This thesis focuses on the development of inverse methods for nuclear magnetic res- onance (NMR) correlation or exchange experiments and new fast field cycling (FFC) modelling approaches. Moreover, the theoretical framework to consider fast field cycling as an inverse problem is provided and the possibility to employ established regularization methods for the inversion of NMR dispersion profiles is investigated.

It is shown that the relaxation behaviour of systems with sufficiently understood molecular dynamics such as ionic liquids can be accurately described by simplifying relaxation models. This is further supported by findings from molecular dynamics simulations and physicochemical measurements.

Further, the concept of generalized cross validation was applied to modified to- tal generalized variation (MTGV) regularization and it was shown that deep learning can be employed for inversion of NMR signals from exchange or correlation ex- periments. In addition, the inversion performance of deep learning, Tikhonov and MTGV regularization was compared on a vast data set of simulated NMR signals providing strong evidence of deep learning achieving the best reconstruction results in a clear majority of instances.

Finally, fast field cycling was treated as an inverse problem and MTGV regularization was employed to reconstruct correlation time distributions from NMR dispersion profiles. From this, detailed insights into the molecular dynamics of several cata- lyst samples were obtained previously not accessible with established modelling approaches.