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Identifiability and numerical algebraic geometry.

Daniel J Bates1, Jonathan D Hauenstein2, Nicolette Meshkat3

  • 1Department of Mathematics, United States Naval Academy, Annapolis, MD, United States of America.

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Summary
This summary is machine-generated.

This study introduces numerical algebraic geometry and differential algebra to assess model identifiability in mathematical modeling. The methods determine if model parameters are uniquely identifiable from data and compute the identifiability degree or reparameterize unidentifiable models.

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Area of Science:

  • Mathematical Modeling
  • Computational Mathematics
  • Systems Biology

Background:

  • Model analysis often faces challenges in determining unknown parameters from input-output data.
  • Model identifiability is crucial for parameter estimation and reliable predictions.
  • Unidentifiable models require reparameterization to yield identifiable functions.

Purpose of the Study:

  • To develop and demonstrate novel numerical techniques for assessing model identifiability.
  • To compute the identifiability degree for identifiable models.
  • To derive algebraically independent identifiable functions for unidentifiable models.

Main Methods:

  • Application of numerical algebraic geometry to polynomial and rational ordinary differential equations.
  • Development of a novel numerical differential algebra technique.
  • Utilizing computational methods to analyze parameter identifiability.

Main Results:

  • A method to determine if a model is identifiable or unidentifiable using numerical algebraic geometry.
  • A novel approach for computing the identifiability degree of identifiable models.
  • A new numerical differential algebra technique for finding identifiable functions in unidentifiable models.

Conclusions:

  • Numerical algebraic geometry and differential algebra provide powerful tools for model identifiability analysis.
  • The presented techniques offer novel solutions for both identifiable and unidentifiable model scenarios.
  • Demonstrated effectiveness through various examples, advancing parameter estimation in complex systems.