Date: 2015-10-09

Time: 15:30-16:30

Location: BURN 1205

Abstract:

Spatio-temporal data are abundant in many scientific fields; examples include daily satellite images of the earth, hourly temperature readings from multiple weather stations, and the spread of an infectious disease over a particular region. In many instances the spatio-temporal data are accompanied by mathematical models expressed in terms of partial differential equations (PDEs). These PDEs determine the theoretical aspects of the behavior of the physical, chemical or biological phenomena considered. Azzimonti (2013) showed that including the associated PDE as a regularization term as opposed to the conventional two-dimensional Laplacian provides a considerable improvement in the estimation accuracy. The PDEs parameters often have interesting interpretations. Although they are typically unknown and must be inferred from expert knowledge of the phenomena considered. In this talk I will discuss extending the profiling with a parameter cascading procedure outlined in Ramsay et al. (2007) to incorporate PDE parameter estimation. I will also show how, following Sangalli et al. (2013), the estimation procedure can be extended to include finite-element methods (FEMs). This allows the proposed method to account for attributes of the geometry of the physical problem such as irregular shaped domains, external and internal boundary features, as well as strong concavities. Thus this talk will introduce a methodology for data-driven estimates of the parameters of PDEs defined over irregular domains.

Speaker

Michelle Carey is a Postdoctoral Fellow in the Department of Mathematics and Statistics at McGill University, Montréal.