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A Modified Multiple Shooting Algorithm for Parameter Estimation in ODEs Using Adjoint Sensitivity Analysis

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  • Aydogmus, Ozgur
  • TOR, Ali Hakan

Abstract

To increase the predictive power of a model, one needs to estimate its unknown parameters. Almost all parameter estimation techniques in ordinary differential equation models suffer from either a small convergence region or enormous computational cost. The method of multiple shooting, on the other hand, takes its place in between these two extremes. The computational cost of the algorithm is mostly due to the calculation of directional derivatives of objective and constraint functions. Here we modify the multiple shooting algorithm to use the adjoint method in calculating these derivatives. In the literature, this method is known to be a more stable and computationally efficient way of computing gradients of scalar functions. A predator-prey system is used to show the performance of the method and supply all necessary information for a successful and efficient implementation.

Suggested Citation

  • Aydogmus, Ozgur & TOR, Ali Hakan, 2021. "A Modified Multiple Shooting Algorithm for Parameter Estimation in ODEs Using Adjoint Sensitivity Analysis," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    • Handle: RePEc:eee:apmaco:v:390:y:2021:i:c:s0096300320305981
    DOI: 10.1016/j.amc.2020.125644
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    References listed on IDEAS

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    1. Xiaolei Xun & Jiguo Cao & Bani Mallick & Arnab Maity & Raymond J. Carroll, 2013. "Parameter Estimation of Partial Differential Equation Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 1009-1020, September.
    2. Eligius M. T. Hendrix & Boglárka G.-Tóth, 2010. "Nonlinear Programming algorithms," Springer Optimization and Its Applications, in: Introduction to Nonlinear and Global Optimization, chapter 5, pages 91-136, Springer.
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