Parameter Estimation for Ordinary Differential Equations

Speaker: Jonathan Calver (UofT)

We consider the problem of parameter estimation for Ordinary Differential Equations (ODEs). This inverse problem takes the form of a non-linear least squares minimization. To efficiently perform this minimization, a Levenberg-Marquardt optimizer is used. We review several approaches for computing the sensitivity information that is required by the algorithm. These include divided differences, simulation of the variational equations, and a Green’s function method. Numerical experiments are performed to compare the performance of these approaches and demonstrate how each approach can exploit parallelism. We will also briefly discuss how initial guesses on the parameters can be obtained.