Similarity of individual latent dynamics in longitudinal cohort data

Project summary

We consider longitudinal data from clinical cohorts with few individuals. For these, a latent representation is obtained via neural networks and modeled by differential equations. To enable individual dynamic models based on only a small number of observations, individuals similar to each other are determined according to the latent dynamics. Furthermore, also selection of necessary model components is performed locally. For better reflecting unobserved influences, we will consider stochastic differential equations. Development of the corresponding filtering theory will incorporate random and state-dependent observation time points. We will derive error bounds for the estimator of the latent state, which will also serve as a basis for locally performing model selection.

Our methods

  • Combining knowledge- and data-driven modeling
  • Differential equations
  • Neural networks
  • Local perspective

Principal investigator 1

Doctoral researcher position 1

(supervised by PI Binder)


Approaches for combining neural networks with differential equations (ODEs as well as SDEs). This will include approaches for model selection, to obtain patient-specific models.


  • Master’s degree or equivalent in mathematics, (bio-)statistics, computer science or similar
  • Advanced programming skills in, e.g., Julia, Python, or R
  • Ideally, experience in training deep learning models and/or experience in dynamic modeling and (stochastic) differential equations
  • Interest in modeling clinical data

Principal investigator 2

Doctoral researcher position 2

(supervised by PI Schmidt)


Mathematical theory for guiding methods development, in a filtering framework, which will, e.g., provide error bounds and goodness-of-fit approaches for model selection.


  • Master’s degree or equivalent in mathematics
  • Ideally, expertise in stochastic analysis and stochastic differential equations
  • Programming skills in, e.g., Julia, Python, or R

Administrative Manager

Marc Schumacher

Institute of Medical Biometry and Statistics,
Faculty of Medicine and Medical Center –
University of Freiburg