Date of Degree
Computer Sciences | Numerical Analysis and Scientific Computing
Symbolic Computing, Dynamical Systems, Mathematical Software
The task of mathematical modeling involves working with real world phenomena described via parametric ordinary differential equations (ODE). Typically, an ODE model consists of states, parameters, inputs, and outputs. The states represent quantities whose dynamics the model describes, the parameters are quantities that are specific to the phenomenon being studied. Finally, inputs and outputs represent functions that are being added and measured from experiments, respectively. One of the questions that arises in studies of such models, is whether for given input-output setup one can efficiently and correctly estimate the values of parameters or initial conditions. This property of parameters or initial conditions is called structural identifiability. If a parameter can be known uniquely then it is said to be structurally globally identifiable. If there are finitely many values for a parameter then such parameter is locally identifiable. Otherwise, the parameter is unidentifiable. The challenge of determining identifiability of parameters can be computationally heavy. The majority of available tools rely on nontrivial methods of differential algebra. In this work, we study a particular method for globally identifiability analysis based on Gröbner basis of polynomial ideals that arise in identifiability studies. Our aim is to improve the computation of the basis and thus significantly accelerate global identifiability analysis for more advanced differential models. In this work, we will discuss increasing algorithmic efficacy of Gröbner basis computation via weighted orderings and by substituting a carefully selected subset of unidentifiable parameters with random numbers for workload reduction. Finally, we will present a new symbolic-numeric approach to parameter estimation that does not rely on optimization methods and takes advantage of our modification to global identifiability assessment to account for possibility of multiple values of parameters in the model.
Ilmer, Ilia, "Accelerating Parameter Identifiability of Differential Models with Applications to Parameter Estimation" (2023). CUNY Academic Works.
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