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An integration-based method for estimating parameters in a system of differential equations

Journal Article


Abstract


  • The application of ordinary differential equations to modelling the physical world is extensive

    and widely studied in many fields including physics, engineering and bioinformatics.

    Using these models to predict the behaviour of important state variables given particular

    parameter values has been extensively studied. On the other hand the inverse problem

    of predicting parameter values that will fit a solution of a differential equation to observed

    data has traditionally only been considered by using a few methods, many of which

    approach the problem via a least squares fit method. These methods either can only be

    applied when the differential equation being studied has a closed form solution or can

    become very computationally intensive when applying it to a system that can only be

    solved numerically and hence require optimisation algorithms. We propose an integration-

    based method that transforms an ordinary differential equation to an algebraic system

    of equations for which we solve for the unknown parameters in our equation. The method

    is computationally unintensive, can be extended to systems of differential equations and

    the number of parameters that can be estimated is not restricted. We demonstrate the

    method by simulating data, with and without noise, from a number of biological models

    described by ordinary differential equations and then estimate the parameters via the proposed technique.

Publication Date


  • 2013

Citation


  • Holder, A. B. & Rodrigo, M. R. (2013). An integration-based method for estimating parameters in a system of differential equations. Applied Mathematics and Computation, 219 (18), 9700-9708.

Scopus Eid


  • 2-s2.0-84893670997

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/1099

Number Of Pages


  • 8

Start Page


  • 9700

End Page


  • 9708

Volume


  • 219

Issue


  • 18

Place Of Publication


  • http://www.sciencedirect.com/science/article/pii/S0096300313003056

Abstract


  • The application of ordinary differential equations to modelling the physical world is extensive

    and widely studied in many fields including physics, engineering and bioinformatics.

    Using these models to predict the behaviour of important state variables given particular

    parameter values has been extensively studied. On the other hand the inverse problem

    of predicting parameter values that will fit a solution of a differential equation to observed

    data has traditionally only been considered by using a few methods, many of which

    approach the problem via a least squares fit method. These methods either can only be

    applied when the differential equation being studied has a closed form solution or can

    become very computationally intensive when applying it to a system that can only be

    solved numerically and hence require optimisation algorithms. We propose an integration-

    based method that transforms an ordinary differential equation to an algebraic system

    of equations for which we solve for the unknown parameters in our equation. The method

    is computationally unintensive, can be extended to systems of differential equations and

    the number of parameters that can be estimated is not restricted. We demonstrate the

    method by simulating data, with and without noise, from a number of biological models

    described by ordinary differential equations and then estimate the parameters via the proposed technique.

Publication Date


  • 2013

Citation


  • Holder, A. B. & Rodrigo, M. R. (2013). An integration-based method for estimating parameters in a system of differential equations. Applied Mathematics and Computation, 219 (18), 9700-9708.

Scopus Eid


  • 2-s2.0-84893670997

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/1099

Number Of Pages


  • 8

Start Page


  • 9700

End Page


  • 9708

Volume


  • 219

Issue


  • 18

Place Of Publication


  • http://www.sciencedirect.com/science/article/pii/S0096300313003056