# Optimization and profile calculation of ODE models using second order adjoint sensitivity analysis

### Citation

Paul Stapor, Fabian Fröhlich, and Jan Hasenauer, Optimization and profile calculation of ODE models using second order adjoint sensitivity analysis, 2018, Bioinformatics, Volume 34, Issue 13, Pages i151–i159

### Summary

This paper introduces the second-order adjoint sensitivity analysis for parameter estimation in ordinary differential equation (ODE) models.

- The Hessian computational complexity scales linearly with the number of state variables and quadratically with the number of parameters -> good for low-dimensional problems.
- The second-order adjoint sensitivity analysis for the computation of Hessians

and a hybrid optimization-integration-based approach for profile likelihood computation introduced in this paper.

- The second-order adjoint sensitivity analysis scales linearly with the number of parameters and state variables -> good for large scale ODE models.
- it is shown that the hybrid computation method was more than 2-fold faster than the best competitor.