The Geometry of Multiscale Models: Identifiability, Reparameterization, Comparisons, and Parameter Space Exploration

Abstract

This young investigator project aims to incorporate numerical techniques arising from the geometric study of nonlinear polynomial systems into the development, analysis, and simulations associated with multiscale models. This project will proceed in 5 major phases: (1) Use the geometry associated with nonlinear maps to determine the identifiability of a model via numerical linear algebra; (2) Develop a numeric-symbolic algorithm for computing identifiable reparameterizations of models; (3) Use numerical techniques for simplifying models, e.g., through the elimination of state variables, and comparing models of the same phenomenon; (4) Develop a numerical approach for exploring the parameter space of a model, e.g., locating regions having multistability; and (5) Create an open-source implementation of these newly developed algorithms.

Document Details

Document Type
DoD Grant Award
Publication Date
Jan 12, 2017
Source ID
W911NF1510219

Entities

People

  • Jonathan D Hauenstein

Organizations

  • Army Contracting Command
  • United States Army
  • University of Notre Dame

Tags

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Applied Combinatorial Optimization and Logic Circuit Design.
  • Computational Fluid Dynamics (CFD)

Technology Areas

  • Space