9th Kálmán Lecture with Ruth Baker (UOxford) | SFB 1294 "Data Assimilation"

Ruth Baker from Oxford University will be the speaker of our 9th Kálmán Lecture. After her talk there will be opportunity to discuss new DA developments over some hot and cold beverages as well cake.

Ruth Baker (University of Oxford):

What is parameter identifiability, why do we need identifiable models, and what can identifiable models tell us about regulation of the cell cycle?

Mathematical modelling is increasingly integral to the interpretation of experimental data across applied mathematics, particularly in the life sciences where complex dynamical systems are prevalent. Accurate parameter estimation is central to this endeavour: model parameters are used not only to fit observed data but also to infer latent biological processes and generate predictive simulations. A fundamental issue is parameter identifiability—the extent to which model parameters can be uniquely or reliably estimated given the available data. This becomes especially challenging in the context of nonlinear, high-dimensional models that are common in systems biology, where many existing identifiability tools are either underutilised or not well adapted. At the same time, there is growing interest in data-driven modelling approaches, such as universal differential equations (UDEs), which combine mechanistic structure with flexible, learned components. While these approaches offer increased expressive power, they introduce new challenges for identifiability, as the distinction between mechanistic parameters and learned dynamics becomes blurred.

In this talk, I will outline recent progress in developing methods to assess parameter identifiability in both classical mechanistic models and hybrid data-driven frameworks. I will illustrate these approaches using models of cell cycle regulation, including UDE-based formulations calibrated to experimental data, and demonstrate how identifiability analysis can reveal which regulatory mechanisms are supported by the data and how they influence collective cell migration.