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Longitudinal biomedical data are often characterized by a sparse time gridand individual-specific development patterns. Specifically, in epidemiologicalcohort studies and clinical registries we are facing the question of what canbe learned from the data in an early phase of the study, when only a baselinecharacterization and one follow-up measurement are available. Inspired byrecent advances that allow to combine deep learning with dynamic modeling, weinvestigate whether such approaches can be useful for uncovering complexstructure, in particular for an extreme small data setting with only twoobservations time points for each individual. Irregular spacing in time couldthen be used to gain more information on individual dynamics by leveragingsimilarity of individuals. We provide a brief overview of how variationalautoencoders (VAEs), as a deep learning approach, can be linked to ordinarydifferential equations (ODEs) for dynamic modeling, and then specificallyinvestigate the feasibility of such an approach that infers individual-specificlatent trajectories by including regularity assumptions and individuals'similarity. We also provide a description of this deep learning approach as afiltering task to give a statistical perspective. Using simulated data, we showto what extent the approach can recover individual trajectories from ODEsystems with two and four unknown parameters and infer groups of individualswith similar trajectories, and where it breaks down. The results show that suchdynamic deep learning approaches can be useful even in extreme small datasettings, but need to be carefully adapted.

Deep dynamic modeling with just two time points: Can we still allow for individual trajectories?