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

TL;DR

This paper introduces a modified multiple shooting algorithm that employs adjoint sensitivity analysis to improve the efficiency and stability of parameter estimation in ODE models, demonstrated on a predator-prey system.

Contribution

The paper presents a novel modification of the multiple shooting method by integrating adjoint sensitivity analysis for more efficient gradient computation.

Findings

Enhanced computational efficiency in parameter estimation.

Improved stability of the estimation process.

Successful application to a predator-prey model.

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.