, Takacs, CMAME, 2024], for finding a suitable isogeometric function space for a given PDE without sacrificing the tensor-product structure of the underlying spline space. The approach is based on the concept of r-adaptivity, that is, finding a reparameterization of the domain that yields a significantly smaller error than the original parameterization. This is based on the fact that different reparameterizations of the same computational domain lead to different isogeometric function spaces while preserving the geometry. Starting from a multi-patch domain consisting of bilinearly parameterized patches, we aim to find the biquadratic multi-patch parameterization that leads to the isogeometric function space with the smallest best approximation error of the solution. In order to estimate the location of the optimal control points, we employ a trained residual neural network that is applied to the graph surfaces of the approximated solution and its derivatives. The convergence analysis of r-adpativity is different from standard h-adaptivity. While for both approaches the local mesh size is adapted and smaller near the singularities, high variations in mesh size lead to strongly deformed, singular or almost-singular parameterizations, which can reduce the local approximation power. We discuss this issue in more detail and examine the results of our numerical experiments.