Algebraic model prediction for ODE systems

The use of mathematical models in the sciences almost always involves the estimation of unknown parameter values from data. "Sloppiness" has been proposed to study the uncertainty in parameter estimation. Dufresne, Harrington and Raman introduced a unified mathematical framework for sloppiness, rooted in algebra and geometry. Central to this work is the concept of model prediction map [phi], which corresponds to a specific choice of perfect data and a function mapping parameters to the corresponding data prediction. Constructing a model prediction map requires (nearly) solving a moduli problem. Indeed, a model prediction map is a separating morphism for the quotient of parameter space by the equivalence relation induced by perfect data. A solution of the moduli problem would give a geometric structure to the set-theoretic quotient, the construction of a separating morphism can be an intermediate step. For ODE systems with time series data, there are already several constructions of separating morphisms; for steady-state data it is an open problem. A main challenge is that the choice of perfect data that fits more closely to the experimental reality is not naturally algebraic. The objective of this project is to construct an algebraic model prediction map for a class of ODE systems with steady state data.