Geometric approaches to parameter estimation for differential equations.

Parameter estimation for differential equations is a fundamental problem, but work in this area is incomplete. One difficulty is the presence of local minima which trap optimization algorithms, resulting in poor fits. Incorporating geometric features of the differential equations into the optimization algorithms can alleviate this problem. These structural features are combined with numerical improvements via automatic differentiation, and applied to neural models and data related to breathing.

This work has resulted in my becoming interested in statistical inference. If time permits, I will mention some HIV data I have been working with on viral strains which have escaped immune system recognition.