THURSDAY | APRIL 24, 2017 11:30 AM AT COE
Parameter estimation problems in ordinary and partial differential equations constitute a large class of models described by so-called ill-posed (unstable, irregular) operator equations. Here one is trying to identify the coefficients of a differential equation, called system parameters, from observations of the solution to that equation. An extra level of difficulty is added by the fact that even when the differential equation is linear with respect to the solution and its derivatives, the corresponding inverse (parameter estimation) problem is generally nonlinear. If this nonlinear problem is solved with some Newton-type iterative algorithm, an ill-posed linear operator equation needs to be solved at every step of the iterative process. Due to instability, the error accumulates and completely destroys the iterative solution. Thus, for parameter estimation problems, the regularization component of a numerical algorithm becomes highly important.
A considerable number of ill-posed problems comes from epidemiology and infectious disease modeling, since stable estimation of system parameters at the onset of a novel infectious disease is important in assisting public health authorities to rapidly assess the situation in order determine whether the pathogen in question is capable of generating sustained local or global outbreaks. In particular, it is key to characterize the contribution of potential animal reservoirs, (e.g., poultry) as well as human-to-human transmission, to the overall pattern of disease spread. In my talk I will use simple models of infectious diseases to illustrate the reasons for instability and the effect of regularization on computational algorithms for ill-posed problems.
The Mathematics and Statistics Club of Georgia State University was formed in 2005 to provide a community for students interested in math and stats at GSU.
We hold events approximately once a month, and all are welcome to attend.
|Math & Stat Club Officers|
|VP of Recruitment||Akelia White|
|VP of Event Planning||Isabella Nang|
|Dr. Mark Grinshpon|