CAPA: Method for estimating hidden structures determined by unidentifiable mathematical models and time series data based on the Groebner basis on differential algebra

  • Date: –15:00
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
  • Lecturer: Mizuka Komatsu, Kobe University
  • Organiser: Matematiska institutionen
  • Contact person: Florent Bréhard
  • Seminarium

Abstract: In this study, we propose a method to extract the hidden structures that are uniquely determined by observed time series data and unidentifiable state-space models explicitly and exhaustively.

Unidentifiable models are models whose parameters cannot be uniquely determined from given data. It is hard to examine systems described by unidentifiable models because, basically, model parameters are assigned to specific meanings in relation to the modeled system under consideration, and hence the system is examined via estimated parameters. To overcome such difficulty, methods to transform unidentifiable models to identifiable ones are proposed, yet it is not plausible to rearrange models due to, e.g., constraints on experiments.

In this talk, focusing on the fact that the structures determined by observed data and unidentifiable models are uniquely determined as sets, we introduce the concept of the parameter varieties, which are newly defined and proven to actually form the algebraic varieties. A method to derive the explicit representation of the varieties is also provided. In this method, the input-output equations of the models are derived using the Groebner basis on differential algebra at first, and then, the sets of parameters where each of them generates the given data are described as sets of constraints in terms of parameters.

An application of the proposed method to analysis of an unidentifiable model that describes virus dynamics is also shown, in which a new insight on the dynamics that is overlooked by a conventional approach is discovered.