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

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Aydogmus O., TOR A. H.

APPLIED MATHEMATICS AND COMPUTATION, vol.390, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 390
  • Publication Date: 2021
  • Doi Number: 10.1016/j.amc.2020.125644
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, INSPEC, Public Affairs Index, zbMATH, Civil Engineering Abstracts
  • Keywords: Parameter estimation, Multiple shooting algorithm, Adjoint method, DIFFERENTIAL-ALGEBRAIC EQUATIONS
  • Abdullah Gül University Affiliated: Yes


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. (C) 2020 Elsevier Inc. All rights reserved.