In a longitudinal clinical registry, different measurement instruments might have been used for assessing individuals at different time points. To combine them, we investigate deep learning techniques for obtaining a joint latent representation, to which the items of different measurement instruments are mapped. This corresponds to domain adaptation, an established concept in computer science for image data. Using the proposed approach as an example, we evaluate the potential of domain adaptation in a longitudinal cohort setting with a rather small number of time points, motivated by an application with different motor function measurement instruments in a registry of spinal muscular atrophy (SMA) patients. There, we model trajectories in the latent representation by ordinary differential equations (ODEs), where person-specific ODE parameters are inferred from baseline characteristics. The goodness of fit and complexity of the ODE solutions then allows to judge the measurement instrument mappings. We subsequently explore how alignment can be improved by incorporating corresponding penalty terms into model fitting. To systematically investigate the effect of differences between measurement instruments, we consider several scenarios based on modified SMA data, including scenarios where a mapping should be feasible in principle and scenarios where no perfect mapping is available. While misalignment increases in more complex scenarios, some structure is still recovered, even if the availability of measurement instruments depends on patient state. A reasonable mapping is feasible also in the more complex real SMA dataset. These results indicate that domain adaptation might be more generally useful in statistical modeling for longitudinal registry data.