A Homotopy Method for Parameter Estimation of Nonlinear Differential Equations with Multiple Optima

Research output: Contribution to journalArticle

Abstract

A numerical method for estimating multiple parameter values of nonlinear systems arising from biology is presented. The uncertain parameters are modeled as random variables. Then the solutions are expressed as convergent series of orthogonal polynomial expansions in terms of the input random parameters. Homotopy continuation method is employed to solve the resulting polynomial system, and more importantly, to compute the multiple optimal parameter values. Several numerical examples, from a single equation to problems with relatively complicated forms of governing equations, are used to demonstrate the robustness and effectiveness of this numerical method.

Original languageEnglish (US)
Pages (from-to)1314-1324
Number of pages11
JournalJournal of Scientific Computing
Volume74
Issue number3
DOIs
StatePublished - Mar 1 2018

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Homotopy Method
Parameter estimation
Nonlinear Differential Equations
Parameter Estimation
Numerical methods
Differential equations
Homotopy Continuation Method
Numerical Methods
Polynomials
Random Parameters
Uncertain Parameters
Polynomial Systems
Optimal Parameter
Random variables
Orthogonal Polynomials
Biology
Nonlinear systems
Governing equation
Nonlinear Systems
Random variable

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Engineering(all)
  • Computational Theory and Mathematics

Cite this

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abstract = "A numerical method for estimating multiple parameter values of nonlinear systems arising from biology is presented. The uncertain parameters are modeled as random variables. Then the solutions are expressed as convergent series of orthogonal polynomial expansions in terms of the input random parameters. Homotopy continuation method is employed to solve the resulting polynomial system, and more importantly, to compute the multiple optimal parameter values. Several numerical examples, from a single equation to problems with relatively complicated forms of governing equations, are used to demonstrate the robustness and effectiveness of this numerical method.",
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A Homotopy Method for Parameter Estimation of Nonlinear Differential Equations with Multiple Optima. / Hao, Wenrui.

In: Journal of Scientific Computing, Vol. 74, No. 3, 01.03.2018, p. 1314-1324.

Research output: Contribution to journalArticle

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