TSpace

Abstract (summary): We consider the formulation and solution of the inverse problem that arises when fit- ting systems of ordinary differential equations (ODEs) to observed data. This parameter estimation task can be computationally intensive if the ODEs are complex and require the use of numerical methods to approximate their solution. The thesis focuses on ad- dressing a common criticism of the single shooting approach, which is that it can have trouble converging to the globally optimal parameters if a sufficiently good initial guess for the parameters is unavailable. We demonstrate that it is often the case that a good initial guess can be obtained by solving a related inverse problem. We show that gradient based shooting approaches can be effective by investigating how they perform on some challenging test problems from the literature. We also discuss how the approach can be applied to systems of delay differential equations (DDEs). We make use of parallelism and the structure of the underlying ODE models to further improve the computational efficiency. Some existing methods for the efficient computation of the model sensitivities required by a Levenberg-Marquardt least squares optimizer are compared and implemented in a parallel computing environment. The effectiveness of using the adjoint approach for the efficient computation of the gradient required by a BFGS optimizer is also investigated for both systems of ODEs and systems of DDEs. The case of unobserved components of the state vector is then considered and we demonstrate how the structure of the model and the observed data can sometimes be exploited to cope with this situation.